Wikiversity enwikiversity https://en.wikiversity.org/wiki/Wikiversity:Main_Page MediaWiki 1.44.0-wmf.2 first-letter Media Special Talk User User talk Wikiversity Wikiversity talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk School School talk Portal Portal talk Topic Topic talk Collection Collection talk Draft Draft talk TimedText TimedText talk Module Module talk German Language/List of German verbs 0 6432 2684108 2245138 2024-11-12T02:21:49Z 2400:1A00:BB20:7956:F574:7000:D351:9F60 /* t-z */ 2684108 wikitext text/x-wiki {{TOCright}} This is a short list of German verbs useful for the beginner. They are listed in alphabetical order by infinitive. The past tense and past participle are listed after the infinitive, with the English equivalent in parenthesis. Where the stem changes in the present tense, the change is indicated in parenthesis following the infinitive. ===a-c=== *abweisen, wies ab, abgewiesen (to reject) *aus gleichen, glich aus, ausgeglichen (to balance) *backen (bäckt), backte, gebacken (to bake) *befehlen (befiehlt), befahl, befohlen (to order, command) *beginnen, begann, begonnen (to begin) *beißen, biss, gebissen (to bite) *betrügen, betrog, betrogen (to cheat) *beweisen, bewies, bewiesen (to prove) *bewerben (bewirbt), bewarb, beworben (to apply) *biegen, bog, gebogen (to bend) *bieten, bot, geboten (to offer) *binden, band, gebunden (to tie) *bitten, bat, gebeten (to ask) *blasen (bläst), blies, geblasen (to blow) *bleiben, blieb, ist geblieben (to stay, remain) *braten (brät), briet, gebraten (to fry) *brechen (bricht), brach, gebrochen (to break) *brennen, brannte, gebrannt (to burn) *bringen, brachte, gebracht (to bring) ===d-f=== *denken, dachte, gedacht (to think) *dringen, drang, ist gedrungen (to penetrate) *dürfen, darf, durfte, gedürft (to be allowed to) *eilen, eilte, geeilt (to hurry) *einladen (lädt ein), lud ein, eingeladen (to invite) *empfangen (empfängt), empfing, empfangen (to recieve) *empfehlen (empfiehlt), empfahl, empfohlen (to recommend) *entscheiden, entschied, entschieden (to decide) *erklingen, erklang, ist erklungen (to resound) *erscheinen, erschien, ist erschienen (to appear) *ertrinken, ertrank, ist ertrunken (to drown) *essen (isst), aß, gegessen (to eat) *fahren (fährt), fuhr, ist gefahren (to go by vehicle) *fallen (fällt), fiel, ist gefallen (to fall) *fangen (fängt), fing, gefangen (to catch) *finden, fand, gefunden (to find) *fliegen, flog, ist geflogen (to fly) *fliehen, floh, geflohen (to flee) *fressen (frisst), fraß, gefressen, (to eat (of animals)) *frieren, fror, gefroren (to freeze) ===g-k=== *geben (gibt), gab, gegeben (to give) *gehen, ging, ist gegangen (to go) *gelingen, gelang, ist gelungen (to succeed) *genießen, genoss, genossen, (to enjoy) *geraten (gerät), geriet, geraten (to get) *geschehen (geschieht), geschah, ist geschehen (to happen) *gewinnen, gewann, gewonnen (to win) *gießen, goss, gegossen (to water) *gleiten, glitt, ist geglitten (to slide) *greifen, griff, gegriffen (to reach) *haben (hat), hatte, gehabt (to have) *halten (hält), hielt, gehalten (to hold) *hängen, hing, gehangen (to hang) *heben, hob, gehoben (to raise) *heißen, hieß, geheißen (to be called) *helfen (hilft), half, geholfen (to help) *kaufen, kaufte, gekauft (to buy) *kennen, kannte, gekannt (to know) *kommen, kam, ist gekommen *können (kann), konnte, gekonnt (to be able to) *kriechen, kroch, ist gekrochen (to creep) ===l-r=== *lassen (lässt), ließ, gelassen, (to let) *laufen(läuft), lief, ist gelaufen (to walk) *leiden, litt, gelitten (to suffer) *leihen, lieh, geliehen (to lend) *lesen (liest), las, gelesen (to read) *liegen, lag, gelegen (to lie down) *lügen, log, gelogen (to lie) *mahlen, mahlte, gemahlen (to grind) *messen (misst), maß, gemessen (to measure) *mögen (mag), mochte gemocht (to like) :*(möchten is imperfect subjuctive (to want)) *müssen (muss), musste, gemusst (to have to) *nehmen (nimmt), nahm, genommen (to take) *nennen, nannte, genannt (to name) *pfeifen, pfiff, gepfiffen (to whistle) *raten (rät), riet, geraten (to guess) *reiben, rieb, gerieben (to grate) *reißen, riss, gerissen (to tear) *reiten, ritt, ist geritten (to ride on horseback) *rennen, rannte, ist gerannt ( to run) *riechen, roch, gerochen (to smell) *rufen, rief, gerufen ===s=== *saufen (säuft), soff, gesoffen (to drink (of animals)) *scheinen, schien, geschienen (to shine) *schieben, schob, geschoben (to push) *schießen, schoss, geschossen (to shoot) *schlafen (schläft), schlief, geschlafen (to sleep) *schlagen (schlägt), schlug, geschlagen (to beat) *schleichen, schlich, ist geschlichen (to sneak) *schließen, schloss, geschlossen (to lock) *schneiden, schnitt, geschnitten (to cut) *schreiben, schrieb, geschrieben, (to write) *schreien, schrie, geschrien, (to shout) *schweigen, schwieg, geschwiegen (to keep quiet) *schwimmen, schwamm, ist geschwommen (to swim) *sehen (sieht), sah, gesehen (to see) *sein (ist), war, ist gewesen (to be) *singen, sang, gesungen (to sing) *sinken, sank, ist gesunken (to sink) *sitzen, saß, gesessen (to sit) *sprechen (spricht), sprach, gesprochen (to speak) *springen, sprang, ist gesprungen (to spring, jump) *stechen (sticht), stacht, gestochen (to poke) *stehen, stand, gestanden (to stand) *stehlen (stiehlt), stahl, gestohlen (to steal) *steigen, stieg, ist gestiegen (to climb) *sterben (stirbt), starb, ist gestorben (to die) *stoßen (stößt), stieß, gestoßen (to push) *streichen, strich, gestrichen (to stroke) ===t-z=== *tragen (trägt) trog, getragen (to carry) *treiben, trieb, getrieben (to drift) *treten (tritt), trat, ist getreten (to step) *trinken, trank, getrunken (to drink) *tun, tat, getan (to do) *unterscheiden, unterschied, unterschieden (to distinguish) *verbergen (verbirgt), verbarg, verborgen (to hide) *verlieren, verlor, verloren (to lose) *verschwinden, verschwand, ist verschwunden (to disappear) *verweisen, verwies, verwiesen (to banish) *wachsen (wächst), wuchs, ist gewachsen (to grow) *wenden, wandte, gewandt (to turn) *werfen (wirft), warf, geworfen (to throw) *wiegen, wog, gewogen (to weigh) *wissen (weiß), wusste, gewusst (to know) *zerbersten (zerbirst), zerbarst, ist zerborsten (to burst) *ziehen, zog, gezogen (to pull, move) ==Sources== *Strutz, Henry. ''501 German Verbs.'' Barron's Educational Services, Inc. 1992. New York. {{ISBN|0-7641-0284-2}}. * Winkler George,A-LM German Level Three. pp. 369-372. Mimeographed handout. ca 1975. schön immer , danke ==See also == *[[b:German/Grammar/Verbs| Verbs in German wikibook]] [[Category:German verbs|*]] j8cah5i4vsqnkgykg14yavcrcfmyci3 English grammar 0 9269 2683739 2643141 2024-11-11T16:13:36Z 193.61.74.15 separated the noun and proper noun examples as they were grouped together & was unclear which was which 2683739 wikitext text/x-wiki {{launch}} {{Cleanup|[[Help:Wikify|Wikify]]}} ==Introduction== English grammar is the set of structural rules that govern the English language. English is a West Germanic language in the Indo-European language family, whose speakers, called Anglophones, originated in early medieval England on the island of Great Britain. ==Origins of English== English is a West Germanic language. It came from Anglo-Frisian dialects brought to Britain in the mid-5th to 7th centuries AD by Anglo-Saxons who migrated from what is now northwest Germany, southern Denmark and the Netherlands. It is also heavily based on Latin, the language used by the Roman Empire, that existed from 27 BC to around 1453. ==The Grammar== ===Alphabet, Pronunciation, and an Introduction to basic Pronunciation NEEDS EDITING=== === Parts of Speech === There are nine different parts of speech, each with several subcategories. *'''noun''' - a word that names a person, animal, place, thing, or idea. (<i>examples: fireman, dog, church, computer, friendship). </i>A commonly found subcategory of the noun in English is the proper noun, which denotes someone or something's name with a capital letter at the beginning of the word. <i>(examples: Penelope, Russia) </i> *'''verb''' - a word that describes an action or state of existence. The most common verbs you'll see are called 'action verbs', but there exists many other kinds of verbs as well such as the 'auxiliary verb', which gives functional or grammatical meaning to the sentence it appears in. Common examples are 'is' and 'was'. <i> (examples: run, jump, like, want, is) </i> *'''pronoun''' - a word that is used in place of a noun. These are used to decrease redundancy in sentences. The pronoun 'I' is always capitalised in a sentence. <i> (examples: I, you, he, she, we, they) </i> *'''adjective''' - a word that describes a noun <i> (examples: big, red, dark) </i> *'''adverb''' - a word that modifies a verb or adjective (when, where, how) <i> (examples: quickly, yesterday, everywhere) </i> *'''preposition''' - a word that connects a noun or pronoun to a sentence <i> (examples: on, at, by, as, after) </i> *'''conjunction''' - a word that links two words, phrases, or sentences <i> (example: and, or, because) </i> *'''interjection''' - a word that conveys emotion <i> (example: ahem!, egad!, ouch!, yahoo!) </i> *'''articles''' - a word that introduces a noun <i> (example: a, an, the) </i> ===The Basics of the Noun=== This can be used almost anywhere in speech such as when your talking about multiple things like food or even games. ===The Basics of the Verb=== ====Transitivity==== ====The Simple Tenses==== ===The Basics of the Pronoun=== ===The Basics of the Adjective=== ==Subjects and Predicates== === Simple Subject === A simple subject is a noun that tells who or what the sentence is about. Usually a simple subject is one word. Read the following example sentence: Bob jumped. In the sentence, Bob is the simple subject. Bob is the who or what of the sentence. Read the following example sentence: Bob the basketball star jumped three feet in the air. Bob is still the simple subject of the sentence. ===Simple Predicate=== The simple predicate is the verb or verb phrase. It tells what the subject did, is doing, or will do. Read the following example sentence: Bob jumped. In the sentence, jumped is the simple predicate. Jumped is the 'What did he do' of the sentence. Read the following example sentence: Bob the basketball star jumped three feet in the air. Jumped is still the simple predicate of the sentence. ==Syntax, or Sentence Formation== ===Simple Sentences=== ===Helping Verbs in the Past Tense=== To obtain a clear understanding of the helping verb in the English past tense, we must review the simple past, since that is what we will use for our examples. The simple past includes sentences like 'Bob jumped' or 'Bob flew.' However, when we add a helping verb that does not change the actual tense, the main verb reverts to the infinitive. Example: Bob jumped. Bob flew. Bob did jump. Bob did fly. ==Conventions== ==Mood== ==Confusing words, Idioms, Colloquialisms, and Slang== * [[Which word? Situation/Position/Condition|Situation / Position / Condition]] * [[Animal idioms]] ==See also== * [http://www.ece.msstate.edu/academics/writing_resource/grammatical_errors_links.html#apostrophe Apostrophe misuse] * Andrew Rossiter (2020). [https://linguapress.com/grammar/descriptive-grammar-english.htm A Descriptive Grammar of English]. 207 pp. {{ISBN|979-8645611750}} {{dfoot|English}} [[Category:English grammar]] [[Category:English stubs]] [[Category:Grammar stubs]] {{subpagesif}} nwv8gyq72v56xz107knm3t88pltkvgv 2683813 2683739 2024-11-11T16:26:16Z Paste555 2993570 text was two sentences with multiple grammatical errors. this is a page about grammar so I just removed it 2683813 wikitext text/x-wiki {{launch}} {{Cleanup|[[Help:Wikify|Wikify]]}} ==Introduction== English grammar is the set of structural rules that govern the English language. English is a West Germanic language in the Indo-European language family, whose speakers, called Anglophones, originated in early medieval England on the island of Great Britain. ==Origins of English== English is a West Germanic language. It came from Anglo-Frisian dialects brought to Britain in the mid-5th to 7th centuries AD by Anglo-Saxons who migrated from what is now northwest Germany, southern Denmark and the Netherlands. It is also heavily based on Latin, the language used by the Roman Empire, that existed from 27 BC to around 1453. ==The Grammar== ===Alphabet, Pronunciation, and an Introduction to basic Pronunciation NEEDS EDITING=== === Parts of Speech === There are nine different parts of speech, each with several subcategories. *'''noun''' - a word that names a person, animal, place, thing, or idea. (<i>examples: fireman, dog, church, computer, friendship). </i>A commonly found subcategory of the noun in English is the proper noun, which denotes someone or something's name with a capital letter at the beginning of the word. <i>(examples: Penelope, Russia) </i> *'''verb''' - a word that describes an action or state of existence. The most common verbs you'll see are called 'action verbs', but there exists many other kinds of verbs as well such as the 'auxiliary verb', which gives functional or grammatical meaning to the sentence it appears in. Common examples are 'is' and 'was'. <i> (examples: run, jump, like, want, is) </i> *'''pronoun''' - a word that is used in place of a noun. These are used to decrease redundancy in sentences. The pronoun 'I' is always capitalised in a sentence. <i> (examples: I, you, he, she, we, they) </i> *'''adjective''' - a word that describes a noun <i> (examples: big, red, dark) </i> *'''adverb''' - a word that modifies a verb or adjective (when, where, how) <i> (examples: quickly, yesterday, everywhere) </i> *'''preposition''' - a word that connects a noun or pronoun to a sentence <i> (examples: on, at, by, as, after) </i> *'''conjunction''' - a word that links two words, phrases, or sentences <i> (example: and, or, because) </i> *'''interjection''' - a word that conveys emotion <i> (example: ahem!, egad!, ouch!, yahoo!) </i> *'''articles''' - a word that introduces a noun <i> (example: a, an, the) </i> ===The Basics of the Noun=== ===The Basics of the Verb=== ====Transitivity==== ====The Simple Tenses==== ===The Basics of the Pronoun=== ===The Basics of the Adjective=== ==Subjects and Predicates== === Simple Subject === A simple subject is a noun that tells who or what the sentence is about. Usually a simple subject is one word. Read the following example sentence: Bob jumped. In the sentence, Bob is the simple subject. Bob is the who or what of the sentence. Read the following example sentence: Bob the basketball star jumped three feet in the air. Bob is still the simple subject of the sentence. ===Simple Predicate=== The simple predicate is the verb or verb phrase. It tells what the subject did, is doing, or will do. Read the following example sentence: Bob jumped. In the sentence, jumped is the simple predicate. Jumped is the 'What did he do' of the sentence. Read the following example sentence: Bob the basketball star jumped three feet in the air. Jumped is still the simple predicate of the sentence. ==Syntax, or Sentence Formation== ===Simple Sentences=== ===Helping Verbs in the Past Tense=== To obtain a clear understanding of the helping verb in the English past tense, we must review the simple past, since that is what we will use for our examples. The simple past includes sentences like 'Bob jumped' or 'Bob flew.' However, when we add a helping verb that does not change the actual tense, the main verb reverts to the infinitive. Example: Bob jumped. Bob flew. Bob did jump. Bob did fly. ==Conventions== ==Mood== ==Confusing words, Idioms, Colloquialisms, and Slang== * [[Which word? Situation/Position/Condition|Situation / Position / Condition]] * [[Animal idioms]] ==See also== * [http://www.ece.msstate.edu/academics/writing_resource/grammatical_errors_links.html#apostrophe Apostrophe misuse] * Andrew Rossiter (2020). [https://linguapress.com/grammar/descriptive-grammar-english.htm A Descriptive Grammar of English]. 207 pp. {{ISBN|979-8645611750}} {{dfoot|English}} [[Category:English grammar]] [[Category:English stubs]] [[Category:Grammar stubs]] {{subpagesif}} 2ghxu7bmxpxaen27ueahndi8xbzqp6g Portal:Mathematics/Featured Picture 102 23502 2683451 2428039 2024-11-11T14:04:21Z 103.225.57.30 I changed the way of language. 2683451 wikitext text/x-wiki <!-- Add featured pictures to the list below as a link. The displayed picture is selected randomly from this list. --> == Featured Pictures == * [[File:BesselY plot.svg|thumb|center|500x500px|Solutions of the Bessel differential equation.]] * [[File:EnneperSurfaceAnimated.gif|thumb|center|500x500px|A portion of the Enneper Surface]] * [[File:Quadratic Formula.jpg|thumb|center|500x499px|Quadratic formula|alt=The formula for Quadratic Equation -]] * [[File:Midpoint.svg|thumb|center|alt=Midpoint Formula With A Example WIth No Arrows|500x500px|Midpoint]] * [[File:Distance Formula.svg|thumb|center|alt=Distance With A Triangle with the formula split.|500x500px|Distance ]] pp2zk0xcf1rfxcjry5v2lmryj7fst09 Aircrafts and aerodynamics 0 28327 2684114 2683412 2024-11-12T02:43:33Z CanadianWikiReader 2993500 Changed a few links. 2684114 wikitext text/x-wiki == Airplane Parts == The main parts of an aircraft are: * the [[fuselage]]; * the [[Wing|wings]]; * the [[Empennage|tail section]] ([[empennage]]); * the [[engine]](s); * the [[landing gear]]. The [[fuselage]] is the main body of the aircraft, holding the crew, passengers, as well as cargo. The [[wings]] are the main source of lift on an airplane. They work through forcing [[Lift (force)|pressure]] from the air onto its bottom half, thus lifting the plane up. The [[Empennage|tail section]] (or [[empennage]]) is the structure at the rear of the aircraft that helps stabilize the plane during flight, similar to feathers on an arrow. The [[engine]] is located in the front or on the wings of an aircraft. It creates mechanical energy through the use of [[aviation fuel]]. The [[landing gear]] is the undercarriage of the aircraft and is used for [[taxiing]], [[takeoff]], and [[landing]]. Attached to it are wheels that allows it to maneuver when making contact with the ground. The control surfaces include: * the ailerons; * the elevators and stabilators; * the rudder; and * the trim syste__NOTOC__ms. == Aircraft Forces == === Four Forces on an Airplane === The four forces which act upon an aircraft in flight are: # [[Lift]] # Drag # Thrust # Weight :[[Lift]] acts upwards at right angles to the airflow through the center of pressure. In simple terms, Lift is perpendicular to the Relative Wind. :Drag is the resistance opposing the forward motion of the aircraft. It acts parallel and in the reverse direction of the aircraft's movement. Drag opposes thrust. :Thrust is the forward propulsive force provided by the engines. :Weight is the force acting vertically downward due to gravity. Weight opposes lift. == Aerodynamics == === Pressure === == Resources == [http://www.grc.nasa.gov/WWW/K-12/airplane/bga.html NASA's Beginners Guide to Aerodynamics] - Supplement your of study aerodynamics at your own pace and to your own level of interest. Some of the topics included are: Newton's basic equations of motion; the motion of a free falling object, that neglects the effects of aerodynamics; the terminal velocity of a falling object subject to both weight and air resistance; the three forces (lift, drag, and weight) that act on a glider; and finally, the four forces that act on a powered airplane. There are many interactive pages designed to illustrate aerodynamics. [http://www.flightcentral.net/gs-lessons/aerodynamics/player.html Aerodynamics Lesson] - Gold Seal Master CFI trainer Robert Still video presents basics of Aerodynamics in an easy to understand format. [http://www.av8n.com/how/ See How It Flies] - Free online book (in HTML format) running through aerodynamics and techniques for flight. [[w:Aircraft|Wikipedia Aircraft]] - A definition of Aircraft and examples of various types of aircraft. [[w:Aerodynamics|Wikipedia Aerodynamics]] - Technical overview of aerodynamics and the physics of flight. [http://www.faa.gov/aircraft/ FAA Aircraft] - FAA information on Registration and Certification of Aircraft, Advisories and Guidance, Regulations and Policy, Forms, and Technical Information. Includes a searchable database of aircraft registered in the US. [[Category:Physics]] [[Category:Aviation]] [[Category:Aerodynamics]] pc8h7nb18o1axq7g8j2a48vy84pfimr Aviation Weather 0 28329 2684110 2681751 2024-11-12T02:33:42Z CanadianWikiReader 2993500 2684110 wikitext text/x-wiki == Online Courses == [http://www.flightcentral.net/gs-lessons/wxtheory/player.html Aviation Weather Theory] ==The pilot's weather tools== To accurately gather [[weather data]] to ensure a successful [[flight]], pilots have access to many different resources that inform them of what the [[weather]] is up to. == METARs == Every pilot and even student for that matter has been exposed to a [http://www.pilotpedia.com/wiki/index.php/METAR METAR]. Roughly translated from the French as METeorlogical Aviation Routine weather Reports, a METAR is the hourly surface weather observation issued 5 minutes before the hour. It is available to the aviation community and used by the National Weather Service to determine an airport's flying conditions ([[Instrument Flight Rules|IFR]], [[Marginal Visual Flight Rules|MVFR]], [[Visual Flight Rules|VFR]]). You can obtain these from a variety of places both online and by phone. This is the basic knowledge of what ground school consists of on this topic other than deciphering its acronyms. Although as a pilot, sometimes its nice to know a little about how these services came to be without going too much into detail. Funny enough, the change to our current acronym of METAR is fairly recent. ====History==== Before the current interpretation of weather data, there were two formats, and, in rough terms, it was "us and them" or rather, to be more precise, the North American countries reported weather differently from the rest of the world. North Americans were using SAO or "Surface Aviation Observation" (which was adopted in the 1950s), while the rest of the world was using the currently known METAR or "METeorological Aviation Routine weather reports". The FAA, which determines aviation requirements in the US, became increasingly aware that expanding numbers of international flights and pilots alike was creating a strong need to standardize weather report interpretations internationally. The [[National Weather Service]] standardized the weather reports into what we now know as METARs. To reduce the stress on US aviation citizens, the metric system was kept to a minimum: for example, the winds were kept in knots instead of meters per second, visibility in miles, altimeter settings in inches of mercury instead of hectopascals (hPa), and RVR continued in feet. Temperatures, however, are converted to Celsius to allow for better conversions. The biggest change is simply the order in which elements are reported. ====Translating METARs==== So in a sense, although the attempt at standardizing weather code from SAO to METAR is apparent, the actual translation is not substantial. Oh and for those of you who are students or pilots that don’t like translating code, there is a reason and a cure. First off do realize that METARs are always originated in code and probably will be for a while. The reason seems to be that with the vast amount of changes and updates to weather reports would overload the system. The great news is that now it is possible to translate the code online either through request from sites such as NOAA or by looking up the code yourself which will put it in simple English. Sometimes this helps those who are new to learn the code and not miss anything during preflight weather preparations. ====A closer look at the METAR==== The following example is a METAR taken from Vancouver International Airport ([[ICAO airport code|CYVR]]) in Vancouver, British Columbia: METAR CYVR 120200Z 14021G27KT 20SM -SHRA FEW030 BKN058 OVC090 10/06 A2982 RMK SC2SC5AC2 PCPN VRY LGT SLP098= Like mentioned above, METARs are observed and posted on an hourly basis. An airport can also issue an METAR that is not on the hour, this observation is called a SPECI. SPECI is abbreviated for special because the report was issued based on a significant change in conditions such as a violent temperature change, cloud layer movement, precipitation, visibility, etc. Looking back at the Vancouver METAR, the observation can be translated as such. '''METAR''': Simply indicated that the observation is a METAR observation. '''CYVR''': This is the aerodrome ident of which the observation originates, in this case, the aerodrome is Vancouver International. '''120200Z''': This is the time of which the METAR was issued, the first two numbers are the date, so ''12'' would mean the twelfth day of the month. The ''0200Z'' is the time indicated in UTC, in aviation, it is indicated as Zulu time hence the Z on the end. The time 0200 can be translated to 2:00. '''14021G27''': This is the current wind observation. The first three numbers indicate the wind direction '''''in degrees true''''' while the following numbers indicate the wind speed measured in knots. From this figure we gather that the wind is at 140 degrees true and is at 21 knots gusting to 27 knots. '''20SM''': Indicates the visibility at the airport; in this case, the visibility is 20 Statute Miles. '''-SHRA''': Means that there is rain showers at the airport, the negative sign at the beginning indicates the severity of the precipitation, a negative sign meaning light, no sign at all meaning moderate, a positive(+) sign meaning heavy. '''FEW030 BKN058 OVC090''': These are the current cloud layers observed. ''FEW030'' is few clouds at 3000 feet ASL, ''BKN058'' is broken clouds at 5800 feet ASL, and ''OVC090'' is overcast clouds at 9000 feet ASL. ''ASL'' is abbreviated for above sea level, and you add two zeros on the end of the numbers to receive the actual altitude of the clouds. '''10/06''': Current temperature and dewpoint, Temperature is 10 degrees celsius while the dewpoint is 6 degrees celsius. '''A2982''': Altimeter setting observed, in this case 29.82 Hg/m '''RMK SC2SC5AC2 PCPN VRY LGT''': Any remarks which the observation has. ''SC2SC5AC2'' indicates that in respect to the observed cloud layers, the clouds are composed of 2 ocatas of strato cumulus clouds, 5 octas of stratocumulus clouds, and 2 octas of alto-cumulus clouds. ''PCPN VRY LGT'' indicates that precipitation is very light. '''SLP098''': Indicates sea level pressure. ==== Quiz ==== <quiz display="simple"> {METARs are roughly translated from the French as _________. |type="[]"} + METeorological Aviation Routine weather Reports || Correct! This is the accurate translation of METAR from French. - METeorological Airline Regular weather Reports || Incorrect. Remember, METAR stands for METeorological Aviation Routine weather Reports. - METeorological Airport Regular weather Reports || Incorrect. The correct translation is METeorological Aviation Routine weather Reports. {Before the current interpretation of weather data, North Americans were using _________ while the rest of the world was using METAR. |type="[]"} + SAO or Surface Aviation Observation || Correct! SAO stands for Surface Aviation Observation. - Surface Aircraft Observation || Incorrect. The correct term is Surface Aviation Observation. - Standard Aviation Observation || Incorrect. Remember, it's Surface Aviation Observation. {The FAA became increasingly aware that expanding numbers of international flights and pilots was creating a need to _________. |type="[]"} + standardize weather report interpretations internationally || Correct! The FAA aimed to standardize weather report interpretations on an international scale. - localize weather report interpretations || Incorrect. The FAA's goal was to standardize, not localize, weather report interpretations. - diversify weather report interpretations || Incorrect. The aim was to standardize, not diversify, the interpretations. {METARs are always originated in code because _________. |type="[]"} + the vast amount of changes and updates to weather reports would overload the system || Correct! Using code for METARs prevents the system from being overwhelmed by frequent changes and updates. - it's easier for pilots to read || Incorrect. The primary reason is to prevent system overload, not ease of reading. - it's an international standard || Incorrect. While METARs are standardized, the main reason for using code is to prevent system overloading. {In the METAR example from Vancouver International Airport, "14021G27" indicates _________. |type="[]"} + the wind is at 140 degrees true and is at 21 knots gusting to 27 knots || Correct! The wind direction is 140 degrees true, with a speed of 21 knots and gusts up to 27 knots. - the wind is at 140 knots and is gusting from 21 to 27 degrees || Incorrect. The first three numbers indicate wind direction, and the following numbers indicate wind speed and gusts. - the wind is at 21 degrees true and is at 140 knots gusting to 27 knots || Incorrect. The wind direction is given first, followed by speed and gusts. {In the METAR example, "FEW030 BKN058 OVC090" refers to _________. |type="[]"} + the current cloud layers observed || Correct! FEW030 means few clouds at 3000 feet, BKN058 means broken clouds at 5800 feet, and OVC090 means overcast clouds at 9000 feet. - the visibility range in miles || Incorrect. These codes specifically refer to cloud layers, not visibility. - the temperature and dewpoint || Incorrect. These codes describe cloud layers, not temperature or dewpoint. </quiz> == Resources == {{Wikisource|Aviation Weather AC 00-6A}} *http://www.nws.noaa.gov/oso/oso1/oso12/overview.htm - National Weather Services *http://www.alaska.faa.gov/fai/afss/metar%20taf/metintro.htm (Also a good source for additional info and abbreviation translations.) *http://www.nwstc.noaa.gov/METEOR/AvnOps/aoc_webpage.htm NOAA National Weather Service Training Center. *http://adds.aviationweather.noaa.gov Aviaition Digital Data Service Aviation Weather Center [[Category:Aviation]] [[Category:Meteorology]] autxacugc12khjfr9gfrnp6lzv8v5ou Writing 0 34668 2683974 2668357 2024-11-11T19:46:23Z Lbeaumont 278565 /* Tips for better writing (mostly for English) */ Added "Request feedback" 2683974 wikitext text/x-wiki This lesson provides a comprehensive exploration of the art of effective writing, providing a universal introduction suitable for all ages. [[File:Fountain pen writing (literacy).jpg|thumb|Good writing is clear thinking made visible.]] {{TOC right | limit|limit=2}} '''Writing''', a uniquely human tool, serves as a visible expression of language, allowing the conveyance of thoughts in diverse ways. Much like spoken language, the possibilities for arranging words are infinite, enabling the communication of ideas, thoughts, images, and emotions. Whether the aim is to inform, persuade, entertain, or a combination of these, the written word remains a powerful means of expression. In the realm of written language, several fundamental components shape the structure of writing. Paragraphs, separated by indentations or line breaks, serve as building blocks. Words, composed of letters, are the basic units of expression. Punctuation marks guide the reader, providing cues for timing and emphasis. Sentences function to encapsulate concise ideas, while paragraphs unite sentences to convey a broader concept. [[Essay|Essays]], whether lengthy or concise, compile paragraphs into cohesive compositions. The diversity of essays spans various types, each serving unique purposes. In the realm of [[fiction]], ideas take on imaginative forms, crafted by the writer's creativity. Conversely, non-fiction endeavors to explore ideas and concepts grounded in reality. This lesson invites writers of all ages to delve into the intricacies of written expression, fostering an understanding of the myriad ways in which words can shape, inform, and enrich our communication. == Tips for better writing (mostly for English) == *Overcome [[/writers block/|writer's block]]. * Follow the [[/basic grammar rules of American English writing/]]. * If you are required to follow a specific [[w:Style_guide|style guide]] or style manual, then: *# obtain a copy of that guide *# study it, and *# follow the requirements of that guide. * Use [[Writing/punctuation marks|correct punctuation]]. ** Full stops, also know as the [[w:Full_stop|period]] character, (.) separate [[w:Sentence_(linguistics)#By_purpose|declarative]] sentences. The [[w:Question_mark|question mark]] (?) is used at the end of a question, and an [[w:Exclamation_mark|exclamation point]] (!) is used after an [[w:Interjection|interjection]] or [[w:Sentence_(linguistics)|exclamation]] to indicate strong feelings or to show [[w:emphasis|emphasis]]. ** Know how to use ''it's'' and ''its''. ''It's'' is always a contraction of "it is"; ''its'' is possessive ("belonging to it"). * [[Writing/Correct use of capital letters|Use capital letters correctly]]. * Use the [[/paragraph as the major organizing element/]]. * Choose [[/suitable sentence length/]]. * [[Good Writing is Clear Thinking Made Visible|Good writing is clear thinking made visible]]. * Be [[Intellectual honesty|Intellectually honest]]. ** [[Living Wisely/Advance no falsehoods|Advance no falsehoods]]. * [[/Good Writing is Precise and Concise/]]. * Choose [[Writing/precise descriptive, and engaging language|precise descriptive, and engaging language]]. ** Do not use words like "very", "good", "get", "thing", or "things" if it can be avoided. * Choose to use or avoid [[/contractions/]] based on the context and [[Writing/Tone|tone]] of the writing. * Do not confuse words (known as [[w:Homonym|homonyms]]) that sound the same yet are spelled differently. ** Examples include: ''their'', ''they're'' and ''there''; ''weather'' and ''whether''; etc. ** Refer to this longer list of [[Writing/commonly_confused_homonyms|commonly confused homonyms]] to avoid misuse. * [[/Read extensively/]] to refine your craft and continually evolve. * Use [[Writing/transition phrases|transition phrases]] skillfully. * Favor [[/active voice/]] over passive voice. * Use [[/poetic phrases/]] skillfully. * Whenever possible, [[/show rather than tell/]] to describe the scene. * Use a [[/variety of phrases/]] during dialogue. * Strive to create [[/great writing/]]. ** [[/Great writing is clever writing/]]. ** [[/Great writing is witty/]]. * [[/Choose the title/]] carefully. It is often best to keep the title concise and to the point. * Write [[Candor|candidly]]. Express your opinions clearly, accurately, and [[Finding Courage|courageously]]. * [[/Requesting Feedback/|Request feedback]]. Improve the work based on the feedback received. * Request writing [[/assistance from ChatGPT/]] (or other [[w:Large_language_model|LLM]]). ** Acknowedge any assistance you receive. * Consider this [[/hypothetical advice on writing from great thinkers/]]. * Edit and [[w:Proofreading|proofread]] everything, even if it is a one-page essay or short [[Email Checklist|email]]. ==Collaborative papers== You can start a collaborative paper in the main namespace, or if you would like to create something individually, please keep it in the user namespace on your userpage or as a subpage to your userpage. * [[Perfection]] * [[On Hatred]] * [[Privacy, Security, and Implied Mutual Exclusion]] ==See also== * [[Writing arts|Writing Arts]] * [[Academic and Legal Research and Writing]] * [[Writing prompts]] ==External links== * [http://www.crockford.com/wrrrld/style.html The Elements of Style by William Strunk, Jr.] [[Category:Writing]] 81nxnn7f93wefewx8t4d2kougpq9mzt The necessities in Numerical Methods 0 119778 2684164 2682357 2024-11-12T07:45:46Z Young1lim 21186 /* Numerical Differentiation */ 2684164 wikitext text/x-wiki == Calculus == === Numerical Differentiation === * Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]]) * Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]]) * Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241111.pdf |pdf]]) * Forward, Backward, Central Divided Difference * High Accuracy Differentiation * Richardson Extrapolation * Unequal Spaced Data Differentiation * Numerical Differentiation with Octave </br> === Numerical Integration === * Trapezoidal Rule * Simpson's 1/3 Rule * Romberg Rule * Gauss-Quadrature Rule * Adaptive Quadrature </br> === Roots of a Nonlinear Equation === </br> === Optimization === </br> </br> == Matrix Algebra == === Simultaneous Linear Equations === * A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]]) </br> === Gaussian Elimination === </br> === LU Decomposition === </br> === Cholesky Decomposition === </br> === LDL Decomposition === </br> === Gauss-Seidel method === </br> === Adequacy of Solutions === </br> === Eigenvalue and Singular Value === </br> === QRD === </br> === SVD === </br> === Iterative methods === </br> </br> == Regression == === Linear Regression === </br> === Non-linear Regression === </br> === Linear Least Squares === </br> </br> == Interpolation == === Polynomial Interpolation === </br> === Linear Splines === </br> === Piecewise Interpolation === </br> </br> == Ordinary Differential Equation == </br> == Partial Differential Equation == </br> == FEM (Finite Element Method) == </br> </br> </br> == Using Symbolic Package in Octave == * Visit http://octave.sourceforge.net/index.html * Download symbolic-1.0.9.tar.gz * In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed. * After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps. ./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 * While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu. == Read some tutorials about symbolic computation == * Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf) * Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf) [[Category:Numerical methods]] == Using SymPy ( a Python library for symbolic mathematics) == </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] jl6f0ho8gj5q08rb5c7ndm6elf8ybrt 2684166 2684164 2024-11-12T07:46:57Z Young1lim 21186 /* Calculus */ 2684166 wikitext text/x-wiki == Calculus == === Numerical Differentiation === * Background on Differentiation ([[Media:NM.Diff.1Background.20240625.pdf |pdf]]) * Continuous Function Differentiation ([[Media:NM.Diff.1ContDiff.20241021.pdf |pdf]]) * Discrete Function Differentiation ([[Media:NM.Diff.1Discrete.20241112.pdf |pdf]]) * Forward, Backward, Central Divided Difference * High Accuracy Differentiation * Richardson Extrapolation * Unequal Spaced Data Differentiation * Numerical Differentiation with Octave </br> === Numerical Integration === * Trapezoidal Rule * Simpson's 1/3 Rule * Romberg Rule * Gauss-Quadrature Rule * Adaptive Quadrature </br> === Roots of a Nonlinear Equation === </br> === Optimization === </br> </br> == Matrix Algebra == === Simultaneous Linear Equations === * A system of linear equations ([[Media:SystemLinearEq.20240521.pdf |pdf]]) </br> === Gaussian Elimination === </br> === LU Decomposition === </br> === Cholesky Decomposition === </br> === LDL Decomposition === </br> === Gauss-Seidel method === </br> === Adequacy of Solutions === </br> === Eigenvalue and Singular Value === </br> === QRD === </br> === SVD === </br> === Iterative methods === </br> </br> == Regression == === Linear Regression === </br> === Non-linear Regression === </br> === Linear Least Squares === </br> </br> == Interpolation == === Polynomial Interpolation === </br> === Linear Splines === </br> === Piecewise Interpolation === </br> </br> == Ordinary Differential Equation == </br> == Partial Differential Equation == </br> == FEM (Finite Element Method) == </br> </br> </br> == Using Symbolic Package in Octave == * Visit http://octave.sourceforge.net/index.html * Download symbolic-1.0.9.tar.gz * In Ubuntu, using the Ubuntu Software Center, I installed GiNac and CLN related software and symbolic package for Octave. But it did not properly installed. * After extracting files from symbolic-1.0.9.tar.gz, I followed the following steps. ./configure ./make ./make INSTALL_PATH=/usr/share/octave/packages/3.2/symbolic-1.0.9 * While doing this, I got an error message related to mkoctfile. So, I used the following command: sudo apt-get install ocatve3.2-headers. Then I was able to install the symbolic packages in the Ubuntu. == Read some tutorials about symbolic computation == * Symbolic Mathematics in Matlab/GNU Octave (http://faraday.elec.uow.edu.au/subjects/annual/ECTE313/Symbolic_Maths.pdf) * Symbolic Computations (http://www.math.ohiou.edu/courses/math344/lecture7.pdf) [[Category:Numerical methods]] == Using SymPy ( a Python library for symbolic mathematics) == </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] g1abmlvoc1vvadovgvlqqvq6vaa57je Linear algebra in plain view 0 132626 2684168 2682361 2024-11-12T08:07:30Z Young1lim 21186 /* Systems of Linear Equations */ 2684168 wikitext text/x-wiki <!----------------------------------------------------------------------> = Part I = == Systems of Linear Equations == * Introduction ([[Media:LEQ.1.A.Introduction.20120827.pdf |pdf]]) * Row Reduction ([[Media:LEQ.2.A.RowReduction.Basic.20150117.pdf |A.pdf]], [[Media:LEQ.2.B.RowReduction.CAS.20150117.pdf |B.pdf]]) * Matrices Operations ([[Media:LEQ.3.A.MatrixOp.20150109.pdf |pdf]]) * Elementary Matrix ([[Media:LEQ.4.A.ElementaryMat.20150115.pdf |pdf]]) * Determinants ([[Media:LEQ.4.A.Determinant.20150113.pdf |pdf]]) * LU Factorization ([[Media:LEQ.5.A.LUFactor.20151014.pdf |pdf]]) <br> == Vector Spaces (I) == * Euclidean Vector Space ([[Media:VSP.1.A.Euclid.20150113.pdf |pdf]]) * Matrix Transformation ([[Media:VSP.2.A.MatrixTrans.20121110.pdf |pdf]]) * General Vector Space ([[Media:VSP.3.A.General.20150121.pdf |pdf]]) * Fundamental Matrix Spaces ([[Media:VSP.3.A.Fundamental.20121124.pdf |pdf]]) * EigenSpaces of a Matrix ([[Media:VSP.5.A.EigenSpace.20121203.pdf |pdf]]) </br> * Fundamental Spaces Note ([[Media:FSpaces.H1.20151211.pdf |H1.pdf]]) * Projection Theorem Note ([[Media:Projection.H2.20151218.pdf |H2.pdf]]) </br> q & a ([[Media:qa.20121211.pdf |pdf]]) </br> == Inner Product Spaces == </br> </br> = Part II = == Systems of Linear Equations == * Solving Systems of Linear Equations ([[Media:SystemLinEq.20240729.pdf |pdf]]) * Reduced Row-Echelon Form ([[Media:RowEchelon.20241111.pdf |pdf]]) * Types of Solution Sets * Homogeneous Systems of Equations * Nonsingular Matrices == Vectors == == Matrices == == Vector Spaces == * Vector Spaces * Subspaces * Linear Independence * Spanning Sets * Bases * Dimension * Properties of Dimension == Determinants == </br> == Eigenvalues == </br> == Linear Transformations == </br> == Representations == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] == '''External Links'''== * [http://tutorial.math.lamar.edu/ Paul's Online Math Notes] * [http://linear.ups.edu/ First Course in Linear Algebra] [[Category:Linear algebra]] q374u57x6na6m35rik1v5s8a0si77fh 2684170 2684168 2024-11-12T08:08:31Z Young1lim 21186 /* Systems of Linear Equations */ 2684170 wikitext text/x-wiki <!----------------------------------------------------------------------> = Part I = == Systems of Linear Equations == * Introduction ([[Media:LEQ.1.A.Introduction.20120827.pdf |pdf]]) * Row Reduction ([[Media:LEQ.2.A.RowReduction.Basic.20150117.pdf |A.pdf]], [[Media:LEQ.2.B.RowReduction.CAS.20150117.pdf |B.pdf]]) * Matrices Operations ([[Media:LEQ.3.A.MatrixOp.20150109.pdf |pdf]]) * Elementary Matrix ([[Media:LEQ.4.A.ElementaryMat.20150115.pdf |pdf]]) * Determinants ([[Media:LEQ.4.A.Determinant.20150113.pdf |pdf]]) * LU Factorization ([[Media:LEQ.5.A.LUFactor.20151014.pdf |pdf]]) <br> == Vector Spaces (I) == * Euclidean Vector Space ([[Media:VSP.1.A.Euclid.20150113.pdf |pdf]]) * Matrix Transformation ([[Media:VSP.2.A.MatrixTrans.20121110.pdf |pdf]]) * General Vector Space ([[Media:VSP.3.A.General.20150121.pdf |pdf]]) * Fundamental Matrix Spaces ([[Media:VSP.3.A.Fundamental.20121124.pdf |pdf]]) * EigenSpaces of a Matrix ([[Media:VSP.5.A.EigenSpace.20121203.pdf |pdf]]) </br> * Fundamental Spaces Note ([[Media:FSpaces.H1.20151211.pdf |H1.pdf]]) * Projection Theorem Note ([[Media:Projection.H2.20151218.pdf |H2.pdf]]) </br> q & a ([[Media:qa.20121211.pdf |pdf]]) </br> == Inner Product Spaces == </br> </br> = Part II = == Systems of Linear Equations == * Solving Systems of Linear Equations ([[Media:SystemLinEq.20240729.pdf |pdf]]) * Reduced Row-Echelon Form ([[Media:RowEchelon.20241112.pdf |pdf]]) * Types of Solution Sets * Homogeneous Systems of Equations * Nonsingular Matrices == Vectors == == Matrices == == Vector Spaces == * Vector Spaces * Subspaces * Linear Independence * Spanning Sets * Bases * Dimension * Properties of Dimension == Determinants == </br> == Eigenvalues == </br> == Linear Transformations == </br> == Representations == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] == '''External Links'''== * [http://tutorial.math.lamar.edu/ Paul's Online Math Notes] * [http://linear.ups.edu/ First Course in Linear Algebra] [[Category:Linear algebra]] eaesu5thiz3kf7x7byvgh4ybx9d0yt4 Understanding Arithmetic Circuits 0 139384 2684001 2683377 2024-11-11T22:03:53Z Young1lim 21186 /* Adder */ 2684001 wikitext text/x-wiki == Adder == * Binary Adder Architecture Exploration ( [[Media:Adder.20131113.pdf|pdf]] ) {| class="wikitable" |- ! Adder type !! Overview !! Analysis !! VHDL Level Design !! CMOS Level Design |- | '''1. Ripple Carry Adder''' || [[Media:VLSI.Arith.1A.RCA.20211108.pdf|A]]|| || [[Media:Adder.rca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.1D.RCA.CMOS.20211108.pdf|pdf]] |- | '''2. Carry Lookahead Adder''' || [[Media:VLSI.Arith.1.A.CLA.20221130.pdf|A]]|| || [[Media:Adder.cla.20140313.pdf|pdf]]|| |- | '''3. Carry Save Adder''' || [[Media:VLSI.Arith.1.A.CSave.20151209.pdf|A]]|| || || |- || '''4. Carry Select Adder''' || [[Media:VLSI.Arith.1.A.CSelA.20191002.pdf|A]]|| || || |- || '''5. Carry Skip Adder''' || [[Media:VLSI.Arith.5A.CSkip.20241112.pdf|A]]|| || || [[Media:VLSI.Arith.5D.CSkip.CMOS.20211108.pdf|pdf]] |- || '''6. Carry Chain Adder''' || [[Media:VLSI.Arith.6A.CCA.20211109.pdf|A]]|| || [[Media:VLSI.Arith.6C.CCA.VHDL.20211109.pdf|pdf]], [[Media:Adder.cca.20140313.pdf|pdf]] || [[Media:VLSI.Arith.6D.CCA.CMOS.20211109.pdf|pdf]] |- || '''7. Kogge-Stone Adder''' || [[Media:VLSI.Arith.1.A.KSA.20140315.pdf|A]]|| || [[Media:Adder.ksa.20140409.pdf|pdf]]|| |- || '''8. Prefix Adder''' || [[Media:VLSI.Arith.1.A.PFA.20140314.pdf|A]]|| || || |- || '''9.1 Variable Block Adder''' || [[Media:VLSI.Arith.1A.VBA.20221110.pdf|A]], [[Media:VLSI.Arith.1B.VBA.20230911.pdf|B]], [[Media:VLSI.Arith.1C.VBA.20240622.pdf|C]]|| || || |- || '''9.2 Multi-Level Variable Block Adder''' || [[Media:VLSI.Arith.1.A.VBA-Multi.20221031.pdf|A]]|| || || |} </br> === Adder Architectures Suitable for FPGA === * FPGA Carry-Chain Adder ([[Media:VLSI.Arith.1.A.FPGA-CCA.20210421.pdf|pdf]]) * FPGA Carry Select Adder ([[Media:VLSI.Arith.1.B.FPGA-CarrySelect.20210522.pdf|pdf]]) * FPGA Variable Block Adder ([[Media:VLSI.Arith.1.C.FPGA-VariableBlock.20220125.pdf|pdf]]) * FPGA Carry Lookahead Adder ([[Media:VLSI.Arith.1.D.FPGA-CLookahead.20210304.pdf|pdf]]) * Carry-Skip Adder </br> == Barrel Shifter == * Barrel Shifter Architecture Exploration ([[Media:Bshift.20131105.pdf|bshfit.vhdl]], [[Media:Bshift.makefile.20131109.pdf|bshfit.makefile]]) </br> '''Mux Based Barrel Shifter''' * Analysis ([[Media:Arith.BShfiter.20151207.pdf|pdf]]) * Implementation </br> == Multiplier == === Array Multipliers === * Analysis ([[Media:VLSI.Arith.1.A.Mult.20151209.pdf|pdf]]) </br> === Tree Mulltipliers === * Lattice Multiplication ([[Media:VLSI.Arith.LatticeMult.20170204.pdf|pdf]]) * Wallace Tree ([[Media:VLSI.Arith.WallaceTree.20170204.pdf|pdf]]) * Dadda Tree ([[Media:VLSI.Arith.DaddaTree.20170701.pdf|pdf]]) </br> === Booth Multipliers === * [[Media:RNS4.BoothEncode.20161005.pdf|Booth Encoding Note]] * Booth Multiplier Note ([[Media:BoothMult.20160929.pdf|H1.pdf]]) </br> == Divider == * Binary Divider ([[Media:VLSI.Arith.1.A.Divider.20131217.pdf|pdf]])</br> </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] [[Category:Digital Circuit Design]] [[Category:FPGA]] avj4l2ix1k6oiab1wqpkchq5o0fr9ag Wikiversity:Newsletters/Tech News 4 162205 2684051 2679927 2024-11-12T00:07:17Z MediaWiki message delivery 983498 /* Tech News: 2024-46 */ new section 2684051 wikitext text/x-wiki {{Archive box|[[/2014/]] · [[/2015/]] · [[/2016/]] · [[/2017/]] · [[/2018/]] · [[/2019/]] · [[/2020/]] · [[/2021/]] · [[/2022/]]}} __TOC__ {{Clear}} == Tech News: 2023-02 == <section begin="technews-2023-W02"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/02|Translations]] are available. '''Recent changes''' * You can use tags to filter edits in the recent changes feed or on your watchlist. You can now use tags to filter out edits you don't want to see. Previously you could only use tags to focus on the edits with those tags. [https://phabricator.wikimedia.org/T174349] * [[Special:WhatLinksHere|Special:WhatLinksHere]] shows all pages that link to a specific page. There is now a [https://wlh.toolforge.org prototype] for how to sort those pages alphabetically. You can see the discussion in the [[phab:T4306|Phabricator ticket]]. * You can now use the [[mw:Special:MyLanguage/Extension:Thanks|thanks]] function on your watchlist and the user contribution page. [https://phabricator.wikimedia.org/T51541] * A wiki page can be moved to give it a new name. You can now get a dropdown menu with common reasons when you move a page. This is so you don't have to write the explanation every time. [https://phabricator.wikimedia.org/T325257] * [[m:Special:MyLanguage/Matrix.org|Matrix]] is a chat tool. You can now use <code>matrix:</code> to create Matrix links on wiki pages. [https://phabricator.wikimedia.org/T326021] * You can filter out translations when you look at the recent changes on multilingual wikis. This didn't hide translation pages. You can now also hide subpages which are translation pages. [https://phabricator.wikimedia.org/T233493] '''Changes later this week''' * [[m:Special:MyLanguage/Real Time Preview for Wikitext|Realtime preview for wikitext]] is a tool which lets editors preview the page when they edit wikitext. It will be enabled for all users of the 2010 wikitext editor. You will find it in the editor toolbar. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2023-01-10|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2023-01-12|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-11|en}}. It will be on all wikis from {{#time:j xg|2023-01-12|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/02|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W02"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:07, 10 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24342971 --> == Tech News: 2023-03 == <section begin="technews-2023-W03"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/03|Translations]] are available. '''Problems''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The URLs in "{{int:last}}" links on page history now contain <bdi lang="zxx" dir="ltr"><code><nowiki>diff=prev&oldid=[revision ID]</nowiki></code></bdi> in place of <bdi lang="zxx" dir="ltr"><code><nowiki>diff=[revision ID]&oldid=[revision ID]</nowiki></code></bdi>. This is to fix a problem with links pointing to incorrect diffs when history was filtered by a tag. Some user scripts may break as a result of this change. [https://phabricator.wikimedia.org/T243569] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-18|en}}. It will be on all wikis from {{#time:j xg|2023-01-19|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Some [[mw:Special:MyLanguage/Talk pages project/Usability|changes to the appearance of talk pages]] have only been available on <code>{{ns:1}}:</code> and <code>{{ns:3}}:</code> namespaces. These will be extended to other talk namespaces, such as <code>{{ns:5}}:</code>. They will continue to be unavailable in non-talk namespaces, including <code>{{ns:4}}:</code> pages (e.g., at the Village Pump). You can [[Special:Preferences#mw-prefsection-editing-discussion|change your preferences]] ([[Special:Preferences#mw-prefsection-betafeatures|beta feature]]). [https://phabricator.wikimedia.org/T325417] *On Wikisources, when an image is zoomed or panned in the Page: namespace, the same zoom and pan settings will be remembered for all Page: namespace pages that are linked to a particular Index: namespace page. [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/ProofreadPage/+/868841] * The Vector 2022 skin will become the default for the English Wikipedia desktop users. The change will take place on January 18 at 15:00 UTC. [[:en:w:Wikipedia:Vector 2022|Learn more]]. '''Future changes''' * The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]], which invites contributors to make technical proposals and vote for tools and improvements, starts next week on 23 January 2023 at 18:00 UTC. You can start drafting your proposals in [[m:Community Wishlist Survey/Sandbox|the CWS sandbox]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/03|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W03"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:10, 17 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24381020 --> == Tech News: 2023-04 == <section begin="technews-2023-W04"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/04|Translations]] are available. '''Problems''' * Last week, for ~15 minutes, all wikis were unreachable for logged-in users and non-cached pages. This was caused by a timing issue. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-17_MediaWiki] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-25|en}}. It will be on all wikis from {{#time:j xg|2023-01-26|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * If you have the Beta Feature for [[mw:Special:MyLanguage/Talk pages project|DiscussionTools]] enabled, the appearance of talk pages will add more information about discussion activity. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/Usability#Status][https://phabricator.wikimedia.org/T317907] * The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]] (CWS), which invites contributors to make technical proposals and vote for tools and improvements, starts on Monday 23 January 2023 at [https://zonestamp.toolforge.org/1674496814 18:00 UTC]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/04|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W04"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:46, 23 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24418874 --> == Tech News: 2023-05 == <section begin="technews-2023-W05"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/05|Translations]] are available. '''Problems''' * Last week, for ~15 minutes, some users were unable to log in or edit pages. This was caused by a problem with session storage. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-24_sessionstore_quorum_issues] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-01|en}}. It will be on all wikis from {{#time:j xg|2023-02-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Wikis that use localized numbering schemes for references need to add new CSS. This will help to show citation numbers the same way in all reading and editing modes. If your wiki would prefer to do it yourselves, please see the [[mw:Special:MyLanguage/Parsoid/Parser Unification/Cite CSS|details and example CSS to copy from]], and also add your wiki to the list. Otherwise, the developers will directly help out starting the week of February 5. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/05|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W05"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:05, 31 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24455949 --> == Tech News: 2023-06 == <section begin="technews-2023-W06"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/06|Translations]] are available. '''Recent changes''' * In the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022 skin]], logged-out users using the full-width toggle will be able to see the setting of their choice even after refreshing pages or opening new ones. This only applies to wikis where Vector 2022 is the default. [https://phabricator.wikimedia.org/T321498] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-08|en}}. It will be on all wikis from {{#time:j xg|2023-02-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Previously, we announced when some wikis would be in read-only for a few minutes because of a switch of their main database. These switches will not be announced any more, as the read-only time has become non-significant. Switches will continue to happen at 7AM UTC on Tuesdays and Thursdays. [https://phabricator.wikimedia.org/T292543#8568433] * Across all the wikis, in the Vector 2022 skin, logged-in users will see the page-related links such as "What links here" in a [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Features/Page_tools|new side menu]]. It will be displayed on the other side of the screen. This change had previously been made on Czech, English, and Vietnamese Wikipedias. [https://phabricator.wikimedia.org/T328692] *[[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] will stop receiving new proposals on [https://zonestamp.toolforge.org/1675706431 Monday, 6 February 2023, at 18:00 UTC]. Proposers should complete any edits by then, to give time for [[m:Special:MyLanguage/Community_Wishlist_Survey/Help_us|translations]] and review. Voting will begin on Friday, 10 February. '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Gadgets and user scripts will be changing to load on desktop and mobile sites. Previously they would only load on the desktop site. It is recommended that wiki administrators audit the [[MediaWiki:Gadgets-definition|gadget definitions]] prior to this change, and add <bdi lang="zxx" dir="ltr"><code>skins=…</code></bdi> for any gadgets which should not load on mobile. [https://phabricator.wikimedia.org/T328610 More details are available]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/06|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W06"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 10:21, 6 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24491749 --> == Tech News: 2023-07 == <section begin="technews-2023-W07"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/07|Translations]] are available. '''Problems''' * On wikis where patrolled edits are enabled, changes made to the [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list|mentor list]] by autopatrolled mentors are not correctly marked as patrolled. It will be fixed later this week. [https://phabricator.wikimedia.org/T328444] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-15|en}}. It will be on all wikis from {{#time:j xg|2023-02-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * The Reply tool and other parts of [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|DiscussionTools]] will be deployed for all editors using the mobile site. You can [[mw:Special:MyLanguage/Talk_pages_project/Mobile#Status_Updates|read more about this decision]]. [https://phabricator.wikimedia.org/T298060] '''Future changes''' * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/07|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W07"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:48, 14 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24540832 --> == Tech News: 2023-08 == <section begin="technews-2023-W08"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/08|Translations]] are available. '''Problems''' * Last week, during planned maintenance of Cloud Services, unforeseen complications forced the team to turn off all tools for 2–3 hours to prevent data corruption. Work is ongoing to prevent similar problems in the future. [https://phabricator.wikimedia.org/T329535] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-22|en}}. It will be on all wikis from {{#time:j xg|2023-02-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). *The voting phase for the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] ends on [https://zonestamp.toolforge.org/1677261621 24 February at 18:00 UTC]. The results of the survey will be announced on 28 February. '''Future changes''' * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W08"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:57, 21 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24570514 --> == Tech News: 2023-09 == <section begin="technews-2023-W09"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/09|Translations]] are available. '''Problems''' * Last week, in some areas of the world, there were problems with loading pages for 20 minutes and saving edits for 55 minutes. These issues were caused by a problem with our caching servers due to unforseen events during a routine maintenance task. [https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_wiki_outage][https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_read_only] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-01|en}}. It will be on all wikis from {{#time:j xg|2023-03-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W09"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:47, 27 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24634242 --> == Tech News: 2023-10 == <section begin="technews-2023-W10"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/10|Translations]] are available. '''Recent changes''' * The Community Wishlist Survey 2023 edition has been concluded. Community Tech has [[m:Special:MyLanguage/Community Wishlist Survey 2023/Results|published the results]] of the survey and will provide an update on what is next in April 2023. * On wikis which use [[mw:Special:MyLanguage/Writing_systems|LanguageConverter]] to handle multiple writing systems, articles which used custom conversion rules in the wikitext (primarily on Chinese Wikipedia) would have these rules applied inconsistently in the table of contents, especially in the Vector 2022 skin. This has now been fixed. [https://phabricator.wikimedia.org/T306862] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-08|en}}. It will be on all wikis from {{#time:j xg|2023-03-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * A search system has been added to the [[Special:Preferences|Preferences screen]]. This will let you find different options more easily. Making it work on mobile devices will happen soon. [https://phabricator.wikimedia.org/T313804] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/10|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W10"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:49, 6 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24676916 --> == Tech News: 2023-11 == <section begin="technews-2023-W11"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/11|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-15|en}}. It will be on all wikis from {{#time:j xg|2023-03-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-cbk_zamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cdowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cebwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ckbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-csbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-itwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304542][https://phabricator.wikimedia.org/T304550] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/11|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W11"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:20, 13 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24700189 --> == Tech News: 2023-12 == <section begin="technews-2023-W12"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/12|Translations]] are available. '''Problems''' * Last week, some users experienced issues loading image thumbnails. This was due to incorrectly cached images. [https://phabricator.wikimedia.org/T331820] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-22|en}}. It will be on all wikis from {{#time:j xg|2023-03-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A link to the user's [[{{#special:CentralAuth}}]] page will appear on [[{{#special:Contributions}}]] — some user scripts which previously added this link may cause conflicts. This feature request was [[:m:Community Wishlist Survey 2023/Admins and patrollers/Add link to CentralAuth on Special:Contributions|voted #17 in the 2023 Community Wishlist Survey]]. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[{{#special:AbuseFilter}}]] edit window will be resizable and larger by default. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Make the AbuseFilter edit window resizable and larger by default|voted #80 in the 2023 Community Wishlist Survey]]. * There will be a new option for Administrators when they are unblocking a user, to add the unblocked user’s user page to their watchlist. This will work both via [[{{#special:Unblock}}]] and via the API. [https://phabricator.wikimedia.org/T257662] '''Meetings''' * You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1679677204 24 March at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia Apps/Office Hours|details and how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/12|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W12"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:25, 21 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24732558 --> == Tech News: 2023-13 == <section begin="technews-2023-W13"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/13|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] condition limit was increased from 1000 to 2000. [https://phabricator.wikimedia.org/T309609] * [[:m:Special:MyLanguage/Global AbuseFilter#Locally disabled actions|Some Global AbuseFilter]] actions will no longer apply to local projects. [https://phabricator.wikimedia.org/T332521] * Desktop users are now able to subscribe to talk pages by clicking on the {{int:discussiontools-newtopicssubscription-button-subscribe-label}} link in the {{int:toolbox}} menu. If you subscribe to a talk page, you receive [[mw:Special:MyLanguage/Notifications|notifications]] when new topics are started on that talk page. This is separate from putting the page on your watchlist or subscribing to a single discussion. [https://phabricator.wikimedia.org/T263821] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-29|en}}. It will be on all wikis from {{#time:j xg|2023-03-30|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''Future changes''' * You will be able to choose [[mw:Special:MyLanguage/VisualEditor/Diffs|visual diffs]] on all [[m:Special:MyLanguage/Help:Page history|history pages]] at the Wiktionaries and Wikipedias. [https://phabricator.wikimedia.org/T314588] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The legacy [[mw:Mobile Content Service|Mobile Content Service]] is going away in July 2023. Developers are encouraged to switch to Parsoid or another API before then to ensure service continuity. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/4MVQQTONJT7FJAXNVOFV3WWVVMCHRINE/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W13"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:13, 28 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24780854 --> == Tech News: 2023-14 == <section begin="technews-2023-W14"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/14|Translations]] are available. '''Recent changes''' * The system for automatically creating categories for the [[mw:Special:MyLanguage/Extension:Babel|Babel]] extension has had several important changes and fixes. One of them allows you to insert templates for automatic category descriptions on creation, allowing you to categorize the new categories. [https://phabricator.wikimedia.org/T211665][https://phabricator.wikimedia.org/T64714][https://phabricator.wikimedia.org/T170654][https://phabricator.wikimedia.org/T184941][https://phabricator.wikimedia.org/T33074] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-05|en}}. It will be on all wikis from {{#time:j xg|2023-04-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Some older [[w:en:Web browser|Web browsers]] will stop being able to use [[w:en:JavaScript|JavaScript]] on Wikimedia wikis from this week. This mainly affects users of Internet Explorer 11. If you have an old web browser on your computer you can try to upgrade to a newer version. [https://phabricator.wikimedia.org/T178356] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The deprecated <bdi lang="zxx" dir="ltr"><code>jquery.hoverIntent</code></bdi> module has been removed. This module could be used by gadgets and user scripts, to create an artificial delay in how JavaScript responds to a hover event. Gadgets and user scripts should now use jQuery <bdi lang="zxx" dir="ltr"><code>hover()</code></bdi> or <bdi lang="zxx" dir="ltr"><code>on()</code></bdi> instead. Examples can be found in the [[mw:Special:MyLanguage/ResourceLoader/Migration_guide_(users)#jquery.hoverIntent|migration guide]]. [https://phabricator.wikimedia.org/T311194] * Some of the links in [[{{#special:SpecialPages}}]] will be re-arranged. There will be a clearer separation between links that relate to all users, and links related to your own user account. [https://phabricator.wikimedia.org/T333242] * You will be able to hide the [[mw:Special:MyLanguage/Talk pages project/Replying|Reply button]] in archived discussion pages with a new <bdi lang="zxx" dir="ltr"><code><nowiki>__ARCHIVEDTALK__</nowiki></code></bdi> magic word. There will also be a new <bdi lang="zxx" dir="ltr"><code>.mw-archivedtalk</code></bdi> CSS class for hiding the Reply button in individual sections on a page. [https://phabricator.wikimedia.org/T249293][https://phabricator.wikimedia.org/T295553][https://gerrit.wikimedia.org/r/c/mediawiki/extensions/DiscussionTools/+/738221] '''Future changes''' * The Vega software that creates data visualizations in pages, such as graphs, will be upgraded to the newest version in the future. Graphs that still use the very old version 1.5 syntax may stop working properly. Most existing uses have been found and updated, but you can help to check, and to update any local documentation. [[phab:T260542|Examples of how to find and fix these graphs are available]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W14"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:39, 3 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24820268 --> == Tech News: 2023-15 == <section begin="technews-2023-W15"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/15|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] In the visual editor, it is now possible to edit captions of images in galleries without opening the gallery dialog. This feature request was [[:m:Community Wishlist Survey 2023/Editing/Editable gallery captions in Visual Editor|voted #61 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T190224] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] You can now receive notifications when another user edits your user page. See the "{{int:Echo-category-title-edit-user-page}}" option in [[Special:Preferences#mw-prefsection-echo|your Preferences]]. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Notifications for user page edits|voted #3 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T3876] '''Problems''' * There was a problem with all types of CentralNotice banners still being shown to logged-in users even if they had [[Special:Preferences#mw-prefsection-centralnotice-banners|turned off]] specific banner types. This has now been fixed. [https://phabricator.wikimedia.org/T331671] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-12|en}}. It will be on all wikis from {{#time:j xg|2023-04-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-arywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dinwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-elwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-emlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-etwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-euwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-extwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tumwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ffwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiu_vrowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-furwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gcrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gomwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gotwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-guwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304551][https://phabricator.wikimedia.org/T308133] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/15|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W15"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:05, 10 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24851886 --> == Tech News: 2023-16 == <section begin="technews-2023-W16"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/16|Translations]] are available. '''Recent changes''' * You can now see [[mw:Special:MyLanguage/Help:Extension:Kartographer#Show_nearby_articles|nearby articles on a Kartographer map]] with the button for the new feature "{{int:Kartographer-sidebar-nearbybutton}}". Six wikis have been testing this feature since October. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Nearby_articles#Implementation][https://phabricator.wikimedia.org/T334079] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[m:Special:GlobalWatchlist|Special:GlobalWatchlist]] page now has links for "{{int:globalwatchlist-markpageseen}}" for each entry. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Button to mark a single change as read in the global watch list|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334246] '''Problems''' * At Wikimedia Commons, some thumbnails have not been getting replaced correctly after a new version of the image is uploaded. This should be fixed later this week. [https://phabricator.wikimedia.org/T331138][https://phabricator.wikimedia.org/T333042] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] For the last few weeks, some external tools had inconsistent problems with logging-in with OAuth. This has now been fixed. [https://phabricator.wikimedia.org/T332650] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-19|en}}. It will be on all wikis from {{#time:j xg|2023-04-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W16"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:54, 18 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24881071 --> == Tech News: 2023-17 == <section begin="technews-2023-W17"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/17|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The date-selection menu on pages such as [[{{#special:Contributions}}]] will now show year-ranges that are in the current and past decade, instead of the current and future decade. This feature request was [[m:Community Wishlist Survey 2023/Miscellaneous/Change year range shown in date selection popup|voted #145 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334316] '''Problems''' * Due to security issues with the [[mw:Special:MyLanguage/Extension:Graph|Graph extension]], graphs have been disabled in all Wikimedia projects. Wikimedia Foundation teams are working to respond to these vulnerabilities. [https://phabricator.wikimedia.org/T334940] * For a few days, it was not possible to save some kinds of edits on the mobile version of a wiki. This has been fixed. [https://phabricator.wikimedia.org/T334797][https://phabricator.wikimedia.org/T334799][https://phabricator.wikimedia.org/T334794] '''Changes later this week''' * All wikis will be read-only for a few minutes on April 26. This is planned for [https://zonestamp.toolforge.org/1682517653 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-26|en}}. It will be on all wikis from {{#time:j xg|2023-04-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * The Editing team plans an A/B test for [[mw:Special:MyLanguage/Talk pages project/Usability|a usability analysis of the Talk page project]]. The [[mw:Special:MyLanguage/Talk pages project/Usability/Analysis|planned measurements are available]]. Your wiki [[phab:T332946|may be invited to participate]]. Please suggest improvements to the measurement plan at [[mw:Talk:Talk pages project/Usability|the discussion page]]. * [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2023-2024|The Wikimedia Foundation annual plan 2023-2024 draft is open for comment and input]] until May 19. The final plan will be published in July 2023 on Meta-wiki. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W17"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:03, 24 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24933592 --> == Tech News: 2023-18 == <section begin="technews-2023-W18"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/18|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the French and Italian Wikipedias. More languages will be added in the near future. This is part of the [[m:Community Wishlist Survey 2023/Reading/Extend "Who Wrote That?" tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T243711][https://phabricator.wikimedia.org/T270490][https://phabricator.wikimedia.org/T334891] * The [[:commons:Special:MyLanguage/Commons:Video2commons|Video2commons]] tool has been updated. This fixed several bugs related to YouTube uploads. [https://github.com/toolforge/video2commons/pull/162/commits] * The [[{{#special:Preferences}}]] page has been redesigned on mobile web. The new design makes it easier to browse the different categories and settings at low screen widths. You can also now access the page via a link in the Settings menu in the mobile web sidebar. [https://www.mediawiki.org/wiki/Moderator_Tools/Content_moderation_on_mobile_web/Preferences] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-03|en}}. It will be on all wikis from {{#time:j xg|2023-05-04|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W18"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:45, 2 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24966974 --> == Tech News: 2023-19 == <section begin="technews-2023-W19"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/19|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] When you close an image that is displayed via MediaViewer, it will now return to the wiki page instead of going back in your browser history. This feature request was [[m:Community Wishlist Survey 2023/Reading/Return to the article when closing the MediaViewer|voted #65 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T236591] * The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|SyntaxHighlight]] extension now supports <bdi lang="en" dir="ltr"><code>wikitext</code></bdi> as a selected language. Old alternatives that were used to highlight wikitext, such as <bdi lang="en" dir="ltr"><code>html5</code></bdi>, <bdi lang="en" dir="ltr"><code>moin</code></bdi>, and <bdi lang="en" dir="ltr"><code>html+handlebars</code></bdi>, can now be replaced. [https://phabricator.wikimedia.org/T29828] * [[mw:Special:MyLanguage/Manual:Creating pages with preloaded text|Preloading text to new pages/sections]] now supports preloading from localized MediaWiki interface messages. [https://cs.wikipedia.org/wiki/User_talk:Martin_Urbanec_(WMF)?action=edit&section=new&preload=MediaWiki:July Here is an example] at the {{int:project-localized-name-cswiki/en}} that uses <bdi lang="zxx" dir="ltr"><code><nowiki>preload=MediaWiki:July</nowiki></code></bdi>. [https://phabricator.wikimedia.org/T330337] '''Problems''' * Graph Extension update: Foundation developers have completed upgrading the visualization software to Vega5. Existing community graphs based on Vega2 are no longer compatible. Communities need to update local graphs and templates, and shared lua modules like <bdi lang="de" dir="ltr">[[w:de:Modul:Graph]]</bdi>. The [https://vega.github.io/vega/docs/porting-guide/ Vega Porting guide] provides the most comprehensive detail on migration from Vega2 and [https://www.mediawiki.org/w/index.php?title=Template:Graph:PageViews&action=history here is an example migration]. Vega5 has currently just been enabled on mediawiki.org to provide a test environment for communities. [https://phabricator.wikimedia.org/T334940#8813922] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-10|en}}. It will be on all wikis from {{#time:j xg|2023-05-11|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Until now, all new OAuth apps went through manual review. Starting this week, apps using identification-only or basic authorizations will not require review. [https://phabricator.wikimedia.org/T67750] '''Future changes''' * During the next year, MediaWiki will stop using IP addresses to identify logged-out users, and will start automatically assigning unique temporary usernames. Read more at [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates|IP Editing: Privacy Enhancement and Abuse Mitigation/Updates]]. You can [[m:Talk:IP Editing: Privacy Enhancement and Abuse Mitigation#What should it look like?|join the discussion]] about the [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates#What will temporary usernames look like?|format of the temporary usernames]]. [https://phabricator.wikimedia.org/T332805] * There will be an [[:w:en:A/B testing|A/B test]] on 10 Wikipedias where the Vector 2022 skin is the default skin. Half of logged-in desktop users will see an interface where the different parts of the page are more clearly separated. You can [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2023-05 Zebra9 A/B test|read more]]. [https://phabricator.wikimedia.org/T333180][https://phabricator.wikimedia.org/T335972] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] <code>jquery.tipsy</code> will be removed from the MediaWiki core. This will affect some user scripts. Many lines with <code>.tipsy(</code> can be commented out. <code>OO.ui.PopupWidget</code> can be used to keep things working like they are now. You can [[phab:T336019|read more]] and [[:mw:Help:Locating broken scripts|read about how to find broken scripts]]. [https://phabricator.wikimedia.org/T336019] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W19"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:36, 9 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24998636 --> == Tech News: 2023-20 == <section begin="technews-2023-W20"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/20|Translations]] are available. '''Problems''' * Citations that are automatically generated based on [[d:Q33057|ISBN]] are currently broken. This affects citations made with the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]], and the use of the citoid API in gadgets and user scripts. Work is ongoing to restore this feature. [https://phabricator.wikimedia.org/T336298] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-17|en}}. It will be on all wikis from {{#time:j xg|2023-05-18|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-gorwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hakwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hifwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-htwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-igwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ilowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-inhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308134] '''Future changes''' * There is a recently formed team at the Wikimedia Foundation which will be focusing on experimenting with new tools. Currently they are building [[m:Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI|a prototype ChatGPT plugin that allows information generated by ChatGPT to be properly attributed]] to the Wikimedia projects. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget and userscript developers should replace <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> with <bdi lang="zxx" dir="ltr"><code>mediawiki.cookie</code></bdi>. The <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> library will be removed in ~1 month, and staff developers will run a script to replace any remaining uses at that time. [https://phabricator.wikimedia.org/T336018] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W20"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:45, 15 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25011501 --> == Tech News: 2023-21 == <section begin="technews-2023-W21"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/21|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The "recent edits" time period for page watchers is now 30 days. It used to be 180 days. This was a [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Change information about the number of watchers on a page|Community Wishlist Survey proposal]]. [https://phabricator.wikimedia.org/T336250] '''Changes later this week''' * An [[mw:special:MyLanguage/Growth/Positive reinforcement#Impact|improved impact module]] will be available at Wikipedias. The impact module is a feature available to newcomers [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer homepage|at their personal homepage]]. It will show their number of edits, how many readers their edited pages have, how many thanks they have received and similar things. It is also accessible by accessing Special:Impact. [https://phabricator.wikimedia.org/T336203] * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-24|en}}. It will be on all wikis from {{#time:j xg|2023-05-25|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W21"/> 16:55, 22 May 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25028325 --> == Tech News: 2023-22 == <section begin="technews-2023-W22"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/22|Translations]] are available. '''Recent changes''' * Citations can once again be added automatically from ISBNs, thanks to Zotero's ISBN searches. The current data sources are the Library of Congress (United States), the Bibliothèque nationale de France (French National Library), and K10plus ISBN (German repository). Additional data source searches can be [[mw:Citoid/Creating Zotero translators|proposed to Zotero]]. The ISBN labels in the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]] will reappear later this week. [https://phabricator.wikimedia.org/T336298#8859917] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The page [[{{#special:EditWatchlist}}]] now has "{{int:watchlistedit-normal-check-all}}" options to select all the pages within a namespace. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Watchlist edit - "check all" checkbox|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334252] '''Problems''' * For a few days earlier this month, the "Add interlanguage link" item in the Tools menu did not work properly. This has now been fixed. [https://phabricator.wikimedia.org/T337081] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-31|en}}. It will be on all wikis from {{#time:j xg|2023-06-01|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * VisualEditor will be switched to a new backend on [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/small.dblist small] and [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/medium.dblist medium] wikis this week. Large wikis will follow in the coming weeks. This is part of the effort to move Parsoid into MediaWiki core. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W22"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:03, 29 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25079963 --> == Tech News: 2023-23 == <section begin="technews-2023-W23"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/23|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Help:Extension:RealMe|RealMe]] extension allows you to mark URLs on your user page as verified for Mastodon and similar software. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] Citation and footnote editing can now be started from the reference list when using the visual editor. This feature request was [[m:Community Wishlist Survey 2023/Citations/Allow citations to be edited in the references section with VisualEditor|voted #2 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T54750] * Previously, clicking on someone else's link to Recent Changes with filters applied within the URL could unintentionally change your preference for "{{int:Rcfilters-group-results-by-page}}". This has now been fixed. [https://phabricator.wikimedia.org/T202916#8874081] '''Problems''' * For a few days last week, some tools and bots returned outdated information due to database replication problems, and may have been down entirely while it was being fixed. These issues have now been fixed. [https://phabricator.wikimedia.org/T337446] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-07|en}}. It will be on all wikis from {{#time:j xg|2023-06-08|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Bots will no longer be prevented from making edits because of URLs that match the [[mw:Special:MyLanguage/Extension:SpamBlacklist|spam blacklist]]. [https://phabricator.wikimedia.org/T313107] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W23"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:52, 5 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25114640 --> == Tech News: 2023-24 == <section begin="technews-2023-W24"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/24|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the Dutch, German, Hungarian, Indonesian, Japanese, Polish and Portuguese Wikipedias. This was the [[m:Community Wishlist Survey 2023/Reading/Extend "Who Wrote That?" tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334891] * The [[mw:Special:MyLanguage/Structured Data Across Wikimedia/Search Improvements#Search Preview panel|Search Preview panel]] has been deployed on four Wikipedias (Catalan, Dutch, Hungarian and Norwegian). The panel will show an image related to the article (if existing), the top sections of the article, related images (coming from MediaSearch on Commons), and eventually the sister projects associated with the article. [https://phabricator.wikimedia.org/T306341] * The [[:mw:Special:MyLanguage/Help:Extension:RealMe#Verifying_a_link_on_non-user_pages|RealMe]] extension now allows administrators to verify URLs for any page, for Mastodon and similar software. [https://phabricator.wikimedia.org/T324937] * The default project license [https://lists.wikimedia.org/hyperkitty/list/wikimediaannounce-l@lists.wikimedia.org/thread/7G6XPWZPQFLZ2JANN3ZX6RT4DVUI3HZQ/ has been officially upgraded] to CC BY-SA 4.0. The software interface messages have been updated. Communities should feel free to start updating any mentions of the old CC BY-SA 3.0 licensing within policies and related documentation pages. [https://phabricator.wikimedia.org/T319064] '''Problems''' * For three days last month, some Wikipedia pages edited with VisualEditor or DiscussionTools had an unintended <code><nowiki>__TOC__</nowiki></code> (or its localized form) added during an edit. There is [[mw:Parsoid/Deployments/T336101_followup|a listing of affected pages sorted by wiki]], that may still need to be fixed. [https://phabricator.wikimedia.org/T336101] * Currently, the "{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}" feature in VisualEditor is broken. Existing <code><nowiki>{{DEFAULTSORT:...}}</nowiki></code> keywords incorrectly appear as missing templates in VisualEditor. Developers are exploring how to fix this. In the meantime, those wishing to edit the default sortkey of a page are advised to switch to source editing. [https://phabricator.wikimedia.org/T337398] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Last week, an update to the delete form may have broken some gadgets or user scripts. If you need to manipulate (empty) the reason field, replace <bdi lang="zxx" dir="ltr"><code>#wpReason</code></bdi> with <bdi lang="zxx" dir="ltr" style="white-space: nowrap;"><code>#wpReason > input</code></bdi>. See [https://cs.wikipedia.org/w/index.php?title=MediaWiki%3AGadget-CleanDeleteReasons.js&diff=22859956&oldid=12794189 an example fix]. [https://phabricator.wikimedia.org/T337809] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-14|en}}. It will be on all wikis from {{#time:j xg|2023-06-15|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * VisualEditor will be switched to a new backend on English Wikipedia on Monday, and all other [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/large.dblist large] wikis on Thursday. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529] '''Future changes''' * From 5 June to 17 July, the Foundation's [[:mw:Wikimedia Security Team|Security team]] is holding a consultation with contributors regarding a draft policy to govern the use of third-party resources in volunteer-developed gadgets and scripts. Feedback and suggestions are warmly welcome at [[m:Special:MyLanguage/Third-party resources policy|Third-party resources policy]] on meta-wiki. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W24"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:51, 12 June 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25133779 --> == Tech News: 2023-25 == <section begin="technews-2023-W25"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/25|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Flame graphs are now available in WikimediaDebug. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/JXNQD3EHG5V5QW5UXFDPSHQG4MJ3FWJQ/][https://techblog.wikimedia.org/2023/06/08/flame-graphs-arrive-in-wikimediadebug/] '''Changes later this week''' * There is no new MediaWiki version this week. * There is now a toolbar search popup in the visual editor. You can trigger it by typing <code>\</code> or pressing <code>ctrl + shift + p</code>. It can help you quickly access most tools in the editor. [https://commons.wikimedia.org/wiki/File:Visual_editor_toolbar_search_feature.png][https://phabricator.wikimedia.org/T66905] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W25"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:08, 19 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25159510 --> == Tech News: 2023-26 == <section begin="technews-2023-W26"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/26|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Action API modules and Special:LinkSearch will now add a trailing <bdi lang="zxx" dir="ltr"><code>/</code></bdi> to all <bdi lang="zxx" dir="ltr"><code>prop=extlinks</code></bdi> responses for bare domains. This is part of the work to remove duplication in the <code>externallinks</code> database table. [https://phabricator.wikimedia.org/T337994] '''Problems''' * Last week, search was broken on Commons and Wikidata for 23 hours. [https://phabricator.wikimedia.org/T339810][https://wikitech.wikimedia.org/wiki/Incidents/2023-06-18_search_broken_on_wikidata_and_commons] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-28|en}}. It will be on all wikis from {{#time:j xg|2023-06-29|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Minerva skin now applies more predefined styles to the <bdi lang="zxx" dir="ltr"><code>.mbox-text</code></bdi> CSS class. This enables support for mbox templates that use divs instead of tables. Please make sure that the new styles won't affect other templates in your wiki. [https://gerrit.wikimedia.org/r/c/mediawiki/skins/MinervaNeue/+/930901/][https://phabricator.wikimedia.org/T339040] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadgets will now load on both desktop and mobile by default. Previously, gadgets loaded only on desktop by default. Changing this default using the <bdi lang="zxx" dir="ltr"><code>|targets=</code></bdi> parameter is also deprecated and should not be used. You should make gadgets work on mobile or disable them based on the skin (with the <bdi lang="zxx" dir="ltr"><code>|skins=</code></bdi> parameter in <bdi lang="en" dir="ltr">MediaWiki:Gadgets-definition</bdi>) rather than whether the user uses the mobile or the desktop website. Popular gadgets that create errors on mobile will be disabled by developers on the Minerva skin as a temporary solution. [https://phabricator.wikimedia.org/T127268] * All namespace tabs now have the same browser [[m:Special:MyLanguage/Help:Keyboard_shortcuts|access key]] by default. Previously, custom and extension-defined namespaces would have to have their access keys set manually on-wiki, but that is no longer necessary. [https://phabricator.wikimedia.org/T22126] * The review form of the Flagged Revisions extension now uses the standardized [[mw:Special:MyLanguage/Codex|user interface components]]. [https://phabricator.wikimedia.org/T191156] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] How media is structured in the parser's HTML output will change in the coming weeks at [[:wikitech:Deployments/Train#Thursday|group2 wikis]]. This change improves the accessibility of content. You may need to update your site-CSS, or userscripts and gadgets. There are [[mw:Special:MyLanguage/Parsoid/Parser_Unification/Media_structure/FAQ|details on what code to check, how to update the code, and where to report any related problems]]. [https://phabricator.wikimedia.org/T314318] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W26"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:18, 26 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25202311 --> == Tech News: 2023-27 == <section begin="technews-2023-W27"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/27|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the rolling out of the [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|audio links that play on click]] wishlist proposal, [https://noc.wikimedia.org/conf/highlight.php?file=dblists/small.dblist small wikis] will now be able to use the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline audio player mode|inline audio player]] that is implemented by the [[mw:Extension:Phonos|Phonos]] extension. [https://phabricator.wikimedia.org/T336763] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] From this week all gadgets automatically load on mobile and desktop sites. If you see any problems with gadgets on your wikis, please adjust the [[mw:Special:MyLanguage/Extension:Gadgets#Options|gadget options]] in your gadget definitions file. [https://phabricator.wikimedia.org/T328610] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-05|en}}. It will be on all wikis from {{#time:j xg|2023-07-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W27"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:51, 3 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25231546 --> == Tech News: 2023-28 == <section begin="technews-2023-W28"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/28|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Structured Data Across Wikimedia/Section-level Image Suggestions|Section-level Image Suggestions feature]] has been deployed on seven Wikipedias (Portuguese, Russian, Indonesian, Catalan, Hungarian, Finnish and Norwegian Bokmål). The feature recommends images for articles on contributors' watchlists that are a good match for individual sections of those articles. * [[:m:Special:MyLanguage/Global AbuseFilter|Global abuse filters]] have been enabled on all Wikimedia projects, except English and Japanese Wikipedias (who opted out). This change was made following a [[:m:Requests for comment/Make global abuse filters opt-out|global request for comments]]. [https://phabricator.wikimedia.org/T341159] * [[{{#special:BlockedExternalDomains}}]] is a new tool for administrators to help fight spam. It provides a clearer interface for blocking plain domains (and their subdomains), is more easily searchable, and is faster for the software to process for each edit on the wiki. It does not support regex (for complex cases), nor URL path-matching, nor the [[MediaWiki:Spam-whitelist|MediaWiki:Spam-whitelist]], but otherwise it replaces most of the functionalities of the existing [[MediaWiki:Spam-blacklist|MediaWiki:Spam-blacklist]]. There is a Python script to help migrate all simple domains into this tool, and more feature details, within [[mw:Special:MyLanguage/Manual:BlockedExternalDomains|the tool's documentation]]. It is available at all wikis except for Meta-wiki, Commons, and Wikidata. [https://phabricator.wikimedia.org/T337431] * The WikiEditor extension was updated. It includes some of the most frequently used features of wikitext editing. In the past, many of its messages could only be translated by administrators, but now all regular translators on translatewiki can translate them. Please check [https://translatewiki.net/wiki/Special:MessageGroupStats?group=ext-wikieditor&messages=&x=D#sortable:0=asc the state of WikiEditor localization into your language], and if the "Completion" for your language shows anything less than 100%, please complete the translation. See [https://lists.wikimedia.org/hyperkitty/list/wikitech-ambassadors@lists.wikimedia.org/thread/D4YELU2DXMZ75PGELUOKXXMFF3FH45XA/ a more detailed explanation]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-12|en}}. It will be on all wikis from {{#time:j xg|2023-07-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * The default protocol of [[{{#special:LinkSearch}}]] and API counterparts has changed from http to both http and https. [https://phabricator.wikimedia.org/T14810] * [[{{#special:LinkSearch}}]] and its API counterparts will now search for all of the URL provided in the query. It used to be only the first 60 characters. This feature was requested fifteen years ago. [https://phabricator.wikimedia.org/T17218] '''Future changes''' * There is an experiment with a [[:w:en:ChatGPT|ChatGPT]] plugin. This is to show users where the information is coming from when they read information from Wikipedia. It has been tested by Wikimedia Foundation staff and other Wikimedians. Soon all ChatGPT plugin users can use the Wikipedia plugin. This is the same plugin which was mentioned in [[m:Special:MyLanguage/Tech/News/2023/20|Tech News 2023/20]]. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI] * There is an ongoing discussion on a [[m:Special:MyLanguage/Third-party resources policy|proposed Third-party resources policy]]. The proposal will impact the use of third-party resources in gadgets and userscripts. Based on the ideas received so far, policy includes some of the risks related to user scripts and gadgets loading third-party resources, some best practices and exemption requirements such as code transparency and inspectability. Your feedback and suggestions are warmly welcome until July 17, 2023 on [[m:Talk:Third-party resources policy|on the policy talk page]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/28|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W28"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:54, 10 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25278797 --> == Tech News: 2023-29 == <section begin="technews-2023-W29"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/29|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] We are now serving 1% of all global user traffic from [[w:en:Kubernetes|Kubernetes]] (you can [[wikitech:MediaWiki On Kubernetes|read more technical details]]). We are planning to increment this percentage regularly. You can [[phab:T290536|follow the progress of this work]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-19|en}}. It will be on all wikis from {{#time:j xg|2023-07-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki [[mw:Special:MyLanguage/Help:System_message|system messages]] will now look for available local fallbacks, instead of always using the default fallback defined by software. This means wikis no longer need to override each language on the [[mw:Special:MyLanguage/Manual:Language#Fallback_languages|fallback chain]] separately. For example, English Wikipedia doesn't have to create <bdi lang="zxx" dir="ltr"><code>en-ca</code></bdi> and <bdi lang="zxx" dir="ltr"><code>en-gb</code></bdi> subpages with a transclusion of the base pages anymore. This makes it easier to maintain local overrides. [https://phabricator.wikimedia.org/T229992] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The <bdi lang="zxx" dir="ltr"><code>action=growthsetmentorstatus</code></bdi> API will be deprecated with the new MediaWiki version. Bots or scripts calling that API should use the <bdi lang="zxx" dir="ltr"><code>action=growthmanagementorlist</code></bdi> API now. [https://phabricator.wikimedia.org/T321503] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W29"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:08, 17 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25289122 --> == Tech News: 2023-30 == <section begin="technews-2023-W30"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/30|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] On July 18, the Wikimedia Foundation launched a survey about the [[:mw:Technical_decision_making|technical decision making process]] for people who do technical work that relies on software that is maintained by the Foundation or affiliates. If this applies to you, [https://wikimediafoundation.limesurvey.net/885471 please take part in the survey]. The survey will be open for three weeks, until August 7. You can find more information in [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/Q7DUCFA75DXG3G2KHTO7CEWMLCYTSDB2/|the announcement e-mail on wikitech-l]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-26|en}}. It will be on all wikis from {{#time:j xg|2023-07-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W30"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 02:20, 25 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25332248 --> == Tech News: 2023-31 == <section begin="technews-2023-W31"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/31|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Synchronizer|Synchronizer]] tool is now available to keep Lua modules synced across Wikimedia wikis, along with [[mw:Multilingual Templates and Modules|updated documentation]] to develop global Lua modules and templates. * The tag filter on [[{{#special:NewPages}}]] and revision history pages can now be inverted. For example, you can hide edits that were made using an automated tool. [https://phabricator.wikimedia.org/T334337][https://phabricator.wikimedia.org/T334338] * The Wikipedia [[:w:en:ChatGPT|ChatGPT]] plugin experiment can now be used by ChatGPT users who can use plugins. You can participate in a [[:m:Talk:Wikimedia Foundation Annual Plan/2023-2024/Draft/Future Audiences#Announcing monthly Future Audiences open "office hours"|video call]] if you want to talk about this experiment or similar work. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI] '''Problems''' * It was not possible to generate a PDF for pages with non-Latin characters in the title, for the last two weeks. This has now been fixed. [https://phabricator.wikimedia.org/T342442] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-02|en}}. It will be on all wikis from {{#time:j xg|2023-08-03|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Tuesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-kawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kaawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kabwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-knwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kshwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kwwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308135] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W31"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:54, 31 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25362228 --> == Tech News: 2023-32 == <section begin="technews-2023-W32"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/32|Translations]] are available. '''Recent changes''' * Mobile Web editors can now [[mw:Special:MyLanguage/Reading/Web/Advanced_mobile_contributions#August_1,_2023_-_Full-page_editing_added_on_mobile|edit a whole page at once]]. To use this feature, turn on "{{int:Mobile-frontend-mobile-option-amc}}" in your settings and use the "{{int:Minerva-page-actions-editfull}}" button in the "{{int:Minerva-page-actions-overflow}}" menu. [https://phabricator.wikimedia.org/T203151] '''Changes later this week''' * There is no new MediaWiki version this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W32"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:20, 7 August 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25420038 --> == Tech News: 2023-33 == <section begin="technews-2023-W33"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/33|Translations]] are available. '''Recent changes''' * The Content translation system is no longer using Youdao's [[mw:Special:MyLanguage/Help:Content_translation/Translating/Initial_machine_translation|machine translation service]]. The service was in place for several years, but due to no usage, and availability of alternatives, it was deprecated to reduce maintenance overheads. Other services which cover the same languages are still available. [https://phabricator.wikimedia.org/T329137] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-16|en}}. It will be on all wikis from {{#time:j xg|2023-08-17|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-lawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ladwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lezwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lfnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-liwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lijwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lmowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ltgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-maiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-map_bmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mdfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kywiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308136] <!-- TODO replace wiki codes --> '''Future changes''' * A few gadgets/user scripts which add icons to the Minerva skin need to have their CSS updated. There are more details available including a [[phab:T344067|search for all existing instances and how to update them]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W33"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 05:59, 15 August 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25428668 --> == Tech News: 2023-34 == <section begin="technews-2023-W34"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/34|Translations]] are available. '''Recent changes''' * The [https://gdrive-to-commons.toolforge.org/ GDrive to Commons Uploader] tool is now available. It enables [[m:Special:MyLanguage/GDrive to Commons Uploader|securely selecting and uploading files]] from your Google Drive directly to Wikimedia Commons. [https://phabricator.wikimedia.org/T267868] * From now on, we will announce new Wikimedia wikis in Tech News, so you can update any tools or pages. ** Since the last edition, two new wikis have been created: *** a Wiktionary in [[d:Q7121294|Pa'O]] ([[wikt:blk:|<code>wikt:blk:</code>]]) [https://phabricator.wikimedia.org/T343540] *** a Wikisource in [[d:Q34002|Sundanese]] ([[s:su:|<code>s:su:</code>]]) [https://phabricator.wikimedia.org/T343539] ** To catch up, the next most recent six wikis are: *** Wikifunctions ([[f:|<code>f:</code>]]) [https://phabricator.wikimedia.org/T275945] *** a Wiktionary in [[d:Q2891049|Mandailing]] ([[wikt:btm:|<code>wikt:btm:</code>]]) [https://phabricator.wikimedia.org/T335216] *** a Wikipedia in [[d:Q5555465|Ghanaian Pidgin]] ([[w:gpe:|<code>w:gpe:</code>]]) [https://phabricator.wikimedia.org/T335969] *** a Wikinews in [[d:Q3111668|Gungbe]] ([[n:guw:|<code>n:guw:</code>]]) [https://phabricator.wikimedia.org/T334394] *** a Wiktionary in [[d:Q33522|Kabardian]] ([[wikt:kbd:|<code>wikt:kbd:</code>]]) [https://phabricator.wikimedia.org/T333266] *** a Wikipedia in [[d:Q35570|Fante]] ([[w:fat:|<code>w:fat:</code>]]) [https://phabricator.wikimedia.org/T335016] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-23|en}}. It will be on all wikis from {{#time:j xg|2023-08-24|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There is an existing [[mw:Stable interface policy|stable interface policy]] for MediaWiki backend code. There is a [[mw:User:Jdlrobson/Stable interface policy/frontend|proposed stable interface policy for frontend code]]. This is relevant for anyone who works on gadgets or Wikimedia frontend code. You can read it, discuss it, and let the proposer know if there are any problems. [https://phabricator.wikimedia.org/T344079] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W34"/> 15:25, 21 August 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25497111 --> == Tech News: 2023-35 == <section begin="technews-2023-W35"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/35|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Community Wishlist Survey 2022/Better diff handling of paragraph splits|better diff handling of paragraph splits]], improved detection of splits is being rolled out. Over the last two weeks, we deployed this support to [[wikitech:Deployments/Train#Groups|group0]] and group1 wikis. This week it will be deployed to group2 wikis. [https://phabricator.wikimedia.org/T341754] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] All [[{{#special:Contributions}}]] pages now show the user's local edit count and the account's creation date. [https://phabricator.wikimedia.org/T324166] * Wikisource users can now use the <bdi lang="zxx" dir="ltr"><code>prpbengalicurrency</code></bdi> label to denote Bengali currency characters as page numbers inside the <bdi lang="zxx" dir="ltr"><code><nowiki><pagelist></nowiki></code></bdi> tag. [https://phabricator.wikimedia.org/T268932] * Two preferences have been relocated. The preference "{{int:visualeditor-preference-visualeditor}}" is now shown on the [[Special:Preferences#mw-prefsection-editing|"{{int:prefs-editing}}" tab]] at all wikis. Previously it was shown on the "{{int:prefs-betafeatures}}" tab at some wikis. The preference "{{int:visualeditor-preference-newwikitexteditor-enable}}" is now also shown on the "{{int:prefs-editing}}" tab at all wikis, instead of the "{{int:prefs-betafeatures}}" tab. [https://phabricator.wikimedia.org/T335056][https://phabricator.wikimedia.org/T344158] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-30|en}}. It will be on all wikis from {{#time:j xg|2023-08-31|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] New signups for a Wikimedia developer account will start being pushed towards <bdi lang="en" dir="ltr">[https://idm.wikimedia.org/ idm.wikimedia.org]</bdi>, rather than going via Wikitech. [[wikitech:IDM|Further information about the new system is available]]. * All right-to-left language wikis, plus Korean, Armenian, Ukrainian, Russian, and Bulgarian Wikipedias, will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. This feature will come to more wikis in future weeks. [https://phabricator.wikimedia.org/T267921] '''Future changes''' * The removal of the [[mw:Special:MyLanguage/Extension:DoubleWiki|DoubleWiki extension]] is being discussed. This extension currently allows Wikisource users to view articles from multiple language versions side by side when the <bdi lang="zxx" dir="ltr"><code><=></code></bdi> symbol next to a specific language edition is selected. Comments on this are welcomed at [[phab:T344544|the phabricator task]]. * A proposal has been made to merge the second hidden-categories list (which appears below the wikitext editing form) with the main list of categories (which is further down the page). [[phab:T340606|More information is available on Phabricator]]; feedback is welcome! '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W35"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:00, 28 August 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25510866 --> == Tech News: 2023-36 == <section begin="technews-2023-W36"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/36|Translations]] are available. '''Recent changes''' * [[m:Wikisource_EditInSequence|EditInSequence]], a feature that allows users to edit pages faster on Wikisource has been moved to a Beta Feature based on community feedback. To enable it, you can navigate to the [[Special:Preferences#mw-prefsection-betafeatures|beta features tab in Preferences]]. [https://phabricator.wikimedia.org/T308098] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Generate Audio for IPA|Generate Audio for IPA]] and [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|Audio links that play on click]] wishlist proposals, the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline_audio_player_mode|inline audio player mode]] of [[mw:Extension:Phonos|Phonos]] has been deployed to all projects. [https://phabricator.wikimedia.org/T336763] * There is a new option for Administrators when they are changing the usergroups for a user, to add the user’s user page to their watchlist. This works both via [[{{#special:UserRights}}]] and via the API. [https://phabricator.wikimedia.org/T272294] * One new wiki has been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q34318|Talysh]] ([[w:tly:|<code>w:tly:</code>]]) [https://phabricator.wikimedia.org/T345166] '''Problems''' * The [[mw:Special:MyLanguage/Extension:LoginNotify|LoginNotify extension]] was not sending notifications since January. It has now been fixed, so going forward, you may see notifications for failed login attempts, and successful login attempts from a new device. [https://phabricator.wikimedia.org/T344785] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-06|en}}. It will be on all wikis from {{#time:j xg|2023-09-07|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-mhrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-miwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-minwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mtwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mwlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-myvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mznwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-napwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ndswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nds_nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-novwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nqowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nrmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nsowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ocwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-olowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-omwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-orwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-oswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pagwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-papwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pcdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pdcwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pflwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pihwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pnbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pntwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pswiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308137][https://phabricator.wikimedia.org/T308138] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W36"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:33, 4 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25566983 --> == Tech News: 2023-37 == <section begin="technews-2023-W37"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/37|Translations]] are available. '''Recent changes''' * [[mw:Special:MyLanguage/ORES|ORES]], the revision evaluation service, is now using a new open-source infrastructure on all wikis except for English Wikipedia and Wikidata. These two will follow this week. If you notice any unusual results from the Recent Changes filters that are related to ORES (for example, "{{int:ores-rcfilters-damaging-title}}" and "{{int:ores-rcfilters-goodfaith-title}}"), please [[mw:Talk:Machine Learning|report them]]. [https://phabricator.wikimedia.org/T342115] * When you are logged in on one Wikimedia wiki and visit a different Wikimedia wiki, the system tries to log you in there automatically. This has been unreliable for a long time. You can now visit the login page to make the system try extra hard. If you feel that made logging in better or worse than it used to be, your feedback is appreciated. [https://phabricator.wikimedia.org/T326281] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-13|en}}. It will be on all wikis from {{#time:j xg|2023-09-14|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/Technical decision making|Technical Decision-Making Forum Retrospective]] team invites anyone involved in the technical field of Wikimedia projects to signup to and join [[mw:Technical decision making/Listening Sessions|one of their listening sessions]] on 13 September. Another date will be scheduled later. The goal is to improve the technical decision-making processes. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Better diff handling of paragraph splits|Better diff handling of paragraph splits]] wishlist proposal, the inline switch widget in diff pages is being rolled out this week to all wikis. The inline switch will allow viewers to toggle between a unified inline or two-column diff wikitext format. [https://phabricator.wikimedia.org/T336716] '''Future changes''' * All wikis will be read-only for a few minutes on 20 September. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T345263] * The Enterprise API is launching a new feature called "[http://breakingnews-beta.enterprise.wikimedia.com/ breaking news]". Currently in BETA, this attempts to identify likely "newsworthy" topics as they are currently being written about in any Wikipedia. Your help is requested to improve the accuracy of its detection model, especially on smaller language editions, by recommending templates or identifiable editing patterns. See more information at [[mw:Special:MyLanguage/Wikimedia Enterprise/Breaking news|the documentation page]] on MediaWiki or [[m:Special:MyLanguage/Wikimedia Enterprise/FAQ#What is Breaking News|the FAQ]] on Meta. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W37"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:07, 11 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25589064 --> == Tech News: 2023-38 == <section begin="technews-2023-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/38|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki now has a [[mw:Stable interface policy/frontend|stable interface policy for frontend code]] that more clearly defines how we deprecate MediaWiki code and wiki-based code (e.g. gadgets and user scripts). Thank you to everyone who contributed to the content and discussions. [https://phabricator.wikimedia.org/T346467][https://phabricator.wikimedia.org/T344079] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-20|en}}. It will be on all wikis from {{#time:j xg|2023-09-21|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * All wikis will be read-only for a few minutes on September 20. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] [https://phabricator.wikimedia.org/T345263] * All wikis will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. [https://phabricator.wikimedia.org/T267921] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The team investigating the Graph Extension posted [[mw:Extension:Graph/Plans#Proposal|a proposal for reenabling it]] and they need your input. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W38"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:19, 18 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25623533 --> == Tech News: 2023-39 == <section begin="technews-2023-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/39|Translations]] are available. '''Recent changes''' * The Vector 2022 skin will now remember the pinned/unpinned status for the Table of Contents for all logged-out users. [https://phabricator.wikimedia.org/T316060] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-27|en}}. It will be on all wikis from {{#time:j xg|2023-09-28|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The ResourceLoader <bdi lang="zxx" dir="ltr"><code><nowiki>mediawiki.ui</nowiki></code></bdi> modules are now deprecated as part of the move to Vue.js and Codex. There is a [[mw:Codex/Migrating_from_MediaWiki_UI|guide for migrating from MediaWiki UI to Codex]] for any tools that use it. More [[phab:T346468|details are available in the task]] and your questions are welcome there. * Gadget definitions will have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new "namespaces" option]]. The option takes a list of namespace IDs. Gadgets that use this option will only load on pages in the given namespaces. '''Future changes''' * New variables will be added to [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]]: <code><bdi lang="zxx" dir="ltr">global_account_groups</bdi></code> and <code><bdi lang="zxx" dir="ltr">global_account_editcount</bdi></code>. They are available only when an account is being created. You can use them to prevent blocking automatic creation of accounts when users with many edits elsewhere visit your wiki for the first time. [https://phabricator.wikimedia.org/T345632][https://www.mediawiki.org/wiki/Special:MyLanguage/Extension:AbuseFilter/Rules_format] '''Meetings''' * You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1698426015 27 October at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia_Apps/Office_Hours#October_2023|details and how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W39"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:51, 26 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25655264 --> == Tech News: 2023-40 == <section begin="technews-2023-W40"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/40|Translations]] are available. '''Recent changes''' * There is a new [[Special:Preferences#mw-prefsection-rendering-advancedrendering|user preference]] for "{{int:tog-forcesafemode}}". This setting will make pages load without including any on-wiki JavaScript or on-wiki stylesheet pages. It can be useful for debugging broken JavaScript gadgets. [https://phabricator.wikimedia.org/T342347] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget definitions now have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new "<var>contentModels</var>" option]]. The option takes a list of page content models, like <code><bdi lang="zxx" dir="ltr">wikitext</bdi></code> or <code><bdi lang="zxx" dir="ltr">css</bdi></code>. Gadgets that use this option will only load on pages with the given content models. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.29|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-04|en}}. It will be on all wikis from {{#time:j xg|2023-10-05|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Vector 2022 skin will no longer use the custom styles and scripts of Vector legacy (2010). The change will be made later this year or in early 2024. See [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|how to adjust the CSS and JS pages on your wiki]]. [https://phabricator.wikimedia.org/T331679] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W40"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:26, 3 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25686930 --> == Tech News: 2023-41 == <section begin="technews-2023-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/41|Translations]] are available. '''Recent changes''' * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q33291|Fon]] ([[w:fon:|<code>w:fon:</code>]]) [https://phabricator.wikimedia.org/T347935] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.30|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-11|en}}. It will be on all wikis from {{#time:j xg|2023-10-12|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-swwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-warwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xalwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xmfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zeawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zh_min_nanwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zuwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308139] * At some wikis, newcomers are suggested images from Commons to add to articles without any images. Starting on Tuesday, newcomers at these wikis will be able to add images to unillustrated article sections. The specific wikis are listed under "Images recommendations" [[mw:Special:MyLanguage/Growth/Deployment table|at the Growth team deployment table]]. You can [[mw:Special:MyLanguage/Help:Growth/Tools/Add an image|learn more about this feature.]] [https://phabricator.wikimedia.org/T345940] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In the mobile web skin (Minerva) the CSS ID <bdi lang="zxx" dir="ltr"><code><nowiki>#page-actions</nowiki></code></bdi> will be replaced with <bdi lang="zxx" dir="ltr"><code><nowiki>#p-views</nowiki></code></bdi>. This change is to make it consistent with other skins and to improve support for gadgets and extensions in the mobile skin. A few gadgets may need to be updated; there are [https://phabricator.wikimedia.org/T348267 details and search-links in the task]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W41"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:39, 9 October 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25712895 --> == Tech News: 2023-42 == <section begin="technews-2023-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/42|Translations]] are available. '''Recent changes''' * The [[m:Special:MyLanguage/Help:Unified login|Unified login]] system's edge login should now be fixed for some browsers (Chrome, Edge, Opera). This means that if you visit a new sister project wiki, you should be logged in automatically without the need to click "Log in" or reload the page. Feedback on whether it's working for you is welcome. [https://phabricator.wikimedia.org/T347889] * [[mw:Special:MyLanguage/Manual:Interface/Edit_notice|Edit notices]] are now available within the MobileFrontend/Minerva skin. This feature was inspired by [[w:en:Wikipedia:EditNoticesOnMobile|the gadget on English Wikipedia]]. See more details in [[phab:T316178|T316178]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-18|en}}. It will be on all wikis from {{#time:j xg|2023-10-19|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * In 3 weeks, in the Vector 2022 skin, code related to <bdi lang="zxx" dir="ltr"><code><nowiki>addPortletLink</nowiki></code></bdi> and <bdi lang="zxx" dir="ltr"><code><nowiki>#p-namespaces</nowiki></code></bdi> that was deprecated one year ago will be removed. If you notice tools that should appear next to the "Discussion" tab are then missing, please tell the gadget's maintainers to see [[phab:T347907|instructions in the Phabricator task]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W42"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:47, 16 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25745824 --> == Tech News: 2023-43 == <section begin="technews-2023-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/43|Translations]] are available. '''Recent changes''' * There is a new [[mw:Special:MyLanguage/Wikimedia Language engineering/Newsletter/2023/October|Language and internationalization newsletter]], written quarterly. It contains updates on new feature development, improvements in various language-related technical projects, and related support work. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Source map support has been enabled on all wikis. When you open the debugger in your browser's developer tools, you should be able to see the unminified JavaScript source code. [https://phabricator.wikimedia.org/T47514] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-25|en}}. It will be on all wikis from {{#time:j xg|2023-10-26|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W43"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:16, 23 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25782286 --> == Tech News: 2023-44 == <section begin="technews-2023-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/44|Translations]] are available. '''Recent changes''' * The Structured Content team, as part of its project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]], made some UX improvements to the upload step of choosing own vs not own work ([[phab:T347590|T347590]]), as well as to the licensing step for own work ([[phab:T347756|T347756]]). * The Design Systems team has released version 1.0.0 of [[wmdoc:codex/latest/|Codex]], the new design system for Wikimedia. See the [[mw:Special:MyLanguage/Design_Systems_Team/Announcing_Codex_1.0|full announcement about the release of Codex 1.0.0]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-01|en}}. It will be on all wikis from {{#time:j xg|2023-11-02|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). * Listings on category pages are sorted on each wiki for that language using a [[:w:en:International Components for Unicode|library]]. For a brief period on 2 November, changes to categories will not be sorted correctly for many languages. This is because the developers are upgrading to a new version of the library. They will then use a script to fix the existing categories. This will take a few hours or a few days depending on how big the wiki is. You can [[mw:Special:MyLanguage/Wikimedia Technical Operations/ICU announcement|read more]]. [https://phabricator.wikimedia.org/T345561][https://phabricator.wikimedia.org/T267145] * Starting November 1, the impact module (Special:Impact) will be upgraded by the Growth team. The new impact module shows newcomers more data regarding their impact on the wiki. It was tested by a few wikis during the last few months. [https://phabricator.wikimedia.org/T336203] '''Future changes''' * There is [[mw:Special:MyLanguage/Extension:Graph/Plans#Roadmap|a proposed plan]] for re-enabling the Graph Extension. You can help by reviewing this proposal and [[mw:Extension_talk:Graph/Plans#c-PPelberg_(WMF)-20231020221600-Update:_20_October|sharing what you think about it]]. * The WMF is working on making it possible for administrators to [[mw:Special:MyLanguage/Community_configuration_2.0|edit MediaWiki configuration directly]]. This is similar to previous work on Special:EditGrowthConfig. [[phab:T349757|A technical RfC is running until November 08, where you can provide feedback.]] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W44"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:21, 30 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25801989 --> == Tech News: 2023-45 == <section begin="technews-2023-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/45|Translations]] are available. '''Recent changes''' * In the Vector 2022 skin, the default font-size of a number of navigational elements (tagline, tools menu, navigational links, and more) has been increased slightly to match the font size used in page content. [https://phabricator.wikimedia.org/T346062] '''Problems''' * Last week, there was a problem displaying some recent edits on [https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist a few wikis], for 1-6 hours. The edits were saved but not immediately shown. This was due to a database problem. [https://phabricator.wikimedia.org/T350443] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-08|en}}. It will be on all wikis from {{#time:j xg|2023-11-09|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). * The Growth team will reassign newcomers from former mentors to [[mw:Special:MyLanguage/Growth/Structured mentor list|the currently active mentors]]. They have also changed the notification language to be more user-friendly. [https://phabricator.wikimedia.org/T330071][https://phabricator.wikimedia.org/T327493] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W45"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:05, 6 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25838105 --> == Tech News: 2023-46 == <section begin="technews-2023-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/46|Translations]] are available. '''Recent changes''' * Four new wikis have been created: ** a Wikipedia in [[d:Q7598268|Moroccan Amazigh]] ([[w:zgh:|<code>w:zgh:</code>]]) [https://phabricator.wikimedia.org/T350216] ** a Wikipedia in [[d:Q35159|Dagaare]] ([[w:dga:|<code>w:dga:</code>]]) [https://phabricator.wikimedia.org/T350218] ** a Wikipedia in [[d:Q33017|Toba Batak]] ([[w:bbc:|<code>w:bbc:</code>]]) [https://phabricator.wikimedia.org/T350320] ** a Wikiquote in [[d:Q33151|Banjar]] ([[q:bjn:|<code>q:bjn:</code>]]) [https://phabricator.wikimedia.org/T350217] '''Problems''' * Last week, users who previously visited Meta-Wiki or Wikimedia Commons and then became logged out on those wikis could not log in again. The problem is now resolved. [https://phabricator.wikimedia.org/T350695] * Last week, some pop-up dialogs and menus were shown with the wrong font size. The problem is now resolved. [https://phabricator.wikimedia.org/T350544] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-15|en}}. It will be on all wikis from {{#time:j xg|2023-11-16|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). '''Future changes''' * Reference Previews are coming to many wikis as a default feature. They are popups for references, similar to the [[mw:Special:MyLanguage/Page Previews|PagePreviews feature]]. [[m:WMDE Technical Wishes/ReferencePreviews#Opt-out feature|You can opt out]] of seeing them. If you are [[Special:Preferences#mw-prefsection-gadgets|using the gadgets]] Reference Tooltips or Navigation Popups, you won’t see Reference Previews. [[phab:T282999|Deployment]] is planned for November 22, 2023. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Canary (also known as heartbeat) events will be produced into [https://stream.wikimedia.org/?doc#/streams Wikimedia event streams] from December 11. Streams users are advised to filter out these events, by discarding all events where <bdi lang="zxx" dir="ltr"><code><nowiki>meta.domain == "canary"</nowiki></code></bdi>. Updates to [[mw:Special:MyLanguage/Manual:Pywikibot|Pywikibot]] or [https://github.com/ChlodAlejandro/wikimedia-streams wikimedia-streams] will discard these events by default. [https://phabricator.wikimedia.org/T266798] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W46"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:52, 13 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25859263 --> == Tech News: 2023-47 == <section begin="technews-2023-W47"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/47|Translations]] are available. '''Changes later this week''' * There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-quwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_rupwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_tarawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ruewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rwwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-satwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-shwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-siwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-skwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-slwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-smwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-suwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-szlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tcywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tetwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-towiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tpiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ttwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-twwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tyvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-udmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ugwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-uzwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vecwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vepwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vlswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vowiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308141][https://phabricator.wikimedia.org/T308142][https://phabricator.wikimedia.org/T308143] * The Vector 2022 skin will have some minor visual changes to drop-down menus, column widths, and more. These changes were added to four Wikipedias last week. If no issues are found, these changes will proceed to all wikis this week. These changes will make it possible to add new menus for readability and dark mode. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Updates#November_2023:_Visual_changes,_more_deployments,_and_shifting_focus|Learn more]]. [https://phabricator.wikimedia.org/T347711] '''Future changes''' * There is [[mw:Extension talk:Graph/Plans#Update: 15 November|an update on re-enabling the Graph Extension]]. To speed up the process, Vega 2 will not be supported and only [https://phabricator.wikimedia.org/T335325 some protocols] will be available at launch. You can help by sharing what you think about the plan. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/47|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W47"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:55, 21 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25884616 --> == Tech News: 2023-48 == <section begin="technews-2023-W48"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/48|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-29|en}}. It will be on all wikis from {{#time:j xg|2023-11-30|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki's JavaScript system will now allow <bdi lang="zxx" dir="ltr"><code>async</code>/<code>await</code></bdi> syntax in gadgets and user scripts. Gadget authors should remember that users' browsers may not support it, so it should be used appropriately. [https://phabricator.wikimedia.org/T343499] * The deployment of "[[mw:Special:MyLanguage/Help:Growth/Tools/Add_a_link|Add a link]]" announced [[m:Special:MyLanguage/Tech/News/2023/47|last week]] was postponed. It will resume this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/48|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W48"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:08, 27 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25906379 --> == Tech News: 2023-49 == <section begin="technews-2023-W49"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/49|Translations]] are available. '''Recent changes''' * The spacing between paragraphs on Vector 2022 has been changed from 7px to 14px to match the size of the text. This will make it easier to distinguish paragraphs from sentences. [https://phabricator.wikimedia.org/T351754] * The "{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}" feature in VisualEditor is working again. You no longer need to switch to source editing to edit <bdi lang="zxx" dir="ltr"><code><nowiki>{{DEFAULTSORT:...}}</nowiki></code></bdi> keywords. [https://phabricator.wikimedia.org/T337398] '''Changes later this week''' * There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * On 6 December, people who have the enabled the preference for "{{int:Discussiontools-preference-visualenhancements}}" will notice the [[mw:Special:MyLanguage/Talk pages project/Usability|talk page usability improvements]] appear on pages that include the <bdi lang="zxx" dir="ltr"><code><nowiki>__NEWSECTIONLINK__</nowiki></code></bdi> magic word. If you notice any issues, please [[phab:T352232|share them with the team on Phabricator]]. '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge [[wikitech:News/Toolforge Grid Engine deprecation|Grid Engine shutdown process]] will start on December 14. Maintainers of [[toolforge:grid-deprecation|tools that still use this old system]] should plan to migrate to Kubernetes, or tell the team your plans on Phabricator in the task about your tool, before that date. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/VIWWQKMSQO2ED3TVUR7KPPWRTOBYBVOA/] * Communities using [[mw:Special:MyLanguage/Structured_Discussions|Structured Discussions]] are being contacted regarding [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|the upcoming deprecation of Structured Discussions]]. You can read more about this project, and share your comments, [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|on the project's page]]. '''Events''' * Registration & Scholarship applications are now open for the [[mw:Special:MyLanguage/Wikimedia Hackathon 2024|Wikimedia Hackathon 2024]] that will take place from 3–5 May in Tallinn, Estonia. Scholarship applications are open until 5 January 2024. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/49|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W49"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:50, 4 December 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25914435 --> == Tech News: 2023-50 == <section begin="technews-2023-W50"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/50|Translations]] are available. '''Recent changes''' * On Wikimedia Commons, there are some minor user-interface improvements for the "choosing own vs not own work" step in the UploadWizard. This is part of the Structured Content team's project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]]. [https://phabricator.wikimedia.org/T352707][https://phabricator.wikimedia.org/T352709] '''Problems''' * There was a problem showing the [[mw:Special:MyLanguage/Growth/Personalized first day/Newcomer homepage|Newcomer homepage]] feature with the "impact module" and their page-view graphs, for a few days in early December. This has now been fixed. [https://phabricator.wikimedia.org/T352352][https://phabricator.wikimedia.org/T352349] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-13|en}}. It will be on all wikis from {{#time:j xg|2023-12-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * [[File:Octicons-tools.svg|15px|link=]] The [https://wikimediafoundation.limesurvey.net/796964 2023 Developer Satisfaction Survey] is seeking the opinions of the Wikimedia developer community. Please take the survey if you have any role in developing software for the Wikimedia ecosystem. The survey is open until 5 January 2024, and has an associated [[foundation:Legal:December_2023_Developer_Satisfaction_Survey|privacy statement]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/50|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W50"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 02:12, 12 December 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25945501 --> == Tech News: 2023-51 == <section begin="technews-2023-W51"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/51|Translations]] are available. '''Tech News''' * The next issue of Tech News will be sent out on 8 January 2024 because of [[w:en:Christmas and holiday season|the holidays]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-20|en}}. It will be on all wikis from {{#time:j xg|2023-12-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting December 18, it won't be possible to activate Structured Discussions on a user's own talk page using the Beta feature. The Beta feature option remains available for users who want to deactivate Structured Discussions. This is part of [[mw:Structured Discussions/Deprecation|Structured Discussions' deprecation work]]. [https://phabricator.wikimedia.org/T248309] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There will be full support for redirects in the Module namespace. The "Move Page" feature will leave an appropriate redirect behind, and such redirects will be appropriately recognized by the software (e.g. hidden from [[{{#special:UnconnectedPages}}]]). There will also be support for [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Renaming or moving modules|manual redirects]]. [https://phabricator.wikimedia.org/T120794] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The MediaWiki JavaScript documentation is moving to a new format. During the move, you can read the old docs using [https://doc.wikimedia.org/mediawiki-core/REL1_41/js/ version 1.41]. Feedback about [https://doc.wikimedia.org/mediawiki-core/master/js/ the new site] is welcome on the [[mw:Talk:JSDoc_WMF_theme|project talk page]]. * The Wishathon is a new initiative that encourages collaboration across the Wikimedia community to develop solutions for wishes collected through the [[m:Special:MyLanguage/Community Wishlist Survey|Community Wishlist Survey]]. The first community Wishathon will take place from 15–17 March. If you are interested in a project proposal as a user, developer, designer, or product lead, you can [[m:Special:MyLanguage/Event:WishathonMarch2024|register for the event and read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/51|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W51"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:17, 18 December 2023 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25959059 --> == Tech News: 2024-02 == <section begin="technews-2024-W02"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/02|Translations]] are available. '''Recent changes''' * [https://mediawiki2latex.wmflabs.org/ mediawiki2latex] is a tool that converts wiki content into the formats of LaTeX, PDF, ODT, and EPUB. The code now runs many times faster due to recent improvements. There is also an optional Docker container you can [[b:de:Benutzer:Dirk_Hünniger/wb2pdf/install#Using_Docker|install]] on your local machine. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The way that Random pages are selected has been updated. This will slowly reduce the problem of some pages having a lower chance of appearing. [https://phabricator.wikimedia.org/T309477] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-10|en}}. It will be on all wikis from {{#time:j xg|2024-01-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/02|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W02"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:19, 9 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26026251 --> == Tech News: 2024-03 == <section begin="technews-2024-W03"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/03|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Pages that use the JSON [[mw:Special:MyLanguage/Manual:ContentHandler|contentmodel]] will now use tabs instead of spaces for auto-indentation. This will significantly reduce the page size. [https://phabricator.wikimedia.org/T326065] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] and personal user scripts may now use JavaScript syntax introduced in ES6 (also known as "ES2015") and ES7 ("ES2016"). MediaWiki validates the source code to protect other site functionality from syntax errors, and to ensure scripts are valid in all [[mw:Special:MyLanguage/Compatibility#Browsers|supported browsers]]. Previously, Gadgets could use the <bdi lang="zxx" dir="ltr"><code><nowiki>requiresES6</nowiki></code></bdi> option. This option is no longer needed and will be removed in the future. [https://phabricator.wikimedia.org/T75714] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Manual:Bot passwords|Bot passwords]] and [[mw:Special:MyLanguage/OAuth/Owner-only consumers|owner-only OAuth consumers]] can now be restricted to allow editing only specific pages. [https://phabricator.wikimedia.org/T349957] * You can now [[mw:Special:MyLanguage/Extension:Thanks|thank]] edits made by bots. [https://phabricator.wikimedia.org/T341388] * An update on the status of the Community Wishlist Survey for 2024 [[m:Special:MyLanguage/Community Wishlist Survey/Future Of The Wishlist/January 4, 2024 Update|has been published]]. Please read and give your feedback. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-17|en}}. It will be on all wikis from {{#time:j xg|2024-01-18|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting on January 17, it will not be possible to login to Wikimedia wikis from some specific old versions of the Chrome browser (versions 51–66, released between 2016 and 2018). Additionally, users of iOS 12, or Safari on Mac OS 10.14, may need to login to each wiki separately. [https://phabricator.wikimedia.org/T344791] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> module was deprecated and replaced with the <bdi lang="zxx" dir="ltr"><code>mediawiki.cookie</code></bdi> module last year. A script has now been run to replace any remaining uses, and this week the temporary alias will be removed. [https://phabricator.wikimedia.org/T354966] '''Future changes''' * Wikimedia Deutschland is working to [[m:WMDE Technical Wishes/Reusing references|make reusing references easier]]. They are looking for people who are interested in participating in [https://wikimedia.sslsurvey.de/User-research-into-Reusing-References-Sign-up-Form-2024/en/ individual video calls for user research in January and February]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/03|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W03"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:13, 16 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26074460 --> == Tech News: 2024-04 == <section begin="technews-2024-W04"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/04|Translations]] are available. '''Problems''' * A bug in UploadWizard prevented linking to the userpage of the uploader when uploading. It has now been fixed. [https://phabricator.wikimedia.org/T354529] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-24|en}}. It will be on all wikis from {{#time:j xg|2024-01-25|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/04|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W04"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:03, 23 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26096197 --> == Tech News: 2024-05 == <section begin="technews-2024-W05"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/05|Translations]] are available. '''Recent changes''' * Starting Monday January 29, all talk pages messages' timestamps will become a link. This link is a permanent link to the comment. It allows users to find the comment they are looking for, even if this comment was moved elsewhere. This will affect all wikis except for the English Wikipedia. You can read more about this change [https://diff.wikimedia.org/2024/01/29/talk-page-permalinks-dont-lose-your-threads/ on Diff] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk_pages_permalinking|on Mediawiki.org]].<!-- The Diff post will be published on Monday morning UTC--> [https://phabricator.wikimedia.org/T302011] * There are some improvements to the CAPTCHA to make it harder for spam bots and scripts to bypass it. If you have feedback on this change, please comment on [[phab:T141490|the task]]. Staff are monitoring metrics related to the CAPTCHA, as well as secondary metrics such as account creations and edit counts. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-31|en}}. It will be on all wikis from {{#time:j xg|2024-02-01|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] On February 1, a link will be added to the "Tools" menu to download a [[w:en:QR code|QR code]] that links to the page you are viewing. There will also be a new [[{{#special:QrCode}}]] page to create QR codes for any Wikimedia URL. This addresses the [[m:Community Wishlist Survey 2023/Mobile and apps/Add ability to share QR code for a page in any Wikimedia project|#19 most-voted wish]] from the [[m:Community Wishlist Survey 2023/Results|2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T329973] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] which only work in some skins have sometimes used the <bdi lang="zxx" dir="ltr"><code>targets</code></bdi> option to limit where you can use them. This will stop working this week. You should use the <bdi lang="zxx" dir="ltr"><code>skins</code></bdi> option instead. [https://phabricator.wikimedia.org/T328497] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/05|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W05"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:31, 29 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26137870 --> == Tech News: 2024-06 == <section begin="technews-2024-W06"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/06|Translations]] are available. '''Recent changes''' *The mobile site history pages now use the same HTML as the desktop history pages. If you hear of any problems relating to mobile history usage please point them to [[phab:T353388|the phabricator task]]. *On most wikis, admins can now block users from making specific actions. These actions are: uploading files, creating new pages, moving (renaming) pages, and sending thanks. The goal of this feature is to allow admins to apply blocks that are adequate to the blocked users' activity. [[m:Special:MyLanguage/Community health initiative/Partial blocks#action-blocks|Learn more about "action blocks"]]. [https://phabricator.wikimedia.org/T242541][https://phabricator.wikimedia.org/T280531] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-07|en}}. It will be on all wikis from {{#time:j xg|2024-02-08|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Talk pages permalinks that included diacritics and non-Latin script were malfunctioning. This issue is fixed. [https://phabricator.wikimedia.org/T356199] '''Future changes''' * [[m:WMDE Technical Wishes/ReferencePreviews#24WPs|24 Wikipedias]] with [[mw:Special:MyLanguage/Reference_Tooltips|Reference Tooltips]] as a default gadget are encouraged to remove that default flag. This would make [[mw:Special:MyLanguage/Help:Reference_Previews|Reference Previews]] the new default for reference popups, leading to a more consistent experience across wikis. For [[m:WMDE Technical Wishes/ReferencePreviews#46WPs|46 Wikipedias]] with less than 4 interface admins, the change is already scheduled for mid-February, [[m:Talk:WMDE Technical Wishes/ReferencePreviews#Reference Previews to become the default for previewing references on more wikis.|unless there are concerns]]. The older Reference Tooltips gadget will still remain usable and will override this feature, if it is available on your wiki and you have enabled it in your settings. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/ReferencePreviews#Reference_Previews_to_become_the_default_for_previewing_references_on_more_wikis][https://phabricator.wikimedia.org/T355312] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/06|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W06"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:22, 5 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26180971 --> == Tech News: 2024-07 == <section begin="technews-2024-W07"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/07|Translations]] are available. '''Recent changes''' * The [[d:Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split experiment]] is working and loaded onto 3 test servers. The team in charge is testing the split's impact and requires feedback from WDQS users through the UI or programmatically in different channels. [https://www.wikidata.org/wiki/Wikidata_talk:SPARQL_query_service/WDQS_graph_split][https://phabricator.wikimedia.org/T356773][https://www.wikidata.org/wiki/User:Sannita_(WMF)] Users' feedback will validate the impact of various use cases and workflows around the Wikidata Query service. [https://www.wikidata.org/wiki/Wikidata:SPARQL_query_service/WDQS_backend_update/October_2023_scaling_update][https://www.mediawiki.org/wiki/Wikidata_Query_Service/User_Manual#Federation] '''Problems''' *There was a bug that affected the appearance of visited links when using mobile device to access wiki sites. It made the links appear black; [[phab:T356928|this issue]] is fixed. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-14|en}}. It will be on all wikis from {{#time:j xg|2024-02-15|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] As work continues on the grid engine deprecation,[https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation] tools on the grid engine will be stopped starting on February 14th, 2024. If you have tools actively migrating you can ask for an extension so they are not stopped. [https://wikitech.wikimedia.org/wiki/Portal:Toolforge/About_Toolforge#Communication_and_support] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/07|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W07"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 05:48, 13 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26223994 --> == Tech News: 2024-08 == <section begin="technews-2024-W08"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/08|Translations]] are available. '''Recent changes''' * If you have the "{{int:Tog-enotifwatchlistpages}}" option enabled, edits by bot accounts no longer trigger notification emails. Previously, only minor edits would not trigger the notification emails. [https://phabricator.wikimedia.org/T356984] * There are changes to how user and site scripts load for [[mw:Special:MyLanguage/Skin:Vector/2022| Vector 2022]] on specific wikis. The changes impacted the following Wikis: all projects with [[mw:Special:MyLanguage/Skin:Vector|Vector legacy]] as the default skin, Wikivoyage, and Wikibooks. Other wikis will be affected over the course of the next three months. Gadgets are not impacted. If you have been affected or want to minimize the impact on your project, see [[Phab:T357580| this ticket]]. Please coordinate and take action proactively. *Newly auto-created accounts (the accounts you get when you visit a new wiki) now have the same local notification preferences as users who freshly register on that wiki. It is effected in four notification types listed in the [[phab:T353225|task's description]]. *The maximum file size when using [[c:Special:MyLanguage/Commons:Upload_Wizard|Upload Wizard]] is now 5 GiB. [https://phabricator.wikimedia.org/T191804] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-21|en}}. It will be on all wikis from {{#time:j xg|2024-02-22|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Selected tools on the grid engine have been [[wikitech:News/Toolforge_Grid_Engine_deprecation|stopped]] as we prepare to shut down the grid on March 14th, 2024. The tool's code and data have not been deleted. If you are a maintainer and you want your tool re-enabled reach out to the [[wikitech:Portal:Toolforge/About_Toolforge#Communication_and_support|team]]. Only tools that have asked for extension are still running on the grid. * The CSS <bdi lang="zxx" dir="ltr"><code>[https://developer.mozilla.org/en-US/docs/Web/CSS/filter filter]</code></bdi> property can now be used in HTML <bdi lang="zxx" dir="ltr"><code>style</code></bdi> attributes in wikitext. [https://phabricator.wikimedia.org/T308160] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W08"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 15:36, 19 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26254282 --> == Tech News: 2024-09 == <section begin="technews-2024-W09"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/09|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/VisualEditor_on_mobile|mobile visual editor]] is now the default editor for users who never edited before, at a small group of wikis. [[mw:Special:MyLanguage/VisualEditor_on_mobile/VE_mobile_default#A/B_test_results| Research ]] shows that users using this editor are slightly more successful publishing the edits they started, and slightly less successful publishing non-reverted edits. Users who defined the wikitext editor as their default on desktop will get the wikitext editor on mobile for their first edit on mobile as well. [https://phabricator.wikimedia.org/T352127] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/ResourceLoader/Core modules#mw.config|mw.config]] value <code>wgGlobalGroups</code> now only contains groups that are active in the wiki. Scripts no longer have to check whether the group is active on the wiki via an API request. A code example of the above is: <bdi lang="zxx" dir="ltr"><code>if (/globalgroupname/.test(mw.config.get("wgGlobalGroups")))</code></bdi>. [https://phabricator.wikimedia.org/T356008] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-28|en}}. It will be on all wikis from {{#time:j xg|2024-02-29|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * The right to change [[mw:Special:MyLanguage/Manual:Tags|edit tags]] (<bdi lang="zxx" dir="ltr"><code>changetags</code></bdi>) will be removed from users in Wikimedia sites, keeping it by default for admins and bots only. Your community can ask to retain the old configuration on your wiki before this change happens. Please indicate in [[phab:T355639|this ticket]] to keep it for your community before the end of March 2024. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W09"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:23, 26 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26294125 --> == Tech News: 2024-10 == <section begin="technews-2024-W10"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/10|Translations]] are available. '''Recent changes''' * The <bdi lang="zxx" dir="ltr"><code>Special:Book</code></bdi> page (as well as the associated "Create a book" functionality) provided by the old [[mw:Special:MyLanguage/Extension:Collection|Collection extension]] has been removed from all Wikisource wikis, as it was broken. This does not affect the ability to download normal books, which is provided by the [[mw:Special:MyLanguage/Extension:Wikisource|Wikisource extension]]. [https://phabricator.wikimedia.org/T358437] * [[m:Wikitech|Wikitech]] now uses the next-generation [[mw:Special:MyLanguage/Parsoid|Parsoid]] wikitext parser by default to generate all pages in the Talk namespace. Report any problems on the [[mw:Talk:Parsoid/Parser_Unification/Known_Issues|Known Issues discussion page]]. You can use the [[mw:Special:MyLanguage/Extension:ParserMigration|ParserMigration]] extension to control the use of Parsoid; see the [[mw:Special:MyLanguage/Help:Extension:ParserMigration|ParserMigration help documentation]] for more details. * Maintenance on [https://etherpad.wikimedia.org etherpad] is completed. If you encounter any issues, please indicate in [[phab:T316421|this ticket]]. * [[File:Octicons-tools.svg|12px|link=|alt=| Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] allow interface admins to create custom features with CSS and JavaScript. The <bdi lang="zxx" dir="ltr"><code>Gadget</code></bdi> and <bdi lang="zxx" dir="ltr"><code>Gadget_definition</code></bdi> namespaces and <bdi lang="zxx" dir="ltr"><code>gadgets-definition-edit</code></bdi> user right were reserved for an experiment in 2015, but were never used. These were visible on Special:Search and Special:ListGroupRights. The unused namespaces and user rights are now removed. No pages are moved, and no changes need to be made. [https://phabricator.wikimedia.org/T31272] * A usability improvement to the "Add a citation" in Wikipedia workflow has been made, the insert button was moved to the popup header. [https://phabricator.wikimedia.org/T354847] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-06|en}}. It will be on all wikis from {{#time:j xg|2024-03-07|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233] * The HTML markup of headings and section edit links will be changed later this year to improve accessibility. See [[mw:Special:MyLanguage/Heading_HTML_changes|Heading HTML changes]] for details. The new markup will be the same as in the new Parsoid wikitext parser. You can test your gadget or stylesheet with the new markup if you add <bdi lang="zxx" dir="ltr"><code>?useparsoid=1</code></bdi> to your URL ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Selecting_a_parser_using_a_URL_query_string|more info]]) or turn on Parsoid read views in your user options ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Enabling_via_user_preference|more info]]). * '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/10|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W10"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:47, 4 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26329807 --> == Tech News: 2024-11 == <section begin="technews-2024-W11"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/11|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-13|en}}. It will be on all wikis from {{#time:j xg|2024-03-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * After consulting with various communities, the line height of the text on the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] will be increased to its previous value of 1.65. Different options for typography can also be set using the options in the menu, as needed. [https://phabricator.wikimedia.org/T358498] *The active link color in [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva]] will be changed to provide more consistency with our other platforms and best practices. [https://phabricator.wikimedia.org/T358516] * [[c:Special:MyLanguage/Commons:Structured data|Structured data on Commons]] will no longer ask whether you want to leave the page without saving. This will prevent the “information you’ve entered may not be saved” popups from appearing when no information have been entered. It will also make file pages on Commons load faster in certain cases. However, the popups will be hidden even if information has indeed been entered. If you accidentally close the page before saving the structured data you entered, that data will be lost. [https://phabricator.wikimedia.org/T312315] '''Future changes''' * All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/11|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W11"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:04, 11 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26374013 --> == Tech News: 2024-12 == <section begin="technews-2024-W12"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/12|Translations]] are available. '''Recent changes''' * The notice "Language links are at the top of the page" that appears in the [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]] main menu has been removed now that users have learned the new location of the Language switcher. [https://phabricator.wikimedia.org/T353619] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/IP_Editing:_Privacy_Enhancement_and_Abuse_Mitigation/IP_Info_feature|IP info feature]] displays data from Spur, an IP addresses database. Previously, the only data source for this feature was MaxMind. Now, IP info is more useful for patrollers. [https://phabricator.wikimedia.org/T341395] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge Grid Engine services have been shut down after the final migration process from Grid Engine to Kubernetes. [https://wikitech.wikimedia.org/wiki/Obsolete:Toolforge/Grid][https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation][https://techblog.wikimedia.org/2022/03/14/toolforge-and-grid-engine/] * Communities can now customize the default reasons for undeleting a page by creating [[MediaWiki:Undelete-comment-dropdown]]. [https://phabricator.wikimedia.org/T326746] '''Problems''' * [[m:Special:MyLanguage/WMDE_Technical_Wishes/RevisionSlider|RevisionSlider]] is an interface to interactively browse a page's history. Users in [[mw:Special:MyLanguage/Extension:RevisionSlider/Developing_a_RTL-accessible_feature_in_MediaWiki_-_what_we%27ve_learned_while_creating_the_RevisionSlider|right-to-left]] languages reported RevisionSlider reacting wrong to mouse clicks. This should be fixed now. [https://phabricator.wikimedia.org/T352169] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-20|en}}. It will be on all wikis from {{#time:j xg|2024-03-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * All wikis will be read-only for a few minutes on March 20. This is planned at [https://zonestamp.toolforge.org/1710943200 14:00 UTC]. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/12|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W12"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 17:39, 18 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26410165 --> == Tech News: 2024-13 == <section begin="technews-2024-W13"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/13|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] An update was made on March 18th 2024 to how various projects load site, user JavaScript and CSS in [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]]. A [[phab:T360384|checklist]] is provided for site admins to follow. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-27|en}}. It will be on all wikis from {{#time:j xg|2024-03-28|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W13"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 18:56, 25 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26446209 --> == Tech News: 2024-14 == <section begin="technews-2024-W14"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/14|Translations]] are available. '''Recent changes''' * Users of the [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading|reading accessibility]] beta feature will notice that the default line height for the standard and large text options has changed. [https://phabricator.wikimedia.org/T359030] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-03|en}}. It will be on all wikis from {{#time:j xg|2024-04-04|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * The Wikimedia Foundation has an annual plan. The annual plan decides what the Wikimedia Foundation will work on. You can now read [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product & Technology OKRs#Draft Key Results|the draft key results]] for the Product and Technology department. They are suggestions for what results the Foundation wants from big technical changes from July 2024 to June 2025. You can [[m:Talk:Wikimedia Foundation Annual Plan/2024-2025/Product & Technology OKRs|comment on the talk page]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W14"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 03:36, 2 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26462933 --> == Tech News: 2024-15 == <section begin="technews-2024-W15"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/15|Translations]] are available. '''Recent changes''' * Web browsers can use tools called [[:w:en:Browser extension|extensions]]. There is now a Chrome extension called [[m:Future Audiences/Experiment:Citation Needed|Citation Needed]] which you can use to see if an online statement is supported by a Wikipedia article. This is a small experiment to see if Wikipedia can be used this way. Because it is a small experiment, it can only be used in Chrome in English. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A new [[mw:Special:MyLanguage/Help:Edit Recovery|Edit Recovery]] feature has been added to all wikis, available as a [[Special:Preferences#mw-prefsection-editing|user preference]]. Once you enable it, your in-progress edits will be stored in your web browser, and if you accidentally close an editing window or your browser or computer crashes, you will be prompted to recover the unpublished text. Please leave any feedback on the [[m:Special:MyLanguage/Talk:Community Wishlist Survey 2023/Edit-recovery feature|project talk page]]. This was the #8 wish in the 2023 Community Wishlist Survey. * Initial results of [[mw:Special:MyLanguage/Edit check|Edit check]] experiments [[mw:Special:MyLanguage/Edit_check#4_April_2024|have been published]]. Edit Check is now deployed as a default feature at [[phab:T342930#9538364|the wikis that tested it]]. [[mw:Talk:Edit check|Let us know]] if you want your wiki to be part of the next deployment of Edit check. [https://phabricator.wikimedia.org/T342930][https://phabricator.wikimedia.org/T361727] * Readers using the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] on mobile will notice there has been an improvement in the line height across all typography settings. [https://phabricator.wikimedia.org/T359029] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-10|en}}. It will be on all wikis from {{#time:j xg|2024-04-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * New accounts and logged-out users will get the [[mw:Special:MyLanguage/VisualEditor|visual editor]] as their default editor on mobile. This deployment is made at all wikis except for the English Wikipedia. [https://phabricator.wikimedia.org/T361134] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/15|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W15"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:37, 8 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26564838 --> == Tech News: 2024-16 == <section begin="technews-2024-W16"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/16|Translations]] are available. '''Problems''' * Between 2 April and 8 April, on wikis using [[mw:Special:MyLanguage/Extension:FlaggedRevs|Flagged Revisions]], the "{{Int:tag-mw-reverted}}" tag was not applied to undone edits. In addition, page moves, protections and imports were not autoreviewed. This problem is now fixed. [https://phabricator.wikimedia.org/T361918][https://phabricator.wikimedia.org/T361940] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-17|en}}. It will be on all wikis from {{#time:j xg|2024-04-18|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[mw:Special:MyLanguage/Help:Magic words#DEFAULTSORT|Default category sort keys]] will now affect categories added by templates placed in [[mw:Special:MyLanguage/Help:Cite|footnotes]]. Previously footnotes used the page title as the default sort key even if a different default sort key was specified (category-specific sort keys already worked). [https://phabricator.wikimedia.org/T40435] * A new variable <bdi lang="zxx" dir="ltr"><code>page_last_edit_age</code></bdi> will be added to [[Special:AbuseFilter|abuse filters]]. It tells how many seconds ago the last edit to a page was made. [https://phabricator.wikimedia.org/T269769] '''Future changes''' * Volunteer developers are kindly asked to update the code of their tools and features to handle [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]]. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Four database fields will be removed from database replicas (including [[quarry:|Quarry]]). This affects only the <bdi lang="zxx" dir="ltr"><code>abuse_filter</code></bdi> and <bdi lang="zxx" dir="ltr"><code>abuse_filter_history</code></bdi> tables. Some queries might need to be updated. [https://phabricator.wikimedia.org/T361996] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W16"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:29, 15 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26564838 --> == Tech News: 2024-17 == <section begin="technews-2024-W17"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/17|Translations]] are available. '''Recent changes''' * Starting this week, newcomers editing Wikipedia [[mw:Special:MyLanguage/Growth/Positive reinforcement#Leveling up 3|will be encouraged]] to try structured tasks. [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer tasks|Structured tasks]] have been shown to [[mw:Special:MyLanguage/Growth/Personalized first day/Structured tasks/Add a link/Experiment analysis, December 2021|improve newcomer activation and retention]]. [https://phabricator.wikimedia.org/T348086] * You can [[m:Special:MyLanguage/Coolest Tool Award|nominate your favorite tools]] for the fifth edition of the Coolest Tool Award. Nominations will be open until May 10. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-24|en}}. It will be on all wikis from {{#time:j xg|2024-04-25|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * This is the last warning that by the end of May 2024 the Vector 2022 skin will no longer share site and user scripts/styles with old Vector. For user-scripts that you want to keep using on Vector 2022, copy the contents of [[{{#special:MyPage}}/vector.js]] to [[{{#special:MyPage}}/vector-2022.js]]. There are [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|more technical details]] available. Interface administrators who foresee this leading to lots of technical support questions may wish to send a mass message to your community, as was done on French Wikipedia. [https://phabricator.wikimedia.org/T362701] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W17"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:28, 22 April 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26647188 --> == Tech News: 2024-18 == <section begin="technews-2024-W18"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/18|Translations]] are available. '''Recent changes''' [[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]] * The appearance of talk pages changed for the following wikis: {{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-viwiki/en}}. These wikis participated to a test, where 50% of users got the new design, for one year. As this test [[Mw:Special:MyLanguage/Talk pages project/Usability/Analysis|gave positive results]], the new design is deployed on these wikis as the default design. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] ("{{int:discussiontools-preference-visualenhancements}}"). The deployment will happen at all wikis in the coming weeks. [https://phabricator.wikimedia.org/T341491] * Seven new wikis have been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q33014|Betawi]] ([[w:bew:|<code>w:bew:</code>]]) [https://phabricator.wikimedia.org/T357866] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35708|Kusaal]] ([[w:kus:|<code>w:kus:</code>]]) [https://phabricator.wikimedia.org/T359757] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35513|Igala]] ([[w:igl:|<code>w:igl:</code>]]) [https://phabricator.wikimedia.org/T361644] ** a {{int:project-localized-name-group-wiktionary}} in [[d:Q33541|Karakalpak]] ([[wikt:kaa:|<code>wikt:kaa:</code>]]) [https://phabricator.wikimedia.org/T362135] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q9228|Burmese]] ([[s:my:|<code>s:my:</code>]]) [https://phabricator.wikimedia.org/T361085] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q9237|Malay]] ([[s:ms:|<code>s:ms:</code>]]) [https://phabricator.wikimedia.org/T363039] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q8108|Georgian]] ([[s:ka:|<code>s:ka:</code>]]) [https://phabricator.wikimedia.org/T363085] * You can now [https://translatewiki.net/wiki/Support#Early_access:_Watch_Message_Groups_on_Translatewiki.net watch message groups/projects] on [[m:Special:MyLanguage/translatewiki.net|Translatewiki.net]]. Initially, this feature will notify you of added or deleted messages in these groups. [https://phabricator.wikimedia.org/T348501] * Dark mode is now available on all wikis, on mobile web for logged-in users who opt into the [[Special:MobileOptions|advanced mode]]. This is the early release of the feature. Technical editors are invited to [https://night-mode-checker.wmcloud.org/ check for accessibility issues on wikis]. See [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-04|more detailed guidelines]]. '''Problems''' * [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps can use an alternative visual style without labels, by using <bdi lang="zxx" dir="ltr"><code><nowiki>mapstyle="osm"</nowiki></code></bdi>. This wasn't working in previews, creating the wrong impression that it wasn't supported. This has now been fixed. [https://phabricator.wikimedia.org/T362531] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-01|en}}. It will be on all wikis from {{#time:j xg|2024-05-02|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W18"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 03:33, 30 April 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26689057 --> == Tech News: 2024-19 == <section begin="technews-2024-W19"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/19|Translations]] are available. '''Recent changes''' [[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]] * The appearance of talk pages changed for all wikis, except for Commons, Wikidata and most Wikipedias ([[m:Special:MyLanguage/Tech/News/2024/18|a few]] have already received this design change). You can read the detail of the changes [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|on ''Diff'']]. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] ("{{int:discussiontools-preference-visualenhancements}}"). The deployment will happen at remaining wikis in the coming weeks. [https://phabricator.wikimedia.org/T352087][https://phabricator.wikimedia.org/T319146] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Interface admins now have greater control over the styling of article components on mobile with the introduction of the <code>SiteAdminHelper</code>. More information on how styles can be disabled can be found [[mw:Special:MyLanguage/Extension:WikimediaMessages#Site_admin_helper|at the extension's page]]. [https://phabricator.wikimedia.org/T363932] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] has added article body sections in JSON format and a curated short description field to the existing parsed Infobox. This expansion to the API is also available via Wikimedia Cloud Services. [https://enterprise.wikimedia.com/blog/article-sections-and-description/] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-08|en}}. It will be on all wikis from {{#time:j xg|2024-05-09|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * When you look at the Special:Log page, the first view is labelled "All public logs", but it only shows some logs. This label will now say "Main public logs". [https://phabricator.wikimedia.org/T237729] '''Future changes''' * A new service will be built to replace [[mw:Special:MyLanguage/Extension:Graph|Extension:Graph]]. Details can be found in [[mw:Special:MyLanguage/Extension:Graph/Plans|the latest update]] regarding this extension. * Starting May 21, English Wikipedia and German Wikipedia will get the possibility to activate "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]". This is part of the [[phab:T304110|progressive deployment of this tool to all Wikipedias]]. These communities can [[mw:Special:MyLanguage/Growth/Community configuration|activate and configure the feature locally]]. [https://phabricator.wikimedia.org/T308144] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W19"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:44, 6 May 2024 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26729363 --> == Tech News: 2024-20 == <section begin="technews-2024-W20"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/20|Translations]] are available. '''Recent changes''' * On Wikisource there is a special page listing pages of works without corresponding scan images. Now you can use the new magic word <bdi lang="zxx" dir="ltr"><code>__EXPECTWITHOUTSCANS__</code></bdi> to exclude certain pages (list of editions or translations of works) from that list. [https://phabricator.wikimedia.org/T344214] * If you use the [[Special:Preferences#mw-prefsection-editing|user-preference]] "{{int:tog-uselivepreview}}", then the template-page feature "{{int:Templatesandbox-editform-legend}}" will now also work without reloading the page. [https://phabricator.wikimedia.org/T136907] * [[mw:Special:Mylanguage/Extension:Kartographer|Kartographer]] maps can now specify an alternative text via the <bdi lang="zxx" dir="ltr"><code><nowiki>alt=</nowiki></code></bdi> attribute. This is identical in usage to the <bdi lang="zxx" dir="ltr"><code><nowiki>alt=</nowiki></code></bdi> attribute in the [[mw:Special:MyLanguage/Help:Images#Syntax|image and gallery syntax]]. An exception for this feature is wikis like Wikivoyage where the miniature maps are interactive. [https://phabricator.wikimedia.org/T328137] * The old [[mw:Special:MyLanguage/Extension:GuidedTour|Guided Tour]] for the "[[mw:Special:MyLanguage/Edit Review Improvements/New filters for edit review|New Filters for Edit Review]]" feature has been removed. It was created in 2017 to show people with older accounts how the interface had changed, and has now been seen by most of the intended people. [https://phabricator.wikimedia.org/T217451] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-15|en}}. It will be on all wikis from {{#time:j xg|2024-05-16|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[{{#special:search}}]] results page will now use CSS flex attributes, for better accessibility, instead of a table. If you have a gadget or script that adjusts search results, you should update your script to the new HTML structure. [https://phabricator.wikimedia.org/T320295] '''Future changes''' * In the Vector 2022 skin, main pages will be displayed at full width (like special pages). The goal is to keep the number of characters per line large enough. This is related to the coming changes to typography in Vector 2022. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates|Learn more]]. [https://phabricator.wikimedia.org/T357706] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Two columns of the <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Manual:pagelinks table|pagelinks]]</code></bdi> database table (<bdi lang="zxx" dir="ltr"><code>pl_namespace</code></bdi> and <bdi lang="zxx" dir="ltr"><code>pl_title</code></bdi>) are being dropped soon. Users must use two columns of the new <bdi lang="zxx" dir="ltr"><code>[[mw:special:MyLanguage/Manual:linktarget table|linktarget]]</code></bdi> table instead (<bdi lang="zxx" dir="ltr"><code>lt_namespace</code></bdi> and <bdi lang="zxx" dir="ltr"><code>lt_title</code></bdi>). In your existing SQL queries: *# Replace <bdi lang="zxx" dir="ltr"><code>JOIN pagelinks</code></bdi> with <bdi lang="zxx" dir="ltr"><code>JOIN linktarget</code></bdi> and <bdi lang="zxx" dir="ltr"><code>pl_</code></bdi> with <bdi lang="zxx" dir="ltr"><code>lt_</code></bdi> in the <bdi lang="zxx" dir="ltr"><code>ON</code></bdi> statement *# Below that add <bdi lang="zxx" dir="ltr"><code>JOIN pagelinks ON lt_id = pl_target_id</code></bdi> ** See <bdi lang="en" dir="ltr">[[phab:T222224]]</bdi> for technical reasoning. [https://phabricator.wikimedia.org/T222224][https://phabricator.wikimedia.org/T299947] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W20"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:58, 13 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26762074 --> == Tech News: 2024-21 == <section begin="technews-2024-W21"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/21|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Extension:Nuke|Nuke]] feature, which enables administrators to mass delete pages, will now correctly delete pages which were moved to another title. [https://phabricator.wikimedia.org/T43351] * New changes have been made to the UploadWizard in Wikimedia Commons: the overall layout has been improved, by following new styling and spacing for the form and its fields; the headers and helper text for each of the fields was changed; the Caption field is now a required field, and there is an option for users to copy their caption into the media description. [https://commons.wikimedia.org/wiki/Commons:WMF_support_for_Commons/Upload_Wizard_Improvements#Changes_to_%22Describe%22_workflow][https://phabricator.wikimedia.org/T361049] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-22|en}}. It will be on all wikis from {{#time:j xg|2024-05-23|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML used to render all headings [[mw:Heading_HTML_changes|is being changed to improve accessibility]]. It will change on 22 May in some skins (Timeless, Modern, CologneBlue, Nostalgia, and Monobook). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in all other skins. The developers are also considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W21"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:04, 20 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26786311 --> == Tech News: 2024-22 == <section begin="technews-2024-W22"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/22|Translations]] are available. '''Recent changes''' * Several bugs related to the latest updates to the UploadWizard on Wikimedia Commons have been fixed. For more information, see [[:phab:T365107|T365107]] and [[:phab:T365119|T365119]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In March 2024 a new [[mw:ResourceLoader/Core_modules#addPortlet|addPortlet]] API was added to allow gadgets to create new portlets (menus) in the skin. In certain skins this can be used to create dropdowns. Gadget developers are invited to try it and [[phab:T361661|give feedback]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Some CSS in the Minerva skin has been removed to enable easier community configuration. Interface editors should check the rendering on mobile devices for aspects related to the classes: <bdi lang="zxx" dir="ltr"><code>.collapsible</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.multicol</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.reflist</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.coordinates</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.topicon</code></bdi>. [[phab:T361659|Further details are available on replacement CSS]] if it is needed. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-29|en}}. It will be on all wikis from {{#time:j xg|2024-05-30|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * When you visit a wiki where you don't yet have a local account, local rules such as edit filters can sometimes prevent your account from being created. Starting this week, MediaWiki takes your global rights into account when evaluating whether you can override such local rules. [https://phabricator.wikimedia.org/T316303] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W22"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:15, 28 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26832205 --> == Tech News: 2024-23 == <section begin="technews-2024-W23"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/23|Translations]] are available. '''Recent changes''' * It is now possible for local administrators to add new links to the bottom of the site Tools menu without JavaScript. [[mw:Manual:Interface/Sidebar#Add or remove toolbox sections|Documentation is available]]. [https://phabricator.wikimedia.org/T6086] * The message name for the definition of the tracking category of WikiHiero has changed from "<bdi lang="zxx" dir="ltr"><code>MediaWiki:Wikhiero-usage-tracking-category</code></bdi>" to "<bdi lang="zxx" dir="ltr"><code>MediaWiki:Wikihiero-usage-tracking-category</code></bdi>". [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/wikihiero/+/1035855] * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q5317225|Kadazandusun]] ([[w:dtp:|<code>w:dtp:</code>]]) [https://phabricator.wikimedia.org/T365220] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-05|en}}. It will be on all wikis from {{#time:j xg|2024-06-06|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * Next week, on wikis with the Vector 2022 skin as the default, logged-out desktop users will be able to choose between different font sizes. The default font size will also be increased for them. This is to make Wikimedia projects easier to read. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-06 deployments|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W23"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:35, 3 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26844397 --> == Tech News: 2024-24 == <section begin="technews-2024-W24"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/24|Translations]] are available. '''Recent changes''' * The software used to render SVG files has been updated to a new version, fixing many longstanding bugs in SVG rendering. [https://phabricator.wikimedia.org/T265549] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML used to render all headings [[mw:Heading HTML changes|is being changed to improve accessibility]]. It was changed last week in some skins (Vector legacy and Minerva). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in Vector-2022. The developers are still considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML markup used for citations by [[mw:Special:MyLanguage/Parsoid|Parsoid]] changed last week. In places where Parsoid previously added the <bdi lang="zxx" dir="ltr"><code>mw-reference-text</code></bdi> class, Parsoid now also adds the <bdi lang="zxx" dir="ltr"><code>reference-text</code></bdi> class for better compatibility with the legacy parser. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1036705] '''Problems''' * There was a bug with the Content Translation interface that caused the tools menus to appear in the wrong location. This has now been fixed. [https://phabricator.wikimedia.org/T366374] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-12|en}}. It will be on all wikis from {{#time:j xg|2024-06-13|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The new version of MediaWiki includes another change to the HTML markup used for citations: [[mw:Special:MyLanguage/Parsoid|Parsoid]] will now generate a <bdi lang="zxx" dir="ltr"><code><nowiki><span class="mw-cite-backlink"></nowiki></code></bdi> wrapper for both named and unnamed references for better compatibility with the legacy parser. Interface administrators should verify that gadgets that interact with citations are compatible with the new markup. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1035809] * On multilingual wikis that use the <bdi lang="zxx" dir="ltr"><code><nowiki><translate></nowiki></code></bdi> system, there is a feature that shows potentially-outdated translations with a pink background until they are updated or confirmed. From this week, confirming translations will be logged, and there is a new user-right that can be required for confirming translations if the community [[m:Special:MyLanguage/Requesting wiki configuration changes|requests it]]. [https://phabricator.wikimedia.org/T49177] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W24"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:20, 10 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26893898 --> == Tech News: 2024-25 == <section begin="technews-2024-W25"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/25|Translations]] are available. '''Recent changes''' * People who attempt to add an external link in the visual editor will now receive immediate feedback if they attempt to link to a domain that a project has decided to block. Please see [[mw:Special:MyLanguage/Edit_check#11_June_2024|Edit check]] for more details. [https://phabricator.wikimedia.org/T366751] * The new [[mw:Special:MyLanguage/Extension:CommunityConfiguration|Community Configuration extension]] is available [[testwiki:Special:CommunityConfiguration|on Test Wikipedia]]. This extension allows communities to customize specific features to meet their local needs. Currently only Growth features are configurable, but the extension will support other [[mw:Special:MyLanguage/Community_configuration#Use_cases|Community Configuration use cases]] in the future. [https://phabricator.wikimedia.org/T323811][https://phabricator.wikimedia.org/T360954] * The dark mode [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] is now available on category and help pages, as well as more special pages. There may be contrast issues. Please report bugs on the [[mw:Talk:Reading/Web/Accessibility_for_reading|project talk page]]. [https://phabricator.wikimedia.org/T366370] '''Problems''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Cloud Services tools were not available for 25 minutes last week. This was caused by a faulty hardware cable in the data center. [https://wikitech.wikimedia.org/wiki/Incidents/2024-06-11_WMCS_Ceph] * Last week, styling updates were made to the Vector 2022 skin. This caused unforeseen issues with templates, hatnotes, and images. Changes to templates and hatnotes were reverted. Most issues with images were fixed. If you still see any, [[phab:T367463|report them here]]. [https://phabricator.wikimedia.org/T367480] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-19|en}}. It will be on all wikis from {{#time:j xg|2024-06-20|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting June 18, the [[mw:Special:MyLanguage/Help:Edit check#ref|Reference Edit Check]] will be deployed to [[phab:T361843|a new set of Wikipedias]]. This feature is intended to help newcomers and to assist edit-patrollers by inviting people who are adding new content to a Wikipedia article to add a citation when they do not do so themselves. During [[mw:Special:MyLanguage/Edit_check#Reference_Check_A/B_Test|a test at 11 wikis]], the number of citations added [https://diff.wikimedia.org/?p=127553 more than doubled] when Reference Check was shown to people. Reference Check is [[mw:Special:MyLanguage/Edit check/Configuration|community configurable]]. [https://phabricator.wikimedia.org/T361843]<!-- NOTE: THE DIFF BLOG WILL BE PUBLISHED ON MONDAY --> * [[m:Special:MyLanguage/Mailing_lists|Mailing lists]] will be unavailable for roughly two hours on Tuesday 10:00–12:00 UTC. This is to enable migration to a new server and upgrade its software. [https://phabricator.wikimedia.org/T367521] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W25"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:48, 17 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26911987 --> == Tech News: 2024-26 == <section begin="technews-2024-W26"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/26|Translations]] are available. '''Recent changes''' * Editors will notice that there have been some changes to the background color of text in the diff view, and the color of the byte-change numbers, last week. These changes are intended to make text more readable in both light mode and dark mode, and are part of a larger effort to increase accessibility. You can share your comments or questions [[mw:Talk:Reading/Web/Accessibility for reading|on the project talkpage]]. [https://phabricator.wikimedia.org/T361717] * The text colors that are used for visited-links, hovered-links, and active-links, were also slightly changed last week to improve their accessibility in both light mode and dark mode. [https://phabricator.wikimedia.org/T366515] '''Problems''' * You can [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|copy permanent links to talk page comments]] by clicking on a comment's timestamp. [[mw:Talk pages project/Permalinks|This feature]] did not always work when the topic title was very long and the link was used as a wikitext link. This has been fixed. Thanks to Lofhi for submitting the bug. [https://phabricator.wikimedia.org/T356196] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-26|en}}. It will be on all wikis from {{#time:j xg|2024-06-27|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting 26 June, all talk pages messages' timestamps will become a link at English Wikipedia, making this feature available for you to use at all wikis. This link is a permanent link to the comment. It allows users to find the comment they were linked to, even if this comment has since been moved elsewhere. You can read more about this feature [[DiffBlog:/2024/01/29/talk-page-permalinks-dont-lose-your-threads/|on Diff]] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|on Mediawiki.org]]. [https://phabricator.wikimedia.org/T365974] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W26"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:32, 24 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26989424 --> == Tech News: 2024-27 == <section begin="technews-2024-W27"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/27|Translations]] are available. '''Recent changes''' * Over the next three weeks, dark mode will become available for all users, both logged-in and logged-out, starting with the mobile web version. This fulfils one of the [[m:Special:MyLanguage/Community_Wishlist_Survey_2023/Reading/Dark_mode|top-requested community wishes]], and improves low-contrast reading and usage in low-light settings. As part of these changes, dark mode will also work on User-pages and Portals. There is more information in [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading/Updates#June_2024:_Typography_and_dark_mode_deployments,_new_global_preferences|the latest Web team update]]. [https://phabricator.wikimedia.org/T366364] * Logged-in users can now set [[m:Special:GlobalPreferences#mw-prefsection-rendering-skin-skin-prefs|global preferences for the text-size and dark-mode]], thanks to a combined effort across Foundation teams. This allows Wikimedians using multiple wikis to set up a consistent reading experience easily, for example by switching between light and dark mode only once for all wikis. [https://phabricator.wikimedia.org/T341278] * If you use a very old web browser some features might not work on the Wikimedia wikis. This affects Internet Explorer 11 and versions of Chrome, Firefox and Safari older than 2016. This change makes it possible to use new [[d:Q46441|CSS]] features and to send less code to all readers. [https://phabricator.wikimedia.org/T288287][https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:How_to_make_a_MediaWiki_skin#Using_CSS_variables_for_supporting_different_themes_e.g._dark_mode] * Wikipedia Admins can customize local wiki configuration options easily using [[mw:Special:MyLanguage/Community Configuration|Community Configuration]]. Community Configuration was created to allow communities to customize how some features work, because each language wiki has unique needs. At the moment, admins can configure [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] on their home wikis, in order to better recruit and retain new editors. More options will be provided in the coming months. [https://phabricator.wikimedia.org/T366458] * Editors interested in language issues that are related to [[w:en:Unicode|Unicode standards]], can now discuss those topics at [[mw:Talk:WMF membership with Unicode Consortium|a new conversation space in MediaWiki.org]]. The Wikimedia Foundation is now a [[mw:Special:MyLanguage/WMF membership with Unicode Consortium|member of the Unicode Consortium]], and the coordination group can collaboratively review the issues discussed and, where appropriate, bring them to the attention of the Unicode Consortium. * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2891049|Mandailing]] ([[w:btm:|<code>w:btm:</code>]]) [https://phabricator.wikimedia.org/T368038] '''Problems''' * Editors can once again click on links within the visual editor's citation-preview, thanks to a bug fix by the Editing Team. [https://phabricator.wikimedia.org/T368119] '''Future changes''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 2 weeks. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W27"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:59, 1 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27038456 --> == Tech News: 2024-28 == <section begin="technews-2024-W28"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/28|Translations]] are available. '''Recent changes''' * At the Wikimedia Foundation a new task force was formed to replace the disabled Graph with [[mw:Special:MyLanguage/Extension:Chart/Project|more secure, easy to use, and extensible Chart]]. You can [[mw:Special:MyLanguage/Newsletter:Chart Project|subscribe to the newsletter]] to get notified about new project updates and other news about Chart. * The [[m:Special:MyLanguage/CampaignEvents|CampaignEvents]] extension is now available on Meta-wiki, Igbo Wikipedia, and Swahili Wikipedia, and can be requested on your wiki. This extension helps in managing and making events more visible, giving Event organizers the ability to use tools like the Event registration tool. To learn more about the deployment status and how to request this extension for your wiki, visit the [[m:Special:MyLanguage/CampaignEvents/Deployment_status|CampaignEvents page on Meta-wiki]]. * Editors using the iOS Wikipedia app who have more than 50 edits can now use the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits#Add an image|Add an Image]] feature. This feature presents opportunities for small but useful contributions to Wikipedia. * Thank you to [[mw:MediaWiki Product Insights/Contributor retention and growth/Celebration|all of the authors]] who have contributed to MediaWiki Core. As a result of these contributions, the [[mw:MediaWiki Product Insights/Contributor retention and growth|percentage of authors contributing more than 5 patches has increased by 25% since last year]], which helps ensure the sustainability of the platform for the Wikimedia projects. '''Problems''' * A problem with the color of the talkpage tabs always showing as blue, even for non-existent pages which should have been red, affecting the Vector 2022 skin, [[phab:T367982|has been fixed]]. '''Future changes''' * The Trust and Safety Product team wants to introduce [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] with as little disruption to tools and workflows as possible. Volunteer developers, including gadget and user-script maintainers, are kindly asked to update the code of their tools and features to handle temporary accounts. The team has [[mw:Trust and Safety Product/Temporary Accounts/For developers|created documentation]] explaining how to do the update. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]]. '''Tech News survey''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 1 more week. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/28|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W28"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:31, 8 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27080357 --> == Tech News: 2024-29 == <section begin="technews-2024-W29"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/29|Translations]] are available. '''Tech News survey''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 3 more days. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Wikimedia developers can now officially continue to use both [[mw:Special:MyLanguage/Gerrit|Gerrit]] and [[mw:Special:MyLanguage/GitLab|GitLab]], due to a June 24 decision by the Wikimedia Foundation to support software development on both platforms. Gerrit and GitLab are both code repositories used by developers to write, review, and deploy the software code that supports the MediaWiki software that the wiki projects are built on, as well as the tools used by editors to create and improve content. This decision will safeguard the productivity of our developers and prevent problems in code review from affecting our users. More details are available in the [[mw:GitLab/Migration status|Migration status]] page. * The Wikimedia Foundation seeks applicants for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product and Technology Advisory Council]] (PTAC). This group will bring technical contributors and Wikimedia Foundation together to co-define a more resilient, future-proof technological platform. Council members will evaluate and consult on the movement's product and technical activities, so that we develop multi-generational projects. We are looking for a range of technical contributors across the globe, from a variety of Wikimedia projects. [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal#Joining the PTAC as a technical volunteer|Please apply here by August 10]]. * Editors with rollback user-rights who use the Wikipedia App for Android can use the new [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Anti Vandalism|Edit Patrol]] features. These features include a new feed of Recent Changes, related links such as Undo and Rollback, and the ability to create and save a personal library of user talk messages to use while patrolling. If your wiki wants to make these features available to users who do not have rollback rights but have reached a certain edit threshold, [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android#Contact us|you can contact the team]]. You can [[diffblog:2024/07/10/ِaddressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/|read more about this project on Diff blog]]. * Editors who have access to [[m:Special:MyLanguage/The_Wikipedia_Library|The Wikipedia Library]] can once again use non-open access content in SpringerLinks, after the Foundation [[phab:T368865|contacted]] them to restore access. You can read more about [[m:Tech/News/Recently_resolved_community_tasks|this and 21 other community-submitted tasks that were completed last week]]. '''Changes later this week''' * This week, [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-07 deployments|dark mode will be available on a number of Wikipedias]], both desktop and mobile, for logged-in and logged-out users. Interface admins and user script maintainers are encouraged to check gadgets and user scripts in the dark mode, to find any hard-coded colors and fix them. There are some [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations for dark mode compatibility]] to help. '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Next week, functionaries, volunteers maintaining tools, and software development teams are invited to test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on testwiki. Temporary accounts is a feature that will help improve privacy on the wikis. No further temporary account deployments are scheduled yet. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]]. [https://phabricator.wikimedia.org/T348895] * Editors who upload files cross-wiki, or teach other people how to do so, may wish to join a Wikimedia Commons discussion. The Commons community is discussing limiting who can upload files through the cross-wiki upload/Upload dialog feature to users auto-confirmed on Wikimedia Commons. This is due to the large amount of copyright violations uploaded this way. There is a short summary at [[c:Special:MyLanguage/Commons:Cross-wiki upload|Commons:Cross-wiki upload]] and [[c:Commons:Village pump/Proposals#Deactivate cross-wiki uploads for new users|discussion at Commons:Village Pump]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]]. </div><section end="technews-2024-W29"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:31, 16 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27124561 --> == Tech News: 2024-30 == <section begin="technews-2024-W30"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/30|Translations]] are available. '''Feature News''' * Stewards can now [[:m:Special:MyLanguage/Global_blocks|globally block]] accounts. Before [[phab:T17294|the change]] only IP addresses and IP ranges could be blocked globally. Global account blocks are useful when the blocked user should not be logged out. [[:m:Special:MyLanguage/Global_locks|Global locks]] (a similar tool logging the user out of their account) are unaffected by this change. The new global account block feature is related to the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project, which is a new type of user account that replaces IP addresses of unregistered editors that are no longer made public. * Later this week, Wikimedia site users will notice that the Interface of [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as "Pending Changes") is improved and consistent with the rest of the MediaWiki interface and [[mw:Special:MyLanguage/Codex|Wikimedia's design system]]. The FlaggedRevs interface experience on mobile and [[mw:Special:MyLanguage/Skin:MinervaNeue|Minerva skin]] was inconsistent before it was fixed and ported to [[mw:Special:MyLanguage/Codex|Codex]] by the WMF Growth team and some volunteers. [https://phabricator.wikimedia.org/T191156] * Wikimedia site users can now submit account vanishing requests via [[m:Special:GlobalVanishRequest|GlobalVanishRequest]]. This feature is used when a contributor wishes to stop editing forever. It helps you hide your past association and edit to protect your privacy. Once processed, the account will be locked and renamed. [https://phabricator.wikimedia.org/T367329] * Have you tried monitoring and addressing vandalism in Wikipedia using your phone? [https://diff.wikimedia.org/2024/07/10/%d9%90addressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/ A Diff blog post on Patrolling features in the Mobile App] highlights some of the new capabilities of the feature, including swiping through a feed of recent changes and a personal library of user talk messages for use when patrolling from your phone. * Wikimedia contributors and GLAM (galleries, libraries, archives, and museums) organisations can now learn and measure the impact Wikimedia Commons is having towards creating quality encyclopedic content using the [https://doc.wikimedia.org/generated-data-platform/aqs/analytics-api/reference/commons.html Commons Impact Metrics] analytics dashboard. The dashboard offers organizations analytics on things like monthly edits in a category, the most viewed files, and which Wikimedia articles are using Commons images. As a result of these new data dumps, GLAM organisation can more reliably measure their return on investment for programs bringing content into the digital Commons. [https://diff.wikimedia.org/2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/] '''Project Updates''' * Come share your ideas for improving the wikis on the newly reopened [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]]. The Community Wishlist is Wikimedia’s forum for volunteers to share ideas (called wishes) to improve how the wikis work. The new version of the wishlist is always open, works with both wikitext and Visual Editor, and allows wishes in any language. '''Learn more''' * Have you ever wondered how Wikimedia software works across over 300 languages? This is 253 languages more than the Google Chrome interface, and it's no accident. The Language and Product Localization Team at the Wikimedia Foundation supports your work by adapting all the tools and interfaces in the MediaWiki software so that contributors in our movement who translate pages and strings can translate them and have the sites in all languages. Read more about the team and their upcoming work on [https://diff.wikimedia.org/2024/07/17/building-towards-a-robust-multilingual-knowledge-ecosystem-for-the-wikimedia-movement/ Diff]. * How can Wikimedia build innovative and experimental products while maintaining such heavily used websites? A recent [https://diff.wikimedia.org/2024/07/09/on-the-value-of-experimentation/ blog post] by WMF staff Johan Jönsson highlights the work of the [[m:Future Audiences#Objectives and Key Results|WMF Future Audience initiative]], where the goal is not to build polished products but test out new ideas, such as a [[m:Future_Audiences/Experiments: conversational/generative AI|ChatGPT plugin]] and [[m:Future_Audiences/Experiment:Add a Fact|Add a Fact]], to help take Wikimedia into the future. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]]. </div><section end="technews-2024-W30"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:04, 23 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27142915 --> == Tech News: 2024-31 == <section begin="technews-2024-W31"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/31|Translations]] are available. '''Feature news''' * Editors using the Visual Editor in languages that use non-Latin characters for numbers, such as Hindi, Manipuri and Eastern Arabic, may notice some changes in the formatting of reference numbers. This is a side effect of preparing a new sub-referencing feature, and will also allow fixing some general numbering issues in Visual Editor. If you notice any related problems on your wiki, please share details at the [[m:Talk:WMDE Technical Wishes/Sub-referencing|project talkpage]]. '''Bugs status''' * Some logged-in editors were briefly unable to edit or load pages last week. [[phab:T370304|These errors]] were mainly due to the addition of new [[mw:Special:MyLanguage/Help:Extension:Linter|linter]] rules which led to caching problems. Fixes have been applied and investigations are continuing. * Editors can use the [[mw:Special:MyLanguage/Trust and Safety Product/IP Info|IP Information tool]] to get information about IP addresses. This tool is available as a Beta Feature in your preferences. The tool was not available for a few days last week, but is now working again. Thank you to Shizhao for filing the bug report. You can read about that, and [[m:Tech/News/Recently resolved community tasks#2024-07-25|28 other community-submitted tasks]] that were resolved last week. '''Project updates''' * There are new features and improvements to Phabricator from the Release Engineering and Collaboration Services teams, and some volunteers, including: the search systems, the new task creation system, the login systems, the translation setup which has resulted in support for more languages (thanks to Pppery), and fixes for many edge-case errors. You can [[phab:phame/post/view/316/iterative_improvements/|read details about these and other improvements in this summary]]. * There is an [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|update on the Charts project]]. The team has decided which visualization library to use, which chart types to start focusing on, and where to store chart definitions. * One new wiki has been created: a {{int:project-localized-name-group-wikivoyage}} in [[d:Q9056|Czech]] ([[voy:cs:|<code>voy:cs:</code>]]) [https://phabricator.wikimedia.org/T370905] '''Learn more''' * There is a [[diffblog:2024/07/26/the-journey-to-open-our-first-data-center-in-south-america/|new Wikimedia Foundation data center]] in São Paulo, Brazil which helps to reduce load times. * There is new [[diffblog:2024/07/22/the-perplexing-process-of-uploading-images-to-wikipedia/|user research]] on problems with the process of uploading images. * Commons Impact Metrics are [[diffblog:2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/|now available]] via data dumps and API. * The latest quarterly [[mw:Technical Community Newsletter/2024/July|Technical Community Newsletter]] is now available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W31"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:10, 29 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27164109 --> == Tech News: 2024-32 == <section begin="technews-2024-W32"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/32|Translations]] are available. '''Feature news''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Two new parser functions will be available this week: <code><nowiki>{{</nowiki>[[mw:Special:MyLanguage/Help:Magic_words#dir|#dir]]<nowiki>}}</nowiki></code> and <code><nowiki>{{</nowiki>[[mw:Special:MyLanguage/Help:Magic_words#bcp47|#bcp47]]<nowiki>}}</nowiki></code>. These will reduce the need for <code>Template:Dir</code> and <code>Template:BCP47</code> on Commons and allow us to [[phab:T343131|drop 100 million rows]] from the "what links here" database. Editors at any wiki that use these templates, can help by replacing the templates with these new functions. The templates at Commons will be updated during the Hackathon at Wikimania. [https://phabricator.wikimedia.org/T359761][https://phabricator.wikimedia.org/T366623] * Communities can request the activation of the visual editor on entire namespaces where discussions sometimes happen (for instance ''Wikipedia:'' or ''Wikisource:'' namespaces) if they understand the [[mw:Special:MyLanguage/Help:VisualEditor/FAQ#WPNS|known limitations]]. For discussions, users can already use [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] in these namespaces. * The tracking category "Pages using Timeline" has been renamed to "Pages using the EasyTimeline extension" [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3ATimeline-tracking-category&namespace=8 in TranslateWiki]. Wikis that have created the category locally should rename their local creation to match. '''Project updates''' * Editors who help to organize WikiProjects and similar on-wiki collaborations, are invited to share ideas and examples of successful collaborations with the Campaigns and Programs teams. You can fill out [[m:Special:MyLanguage/Campaigns/WikiProjects|a brief survey]] or share your thoughts [[m:Talk:Campaigns/WikiProjects|on the talkpage]]. The teams are particularly looking for details about successful collaborations on non-English wikis. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The new parser is being rolled out on {{int:project-localized-name-group-wikivoyage}} wikis over the next few months. The {{int:project-localized-name-enwikivoyage}} and {{int:project-localized-name-hewikivoyage}} were [[phab:T365367|switched]] to Parsoid last week. For more information, see [[mw:Parsoid/Parser_Unification|Parsoid/Parser Unification]]. '''Learn more''' * There will be more than 200 sessions at Wikimania this week. Here is a summary of some of the [[diffblog:2024/08/05/interested-in-product-and-tech-here-are-some-wikimania-sessions-you-dont-want-to-miss/|key sessions related to the product and technology area]]. * The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/07-02|Wikimedia Foundation Bulletin]] is available. * The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/July|Language and Internationalization newsletter]] is available. It includes: New design previews for Translatable pages; Updates about MinT for Wiki Readers; the release of Translation dumps; and more. * The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/31|Growth newsletter]] is available. * The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/July 2024|MediaWiki Product Insights newsletter]] is available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W32"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:43, 5 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27233905 --> == Tech News: 2024-33 == <section begin="technews-2024-W33"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/33|Translations]] are available. '''Feature news''' * [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] editors and maintainers can now [[mw:Special:MyLanguage/Extension:AbuseFilter/Actions#Show a CAPTCHA|make a CAPTCHA show if a filter matches an edit]]. This allows communities to quickly respond to spamming by automated bots. [https://phabricator.wikimedia.org/T20110] * [[m:Special:MyLanguage/Stewards|Stewards]] can now specify if global blocks should prevent account creation. Before [[phab:T17273|this change]] by the [[mw:Special:MyLanguage/Trust and Safety Product|Trust and Safety Product]] Team, all global blocks would prevent account creation. This will allow stewards to reduce the unintended side-effects of global blocks on IP addresses. '''Project updates''' * [[wikitech:Help talk:Toolforge/Toolforge standards committee#August_2024_committee_nominations|Nominations are open on Wikitech]] for new members to refresh the [[wikitech:Help:Toolforge/Toolforge standards committee|Toolforge standards committee]]. The committee oversees the Toolforge [[wikitech:Help:Toolforge/Right to fork policy|Right to fork policy]] and [[wikitech:Help:Toolforge/Abandoned tool policy|Abandoned tool policy]] among other duties. Nominations will remain open until at least 2024-08-26. * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2880037|West Coast Bajau]] ([[w:bdr:|<code>w:bdr:</code>]]) [https://phabricator.wikimedia.org/T371757] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W33"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:21, 12 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27253654 --> == Tech News: 2024-34 == <section begin="technews-2024-W34"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/34|Translations]] are available. '''Feature news''' * Editors who want to re-use references but with different details such as page numbers, will be able to do so by the end of 2024, using a new [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Sub-referencing in a nutshell|sub-referencing]] feature. You can read more [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|about the project]] and [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|how to test the prototype]]. * Editors using tracking categories to identify which pages use specific extensions may notice that six of the categories have been renamed to make them more easily understood and consistent. These categories are automatically added to pages that use specialized MediaWiki extensions. The affected names are for: [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aintersection-category&namespace=8 DynamicPageList], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Akartographer-tracking-category&namespace=8 Kartographer], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aphonos-tracking-category&namespace=8 Phonos], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Arss-tracking-category&namespace=8 RSS], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Ascore-use-category&namespace=8 Score], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Awikihiero-usage-tracking-category&namespace=8 WikiHiero]. Wikis that have created the category locally should rename their local creation to match. Thanks to Pppery for these improvements. [https://phabricator.wikimedia.org/T347324] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Technical volunteers who edit modules and want to get a list of the categories used on a page, can now do so using the <code><bdi lang="zxx" dir="ltr">categories</bdi></code> property of <code><bdi lang="zxx" dir="ltr">[[mediawikiwiki:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Title objects|mw.title objects]]</bdi></code>. This enables wikis to configure workflows such as category-specific edit notices. Thanks to SD001 for these improvements. [https://phabricator.wikimedia.org/T50175][https://phabricator.wikimedia.org/T85372] '''Bugs status''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Your help is needed to check if any pages need to be moved or deleted. A maintenance script was run to clean up unreachable pages (due to Unicode issues or introduction of new namespaces/namespace aliases). The script tried to find appropriate names for the pages (e.g. by following the Unicode changes or by moving pages whose titles on Wikipedia start with <code>Talk:WP:</code> so that their titles start with <code>Wikipedia talk:</code>), but it may have failed for some pages, and moved them to <bdi lang="zxx" dir="ltr">[[Special:PrefixIndex/T195546/]]</bdi> instead. Your community should check if any pages are listed there, and move them to the correct titles, or delete them if they are no longer needed. A full log (including pages for which appropriate names could be found) is available in [[phab:P67388]]. * Editors who volunteer as [[mw:Special:MyLanguage/Help:Growth/Mentorship|mentors]] to newcomers on their wiki are once again able to access lists of potential mentees who they can connect with to offer help and guidance. This functionality was restored thanks to [[phab:T372164|a bug fix]]. Thank you to Mbch331 for filing the bug report. You can read about that, and 18 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Project updates''' * The application deadline for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product & Technology Advisory Council]] (PTAC) has been extended to September 16. Members will help by providing advice to Foundation Product and Technology leadership on short and long term plans, on complex strategic problems, and help to get feedback from more contributors and technical communities. Selected members should expect to spend roughly 5 hours per month for the Council, during the one year pilot. Please consider applying, and spread the word to volunteers you think would make a positive contribution to the committee. '''Learn more''' * The [[m:Special:MyLanguage/Coolest Tool Award#2024 Winners|2024 Coolest Tool Awards]] were awarded at Wikimania, in seven categories. For example, one award went to the ISA Tool, used for adding structured data to files on Commons, which was recently improved during the [[m:Event:Wiki Mentor Africa ISA Hackathon 2024|Wiki Mentor Africa Hackathon]]. You can see video demonstrations of each tool at the awards page. Congratulations to this year's recipients, and thank you to all tool creators and maintainers. * The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/08-01|Wikimedia Foundation Bulletin]] is available, and includes some highlights from Wikimania, an upcoming Language community meeting, and other news from the movement. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W34"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:54, 20 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27307284 --> == Tech News: 2024-35 == <section begin="technews-2024-W35"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/35|Translations]] are available. '''Feature news''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Administrators can now test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on test2wiki. This was done to allow cross-wiki testing of temporary accounts, for when temporary accounts switch between projects. The feature was enabled on testwiki a few weeks ago. No further temporary account deployments are scheduled yet. Temporary Accounts is a project to create a new type of user account that replaces IP addresses of unregistered editors which are no longer made public. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]]. * Later this week, editors at wikis that use [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as "Pending Changes") may notice that the indicators at the top of articles have changed. This change makes the system more consistent with the rest of the MediaWiki interface. [https://phabricator.wikimedia.org/T191156] '''Bugs status''' * Editors who use the 2010 wikitext editor, and use the Character Insert buttons, will [[phab:T361465|no longer]] experience problems with the buttons adding content into the edit-summary instead of the edit-window. You can read more about that, and 26 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Project updates''' * [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Please review and vote on [[m:Special:MyLanguage/Community Wishlist/Focus areas|Focus Areas]], which are groups of wishes that share a problem. Focus Areas were created for the newly reopened Community Wishlist, which is now open year-round for submissions. The first batch of focus areas are specific to moderator workflows, around welcoming newcomers, minimizing repetitive tasks, and prioritizing tasks. Once volunteers have reviewed and voted on focus areas, the Foundation will then review and select focus areas for prioritization. * Do you have a project and are willing to provide a three (3) month mentorship for an intern? [[mw:Special:MyLanguage/Outreachy|Outreachy]] is a twice a year program for people to participate in a paid internship that will start in December 2024 and end in early March 2025, and they need mentors and projects to work on. Projects can be focused on coding or non-coding (design, documentation, translation, research). See the Outreachy page for more details, and a list of past projects since 2013. '''Learn more''' * If you're curious about the product and technology improvements made by the Wikimedia Foundation last year, read [[diffblog:2024/08/21/wikimedia-foundation-product-technology-improving-the-user-experience/|this recent highlights summary on Diff]]. * To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Community Configuration - Shaping On-Wiki Functionality Together.webm|Community Configuration - Shaping On-Wiki Functionality Together]] (55 mins) - about the [[mw:Special:MyLanguage/Community Configuration|Community Configuration]] project. ** [[c:File:Wikimania 2024 - Belgrade - Day 1 - Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views.webm|Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views]] (30 mins) - an overview for both technical and non technical audiences, covering some of the challenges and open questions, related to the [[mw:MediaWiki Product Insights|platform evolution, stewardship and developer experiences]] research. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W35"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:33, 26 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27341211 --> == Tech News: 2024-36 == <section begin="technews-2024-W36"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/36|Translations]] are available. '''Weekly highlight''' * Editors and volunteer developers interested in data visualisation can now test the new software for charts. Its early version is available on beta Commons and beta Wikipedia. This is an important milestone before making charts available on regular wikis. You can [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|read more about this project update]] and help to test the charts. '''Feature news''' * Editors who use the [[{{#special:Unusedtemplates}}]] page can now filter out pages which are expected to be there permanently, such as sandboxes, test-cases, and templates that are always substituted. Editors can add the new magic word [[mw:Special:MyLanguage/Help:Magic words#EXPECTUNUSEDTEMPLATE|<code dir="ltr"><nowiki>__EXPECTUNUSEDTEMPLATE__</nowiki></code>]] to a template page to hide it from the listing. Thanks to Sophivorus and DannyS712 for these improvements. [https://phabricator.wikimedia.org/T184633] * Editors who use the New Topic tool on discussion pages, will [[phab:T334163|now be reminded]] to add a section header, which should help reduce the quantity of newcomers who add sections without a header. You can read more about that, and {{formatnum:28}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. * Last week, some Toolforge tools had occasional connection problems. The cause is still being investigated, but the problems have been resolved for now. [https://phabricator.wikimedia.org/T373243] * Translation administrators at multilingual wikis, when editing multiple translation units, can now easily mark which changes require updates to the translation. This is possible with the [[phab:T298852#10087288|new dropdown menu]]. '''Project updates''' * A new draft text of a policy discussing the use of Wikimedia's APIs [[m:Special:MyLanguage/API Policy Update 2024|has been published on Meta-Wiki]]. The draft text does not reflect a change in policy around the APIs; instead, it is an attempt to codify existing API rules. Comments, questions, and suggestions are welcome on [[m:Talk:API Policy Update 2024|the proposed update’s talk page]] until September 13 or until those discussions have concluded. '''Learn more''' * To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Charts, the successor of Graphs - A secure and extensible tool for data visualization.webm|Charts, the successor of Graphs - A secure and extensible tool for data visualization]] (25 mins) – about the above-mentioned Charts project. ** [[c:File:Wikimania 2024 - Ohrid - Day 3 - State of Language Technology and Onboarding at Wikimedia.webm|State of Language Technology and Onboarding at Wikimedia]] (90 mins) – about some of the language tools that support Wikimedia sites, such as [[mw:Special:MyLanguage/Content translation|Content]]/[[mw:Special:MyLanguage/Content translation/Section translation|Section Translation]], [[mw:Special:MyLanguage/MinT|MinT]], and LanguageConverter; also the current state and future of languages onboarding. [https://phabricator.wikimedia.org/T368772] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W36"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:07, 3 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27390268 --> == Tech News: 2024-37 == <section begin="technews-2024-W37"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/37|Translations]] are available. '''Feature news''' * Starting this week, the standard [[mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighter]] will receive new colors that make them compatible in dark mode. This is the first of many changes to come as part of a major upgrade to syntax highlighting. You can learn more about what's to come on the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|help page]]. [https://phabricator.wikimedia.org/T365311][https://phabricator.wikimedia.org/T259059] * Editors of wikis using Wikidata will now be notified of only relevant Wikidata changes in their watchlist. This is because the Lua functions <bdi lang="zxx" dir="ltr"><code>entity:getSitelink()</code></bdi> and <bdi lang="zxx" dir="ltr"><code>mw.wikibase.getSitelink(qid)</code></bdi> will have their logic unified for tracking different aspects of sitelinks to reduce junk notifications from [[m:Wikidata For Wikimedia Projects/Projects/Watchlist Wikidata Sitelinks Tracking|inconsistent sitelinks tracking]]. [https://phabricator.wikimedia.org/T295356] '''Project updates''' * Users of all Wikis will have access to Wikimedia sites as read-only for a few minutes on September 25, starting at 15:00 UTC. This is a planned datacenter switchover for maintenance purposes. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T370962] * Contributors of [[phab:T363538#10123348|11 Wikipedias]], including English will have a new <bdi lang="zxx" dir="ltr"><code>MOS</code></bdi> namespace added to their Wikipedias. This improvement ensures that links beginning with <bdi lang="zxx" dir="ltr"><code>MOS:</code></bdi> (usually shortcuts to the [[w:en:Wikipedia:Manual of Style|Manual of Style]]) are not broken by [[w:en:Mooré|Mooré]] Wikipedia (language code <bdi lang="zxx" dir="ltr"><code>mos</code></bdi>). [https://phabricator.wikimedia.org/T363538] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W37"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 18:52, 9 September 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27424457 --> == Tech News: 2024-38 == <section begin="technews-2024-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/38|Translations]] are available. '''Improvements and Maintenance''' * [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Editors interested in templates can help by reading the latest Wishlist focus area, [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|Template recall and discovery]], and share your feedback on the talkpage. This input helps the Community Tech team to decide the right technical approach to build. Everyone is also encouraged to continue adding [[m:Special:MyLanguage/Community Wishlist|new wishes]]. * The new automated [[{{#special:NamespaceInfo}}]] page helps editors understand which [[mw:Special:MyLanguage/Help:Namespaces|namespaces]] exist on each wiki, and some details about how they are configured. Thanks to DannyS712 for these improvements. [https://phabricator.wikimedia.org/T263513] * [[mw:Special:MyLanguage/Help:Edit check#Reference check|References Check]] is a feature that encourages editors to add a citation when they add a new paragraph to a Wikipedia article. For a short time, the corresponding tag "Edit Check (references) activated" was erroneously being applied to some edits outside of the main namespace. This has been fixed. [https://phabricator.wikimedia.org/T373692] * It is now possible for a wiki community to change the order in which a page’s categories are displayed on their wiki. By default, categories are displayed in the order they appear in the wikitext. Now, wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Tool authors can now access ToolsDB's [[wikitech:Portal:Data Services#ToolsDB|public databases]] from both [[m:Special:MyLanguage/Research:Quarry|Quarry]] and [[wikitech:Superset|Superset]]. Those databases have always been accessible to every [[wikitech:Portal:Toolforge|Toolforge]] user, but they are now more broadly accessible, as Quarry can be accessed by anyone with a Wikimedia account. In addition, Quarry's internal database can now be [[m:Special:MyLanguage/Research:Quarry#Querying Quarry's own database|queried from Quarry itself]]. This database contains information about all queries that are being run and starred by users in Quarry. This information was already public through the web interface, but you can now query it using SQL. You can read more about that, and {{formatnum:20}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. * Any pages or tools that still use the very old CSS classes <bdi lang="zxx" dir="ltr"><code>mw-message-box</code></bdi> need to be updated. These old classes will be removed next week or soon afterwards. Editors can use a [https://global-search.toolforge.org/?q=mw-message-box&regex=1&namespaces=&title= global-search] to determine what needs to be changed. It is possible to use the newer <bdi lang="zxx" dir="ltr"><code>cdx-message</code></bdi> group of classes as a replacement (see [https://doc.wikimedia.org/codex/latest/components/demos/message.html#css-only-version the relevant Codex documentation], and [https://meta.wikimedia.org/w/index.php?title=Tech/Header&diff=prev&oldid=27449042 an example update]), but using locally defined onwiki classes would be best. [https://phabricator.wikimedia.org/T374499] '''Technical project updates''' * Next week, all Wikimedia wikis will be read-only for a few minutes. This will start on September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. This is a planned datacenter switchover for maintenance purposes. [[m:Special:MyLanguage/Tech/Server switch|This maintenance process also targets other services.]] The previous switchover took 3 minutes, and the Site Reliability Engineering teams use many tools to make sure that this essential maintenance work happens as quickly as possible. [https://phabricator.wikimedia.org/T370962] '''Tech in depth''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/August 2024|MediaWiki Product Insights newsletter]] is available. This edition includes details about: research about [[mw:Special:MyLanguage/Manual:Hooks|hook]] handlers to help simplify development, research about performance improvements, work to improve the REST API for end-users, and more. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Auditorium Kyiv - Day 4 - Hackathon Showcase.webm|Hackathon Showcase]] (45 mins) - 19 short presentations by some of the Hackathon participants, describing some of the projects they worked on, such as automated testing of maintenance scripts, a video-cutting command line tool, and interface improvements for various tools. There are [[phab:T369234|more details and links available]] in the Phabricator task. ** [[c:File:Co-Creating a Sustainable Future for the Toolforge Ecosystem.webm|Co-Creating a Sustainable Future for the Toolforge Ecosystem]] (40 mins) - a roundtable discussion for tool-maintainers, users, and supporters of Toolforge about how to make the platform sustainable and how to evaluate the tools available there. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W38"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:02, 17 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27460876 --> == Tech News: 2024-39 == <section begin="technews-2024-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/39|Translations]] are available. '''Weekly highlight''' * All wikis will be [[m:Special:MyLanguage/Tech/Server switch|read-only]] for a few minutes on Wednesday September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. Reading the wikis will not be interrupted, but editing will be paused. These twice-yearly processes allow WMF's site reliability engineering teams to remain prepared to keep the wikis functioning even in the event of a major interruption to one of our data centers. '''Updates for editors''' [[File:Add alt text from a halfsheet, with the article behind.png|thumb|A screenshot of the interface for the Alt Text suggested-edit feature]] * Editors who use the iOS Wikipedia app in Spanish, Portuguese, French, or Chinese, may see the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|Alt Text suggested-edit experiment]] after editing an article, or completing a suggested edit using "[[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project#Hypothesis 2 Add an Image Suggested Edit|Add an image]]". Alt-text helps people with visual impairments to read Wikipedia articles. The team aims to learn if adding alt-text to images is a task that editors can be successful with. Please share any feedback on [[mw:Talk:Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|the discussion page]]. * The Codex color palette has been updated with new and revised colors for the MediaWiki user interfaces. The [[mw:Special:MyLanguage/Design System Team/Color/Design documentation#Updates|most noticeable changes]] for editors include updates for: dark mode colors for Links and for quiet Buttons (progressive and destructive), visited Link colors for both light and dark modes, and background colors for system-messages in both light and dark modes. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] It is now possible to include clickable wikilinks and external links inside code blocks. This includes links that are used within <code><nowiki><syntaxhighlight></nowiki></code> tags and on code pages (JavaScript, CSS, Scribunto and Sanitized CSS). Uses of template syntax <code><nowiki>{{…}}</nowiki></code> are also linked to the template page. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T368166] * Two bugs were fixed in the [[m:Special:MyLanguage/Account vanishing|GlobalVanishRequest]] system by improving the logging and by removing an incorrect placeholder message. [https://phabricator.wikimedia.org/T370595][https://phabricator.wikimedia.org/T372223] * View all {{formatnum:25}} community-submitted {{PLURAL:25|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] From [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]]: ** The API now enables 5,000 on-demand API requests per month and twice-monthly HTML snapshots freely (gratis and libre). More information on the updates and also improvements to the software development kits (SDK) are explained on [https://enterprise.wikimedia.com/blog/enhanced-free-api/ the project's blog post]. While Wikimedia Enterprise APIs are designed for high-volume commercial reusers, this change enables many more community use-cases to be built on the service too. ** The Snapshot API (html dumps) have added beta Structured Contents endpoints ([https://enterprise.wikimedia.com/blog/structured-contents-snapshot-api/ blog post on that]) as well as released two beta datasets (English and French Wikipedia) from that endpoint to Hugging Face for public use and feedback ([https://enterprise.wikimedia.com/blog/hugging-face-dataset/ blog post on that]). These pre-parsed data sets enable new options for researchers, developers, and data scientists to use and study the content. '''In depth''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The Wikidata Query Service (WDQS) is used to get answers to questions using the Wikidata data set. As Wikidata grows, we had to make a major architectural change so that WDQS could remain performant. As part of the [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split project]], we have new SPARQL endpoints available for serving the "[https://query-scholarly.wikidata.org scholarly]" and "[https://query-main.wikidata.org main]" subgraphs of Wikidata. The [http://query.wikidata.org query.wikidata.org endpoint] will continue to serve the full Wikidata graph until March 2025. After this date, it will only serve the main graph. For more information, please see [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/September 2024 scaling update|the announcement on Wikidata]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W39"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:36, 23 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27493779 --> == Tech News: 2024-40 == <section begin="technews-2024-W40"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/40|Translations]] are available. '''Updates for editors''' * Readers of [[phab:T375401|42 more wikis]] can now use Dark Mode. If the option is not yet available for logged-out users of your wiki, this is likely because many templates do not yet display well in Dark Mode. Please use the [https://night-mode-checker.wmcloud.org/ night-mode-checker tool] if you are interested in helping to reduce the number of issues. The [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations page]] provides guidance on this. Dark Mode is enabled on additional wikis once per month. * Editors using the 2010 wikitext editor as their default can access features from the 2017 wikitext editor by adding <code dir=ltr>?veaction=editsource</code> to the URL. If you would like to enable the 2017 wikitext editor as your default, it can be set in [[Special:Preferences#mw-input-wpvisualeditor-newwikitext|your preferences]]. [https://phabricator.wikimedia.org/T239796] * For logged-out readers using the Vector 2022 skin, the "donate" link has been moved from a collapsible menu next to the content area into a more prominent top menu, next to "Create an account". This restores the link to the level of prominence it had in the Vector 2010 skin. [[mw:Readers/2024 Reader and Donor Experiences#Donor Experiences (Key Result WE 3.2 and the related hypotheses)|Learn more]] about the changes related to donor experiences. [https://phabricator.wikimedia.org/T373585] * The CampaignEvents extension provides tools for organizers to more easily manage events, communicate with participants, and promote their events on the wikis. The extension has been [[m:Special:MyLanguage/CampaignEvents/Deployment status|enabled]] on Arabic Wikipedia, Igbo Wikipedia, Swahili Wikipedia, and Meta-Wiki. [[w:zh:Wikipedia:互助客栈/其他#引進CampaignEvents擴充功能|Chinese Wikipedia has decided]] to enable the extension, and discussions on the extension are in progress [[w:es:Wikipedia:Votaciones/2024/Sobre la política de Organizadores de Eventos|on Spanish Wikipedia]] and [[d:Wikidata:Project chat#Enabling the CampaignEvents Extention on Wikidata|on Wikidata]]. To learn how to enable the extension on your wiki, you can visit [[m:Special:MyLanguage/CampaignEvents|the CampaignEvents page on Meta-Wiki]]. * View all {{formatnum:22}} community-submitted {{PLURAL:22|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * Developers with an account on Wikitech-wiki should [[wikitech:Wikitech/SUL-migration|check if any action is required]] for their accounts. The wiki is being changed to use the single-user-login (SUL) system, and other configuration changes. This change will help reduce the overall complexity for the weekly software updates across all our wikis. '''In depth''' * The [[m:Special:MyLanguage/Tech/Server switch|server switch]] was completed successfully last week with a read-only time of [[wikitech:Switch Datacenter#Past Switches|only 2 minutes 46 seconds]]. This periodic process makes sure that engineers can switch data centers and keep all of the wikis available for readers, even if there are major technical issues. It also gives engineers a chance to do maintenance and upgrades on systems that normally run 24 hours a day, and often helps to reveal weaknesses in the infrastructure. The process involves dozens of software services and hundreds of hardware servers, and requires multiple teams working together. Work over the past few years has reduced the time from 17 minutes down to 2–3 minutes. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/66ZW7B2MG63AESQVTXDIFQBDBS766JGW/] '''Meetings and events''' * October 4–6: [[m:Special:MyLanguage/WikiIndaba conference 2024|WikiIndaba Conference's Hackathon]] in Johannesburg, South Africa * November 4–6: [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] in Vienna, Austria '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W40"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:20, 30 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27530062 --> == Tech News: 2024-41 == <section begin="technews-2024-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/41|Translations]] are available. '''Weekly highlight''' * Communities can now request installation of [[mw:Special:MyLanguage/Moderator Tools/Automoderator|Automoderator]] on their wiki. Automoderator is an automated anti-vandalism tool that reverts bad edits based on scores from the new "Revert Risk" machine learning model. You can [[mw:Special:MyLanguage/Extension:AutoModerator/Deploying|read details about the necessary steps]] for installation and configuration. [https://phabricator.wikimedia.org/T336934] '''Updates for editors''' * Translators in wikis where [[mw:Special:MyLanguage/Content translation/Section translation#Try the tool|the mobile experience of Content Translation is available]], can now customize their articles suggestion list from 41 filtering options when using the tool. This topic-based article suggestion feature makes it easy for translators to self-discover relevant articles based on their area of interest and translate them. You can [https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&active-list=suggestions try it with your mobile device]. [https://phabricator.wikimedia.org/T368422] * View all {{formatnum:12}} community-submitted {{PLURAL:12|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * It is now possible for <bdi lang="zxx" dir="ltr"><code><nowiki><syntaxhighlight></nowiki></code></bdi> code blocks to offer readers a "Copy" button if the <bdi lang="zxx" dir="ltr"><code><nowiki>copy=1</nowiki></code></bdi> attribute is [[mw:Special:MyLanguage/Extension:SyntaxHighlight#copy|set on the tag]]. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T40932] * Customized copyright footer messages on all wikis will be updated. The new versions will use wikitext markup instead of requiring editing raw HTML. [https://phabricator.wikimedia.org/T375789] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Later this month, [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] will be rolled out on several pilot wikis. The final list of the wikis will be published in the second half of the month. If you maintain any tools, bots, or gadgets on [[phab:T376499|these 11 wikis]], and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]]. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Rate limiting has been enabled for the code review tools [[Wikitech:Gerrit|Gerrit]] and [[Wikitech:GitLab|GitLab]] to address ongoing issues caused by malicious traffic and scraping. Clients that open too many concurrent connections will be restricted for a few minutes. This rate limiting is managed through [[Wikitech:nftables|nftables]] firewall rules. For more details, see Wikitech's pages on [[Wikitech:Firewall#Throttling with nftables|Firewall]], [[Wikitech:GitLab/Abuse and rate limiting|GitLab limits]] and [[Wikitech:Gerrit/Operations#Throttling IPs|Gerrit operations]]. * Five new wikis have been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q49224|Komering]] ([[w:kge:|<code>w:kge:</code>]]) [https://phabricator.wikimedia.org/T374813] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q36096|Mooré]] ([[m:mos:|<code>m:mos:</code>]]) [https://phabricator.wikimedia.org/T374641] ** a {{int:project-localized-name-group-wiktionary}} in [[d:Q36213|Madurese]] ([[wikt:mad:|<code>wikt:mad:</code>]]) [https://phabricator.wikimedia.org/T374968] ** a {{int:project-localized-name-group-wikiquote}} in [[d:Q2501174|Gorontalo]] ([[q:gor:|<code>q:gor:</code>]]) [https://phabricator.wikimedia.org/T375088] ** a {{int:project-localized-name-group-wikinews}} in [[d:Q56482|Shan]] ([[n:shn:|<code>n:shn:</code>]]) [https://phabricator.wikimedia.org/T375430] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W41"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:42, 7 October 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27557422 --> == Tech News: 2024-42 == <section begin="technews-2024-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/42|Translations]] are available. '''Updates for editors''' * The Structured Discussion extension (also known as Flow) is starting to be removed. This extension is unmaintained and causes issues. It will be replaced by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]], which is used on any regular talk page. [[mw:Special:MyLanguage/Structured Discussions/Deprecation#Deprecation timeline|A first set of wikis]] are being contacted. These wikis are invited to stop using Flow, and to move all Flow boards to sub-pages, as archives. At these wikis, a script will move all Flow pages that aren't a sub-page to a sub-page automatically, starting on 22 October 2024. On 28 October 2024, all Flow boards at these wikis will be set in read-only mode. [https://www.mediawiki.org/wiki/Structured_Discussions/Deprecation][https://phabricator.wikimedia.org/T370722] * WMF's Search Platform team is working on making it easier for readers to perform text searches in their language. A [[phab:T332342|change last week]] on over 30 languages makes it easier to find words with accents and other diacritics. This applies to both full-text search and to types of advanced search such as the <bdi lang="en" dir="ltr">''hastemplate''</bdi> and <bdi lang="en" dir="ltr">''incategory''</bdi> keywords. More technical details (including a few other minor search upgrades) are available. [https://www.mediawiki.org/wiki/User:TJones_%28WMF%29/Notes/Language_Analyzer_Harmonization_Notes#ASCII-folding/ICU-folding_%28T332342%29] * View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[mw:Special:MyLanguage/Help:Edit check|EditCheck]] was installed at Russian Wikipedia, and fixes were made for some missing user interface styles. '''Updates for technical contributors''' * Editors who use the Toolforge tool [[toolforge:copyvios|Earwig's Copyright Violation Detector]] will now be required to log in with their Wikimedia account before running checks using the "search engine" option. This change is needed to help prevent external bots from misusing the system. Thanks to Chlod for these improvements. [https://en.wikipedia.org/wiki/Wikipedia_talk:New_pages_patrol/Reviewers#Authentication_is_now_required_for_search_engine_checks_on_Earwig's_Copyvio_Tool] * [[m:Special:MyLanguage/Phabricator|Phabricator]] users can create tickets and add comments on existing tickets via Email again. [[mw:Special:MyLanguage/Phabricator/Help#Using email|Sending email to Phabricator]] has been fixed. [https://phabricator.wikimedia.org/T356077] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Some HTML elements in the interface are now wrapped with a <code><nowiki><bdi></nowiki></code> element, to make our HTML output more aligned with Web standards. More changes like this will be coming in future weeks. This change might break some tools that rely on the previous HTML structure of the interface. Note that relying on the HTML structure of the interface is [[mw:Special:MyLanguage/Stable interface policy/Frontend#What is not stable?|not recommended]] and might break at any time. [https://phabricator.wikimedia.org/T375975] '''In depth''' * The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/September 2024|MediaWiki Product Insights newsletter]] is available. This edition includes: updates on Wikimedia's authentication system, research to simplify feature development in the MediaWiki platform, updates on Parser Unification and MathML rollout, and more. * The latest quarterly [[mw:Technical Community Newsletter/2024/October|Technical Community Newsletter]] is now available. This edition include: research about improving topic suggestions related to countries, improvements to PHPUnit tests, and more. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W42"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:21, 14 October 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27597254 --> == Tech News: 2024-43 == <section begin="technews-2024-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/43|Translations]] are available. '''Weekly highlight''' * The Mobile Apps team has released an [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh#Phase 1: Creating a user Profile Menu (T373714)|update]] to the iOS app's navigation, and it is now available in the latest App store version. The team added a new Profile menu that allows for easy access to editor features like Notifications and Watchlist from the Article view, and brings the "Donate" button into a more accessible place for users who are reading an article. This is the first phase of a larger planned [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh|navigation refresh]] to help the iOS app transition from a primarily reader-focused app, to an app that fully supports reading and editing. The Wikimedia Foundation has added more editing features and support for on-wiki communication based on volunteer requests in recent years. [[File:IOS App Navigation refresh first phase 05.png|thumb|iOS Wikipedia App's profile menu and contents]] '''Updates for editors''' * Wikipedia readers can now download a browser extension to experiment with some early ideas on potential features that recommend articles for further reading, automatically summarize articles, and improve search functionality. For more details and to stay updated, check out the Web team's [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments|Content Discovery Experiments page]] and [[mw:Special:MyLanguage/Newsletter:Web team's projects|subscribe to their newsletter]]. * Later this month, logged-out editors of [[phab:T376499|these 12 wikis]] will start to have [[mw:Special:Mylanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] created. The list may slightly change - some wikis may be removed but none will be added. Temporary account is a new [[mw:Special:MyLanguage/User account types|type of user account]]. It enhances the logged-out editors' privacy and makes it easier for community members to communicate with them. If you maintain any tools, bots, or gadgets on these 12 wikis, and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]]. Read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|deployment plan across all wikis]]. * View all {{formatnum:33}} community-submitted {{PLURAL:33|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, the [[w:nr:Main Page|South Ndebele]], [[w:rsk:Главни бок|Pannonian Rusyn]], [[w:ann:Uwu|Obolo]], [[w:iba:Lambar Keterubah|Iban]] and [[w:tdd:ᥞᥨᥝᥴ ᥘᥣᥲ ᥖᥥᥰ|Tai Nüa]] Wikipedia languages were created last week. [https://www.wikidata.org/wiki/Q36785][https://www.wikidata.org/wiki/Q35660][https://www.wikidata.org/wiki/Q36614][https://www.wikidata.org/wiki/Q33424][https://www.wikidata.org/wiki/Q36556] * It is now possible to create functions on Wikifunctions using Wikidata lexemes, through the new [[f:Z6005|Wikidata lexeme type]] launched last week. When you go to one of these functions, the user interface provides a lexeme selector that helps you pick a lexeme from Wikidata that matches the word you type. After hitting run, your selected lexeme is retrieved from Wikidata, transformed into a Wikidata lexeme type, and passed into the selected function. Read more about this in [[f:Special:MyLanguage/Wikifunctions:Status updates/2024-10-17#Function of the Week: select representation from lexeme|the latest Wikifunctions newsletter]]. '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Users of the Wikimedia sites can now format dates more easily in different languages with the new <code dir="ltr">{{[[mw:Special:MyLanguage/Help:Extension:ParserFunctions##timef|#timef]]:…}}</code> parser function. For example, <code dir="ltr"><nowiki>{{#timef:now|date|en}}</nowiki></code> will show as "<bdi lang="en" dir="ltr">{{#timef:now|date|en}}</bdi>". Previously, <code dir="ltr"><nowiki>{{#time:…}}</nowiki></code> could be used to format dates, but this required knowledge of the order of the time and date components and their intervening punctuation. <code dir="ltr">#timef</code> (or <code dir="ltr">#timefl</code> for local time) provides access to the standard date formats that MediaWiki uses in its user interface. This may help to simplify some templates on multi-lingual wikis like Commons and Meta. [https://phabricator.wikimedia.org/T223772][https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:ParserFunctions##timef] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Commons and Meta users can now efficiently [[mw:Special:MyLanguage/Help:Magic words#Localization|retrieve the user's language]] using <code dir="ltr"><nowiki>{{USERLANGUAGE}}</nowiki></code> instead of using <code dir="ltr"><nowiki>{{int:lang}}</nowiki></code>. [https://phabricator.wikimedia.org/T4085] * The [[m:Special:MyLanguage/Product and Technology Advisory Council|Product and Tech Advisory Council]] (PTAC) now has its pilot members with representation across Africa, Asia, Europe, North America and South America. They will work to address the [[Special:MyLanguage/Movement Strategy/Initiatives/Technology Council|Movement Strategy's Technology Council]] initiative of having a co-defined and more resilient technological platform. [https://meta.wikimedia.org/wiki/Movement_Strategy/Initiatives/Technology_Council] '''In depth''' * The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/32|Growth newsletter]] is available. It includes: an upcoming Newcomer Homepage Community Updates module, new Community Configuration options, and details on new projects. * The Wikimedia Foundation is [[mw:Special:MyLanguage/Wikimedia Security Team#CNA Partnership|now an official partner of the CVE program]], which is an international effort to catalog publicly disclosed cybersecurity vulnerabilities. This partnership will allow the Security Team to instantly publish [[w:en:Common Vulnerabilities and Exposures|common vulnerabilities and exposures]] (CVE) records that are affecting MediaWiki core, extensions, and skins, along with any other code the Foundation is a steward of. * The [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]] is now [[m:Community Wishlist/Updates#October 16, 2024: Conversations Made Easier: Machine-Translated Wishes Are Here!|testing machine translations]] for Wishlist content. Volunteers can now read machine-translated versions of wishes and dive into discussions even before translators arrive to translate content. '''Meetings and events''' * 24 October - Wiki Education Speaker Series Webinar - [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/N4XTB4G55BUY3M3PNGUAKQWJ7A4UOPAK/ Open Source Tech: Building the Wiki Education Dashboard], featuring Wikimedia interns and a Web developer in the panel. * 20–22 December 2024 - [[m:Special:MyLanguage/Indic Wikimedia Hackathon Bhubaneswar 2024|Indic Wikimedia Hackathon Bhubaneswar 2024]] in Odisha, India. A hackathon for community members, including developers, designers and content editors, to build technical solutions that improve contributors' experiences. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W43"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:52, 21 October 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27634672 --> == Tech News: 2024-44 == <section begin="technews-2024-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/44|Translations]] are available. '''Updates for editors''' * Later in November, the Charts extension will be deployed to the test wikis in order to help identify and fix any issue. A security review is underway to then enable deployment to pilot wikis for broader testing. You can read [[mw:Special:MyLanguage/Extension:Chart/Project/Updates#October 2024: Working towards production deployment|the October project update]] and see the [https://en.wikipedia.beta.wmflabs.org/wiki/Charts latest documentation and examples on Beta Wikipedia]. * View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[w:en:PediaPress|Pediapress.com]], an external service that creates books from Wikipedia, can now use [[mw:Special:MyLanguage/Wikimedia Maps|Wikimedia Maps]] to include existing pre-rendered infobox map images in their printed books on Wikipedia. [https://phabricator.wikimedia.org/T375761] '''Updates for technical contributors''' * Wikis can use [[:mw:Special:MyLanguage/Extension:GuidedTour|the Guided Tour extension]] to help newcomers understand how to edit. The Guided Tours extension now works with [[mw:Special:MyLanguage/Manual:Dark mode|dark mode]]. Guided Tour maintainers can check their tours to see that nothing looks odd. They can also set <code>emitTransitionOnStep</code> to <code>true</code> to fix an old bug. They can use the new flag <code>allowAutomaticBack</code> to avoid back-buttons they don't want. [https://phabricator.wikimedia.org/T73927#10241528] * Administrators in the Wikimedia projects who use the [[mw:Special:MyLanguage/Help:Extension:Nuke|Nuke Extension]] will notice that mass deletions done with this tool have the "Nuke" tag. This change will make reviewing and analyzing deletions performed with the tool easier. [https://phabricator.wikimedia.org/T366068] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W44"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:56, 28 October 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27668811 --> == Tech News: 2024-45 == <section begin="technews-2024-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/45|Translations]] are available. '''Updates for editors''' * Stewards can now make [[m:Special:MyLanguage/Global blocks|global account blocks]] cause global [[mw:Special:MyLanguage/Autoblock|autoblocks]]. This will assist stewards in preventing abuse from users who have been globally blocked. This includes preventing globally blocked temporary accounts from exiting their session or switching browsers to make subsequent edits for 24 hours. Previously, temporary accounts could exit their current session or switch browsers to continue editing. This is an anti-abuse tool improvement for the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project. You can read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|progress on key features for temporary accounts]]. [https://phabricator.wikimedia.org/T368949] * Wikis that have the [[m:Special:MyLanguage/CampaignEvents/Deployment status|CampaignEvents extension enabled]] can now use the [[m:Special:MyLanguage/Campaigns/Foundation Product Team/Event list#October 29, 2024: Collaboration List launched|Collaboration List]] feature. This list provides a new, easy way for contributors to learn about WikiProjects on their wikis. Thanks to the Campaign team for this work that is part of [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product %26 Technology OKRs#WE KRs|the 2024/25 annual plan]]. If you are interested in bringing the CampaignEvents extension to your wiki, you can [[m:Special:MyLanguage/CampaignEvents/Deployment status#How to Request the CampaignEvents Extension for your wiki|follow these steps]] or you can reach out to User:Udehb-WMF for help. * The text color for red links will be slightly changed later this week to improve their contrast in light mode. [https://phabricator.wikimedia.org/T370446] * View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, on multilingual wikis, users [[phab:T216368|can now]] hide translations from the WhatLinksHere special page. '''Updates for technical contributors''' * XML [[m:Special:MyLanguage/Data dumps|data dumps]] have been temporarily paused whilst a bug is investigated. [https://lists.wikimedia.org/hyperkitty/list/xmldatadumps-l@lists.wikimedia.org/message/BXWJDPO5QI2QMBCY7HO36ELDCRO6HRM4/] '''In depth''' * Temporary Accounts have been deployed to six wikis; thanks to the Trust and Safety Product team for [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|this work]], you can read about [[phab:T340001|the deployment plans]]. Beginning next week, Temporary Accounts will also be enabled on [[phab:T378336|seven other projects]]. If you are active on these wikis and need help migrating your tools, please reach out to [[m:User:Udehb-WMF|User:Udehb-WMF]] for assistance. * The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/October|Language and Internationalization newsletter]] is available. It includes: New languages supported in translatewiki or in MediaWiki; New keyboard input methods for some languages; details about recent and upcoming meetings, and more. '''Meetings and events''' * [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] is happening in Vienna, Austria and online from 4 to 6 November 2024. The conference will feature discussions around the usage of MediaWiki software by and within companies in different industries and will inspire and onboard new users. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W45"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:50, 4 November 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27693917 --> == Tech News: 2024-46 == <section begin="technews-2024-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/46|Translations]] are available. '''Updates for editors''' * On wikis with the [[mw:Special:MyLanguage/Help:Extension:Translate|Translate extension]] enabled, users will notice that the FuzzyBot will now automatically create translated versions of categories used on translated pages. [https://phabricator.wikimedia.org/T285463] * View all {{formatnum:29}} community-submitted {{PLURAL:29|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the submitted task to use the [[mw:Special:MyLanguage/Extension:SecurePoll|SecurePoll extension]] for English Wikipedia's special [[w:en:Wikipedia:Administrator elections|administrator election]] was resolved on time. [https://phabricator.wikimedia.org/T371454] '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] In <code dir="ltr">[[mw:MediaWiki_1.44/wmf.2|1.44.0-wmf-2]]</code>, the logic of Wikibase function <code>getAllStatements</code> changed to behave like <code>getBestStatements</code>. Invoking the function now returns a copy of values which are immutable. [https://phabricator.wikimedia.org/T270851] * [https://en.wikipedia.org/api/rest_v1/ Wikimedia REST API] users, such as bot operators and tool maintainers, may be affected by ongoing upgrades. The API will be rerouting some page content endpoints from RESTbase to the newer [[mw:Special:MyLanguage/API:REST API|MediaWiki REST API]] endpoints. The [[phab:T374683|impacted endpoints]] include getting page/revision metadata and rendered HTML content. These changes will be available on testwiki later this week, with other projects to follow. This change should not affect existing functionality, but active users of the impacted endpoints should verify behavior on testwiki, and raise any concerns on the related [[phab:T374683|Phabricator ticket]]. '''In depth''' * Admins and users of the Wikimedia projects [[mw:Special:MyLanguage/Moderator_Tools/Automoderator#Usage|where Automoderator is enabled]] can now monitor and evaluate important metrics related to Automoderator's actions. [https://superset.wmcloud.org/superset/dashboard/unified-automoderator-activity-dashboard/ This Superset dashboard] calculates and aggregates metrics about Automoderator's behaviour on the projects in which it is deployed. Thanks to the Moderator Tools team for this Dashboard; you can visit [[mw:Special:MyLanguage/Moderator Tools/Automoderator/Unified Activity Dashboard|the documentation page]] for more information about this work. [https://phabricator.wikimedia.org/T369488] '''Meetings and events''' * 21 November 2024 ([[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 8:00 UTC|8:00 UTC]] & [[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 16:00 UTC|16:00 UTC]]) - [[c:Commons:WMF support for Commons/Commons community calls|Community call]] with Wikimedia Commons volunteers and stakeholders to help prioritize support efforts for 2025-2026 Fiscal Year. The theme of this call is how content should be organised on Wikimedia Commons. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W46"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:07, 12 November 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27732268 --> 1jl48n2swnguso1h1p7b1me7dn7e5mz U. S. Government/U. S. Branches/Executive Branch 0 191845 2684163 1517366 2024-11-12T06:16:47Z 27.147.228.7 /* See also */ 2684163 wikitext text/x-wiki # The powers and responsibilities of the executive branch is found in Article 2 of the Constitution. # The executive branch is headed by the president of the United States, the chief executive officer of the nation. ===Powers of the Executive Branch=== *Executes the law of the land. *Prepare the annual budget for congressional actions. *Appoint cabinet officers, ambassadors, and federal judges. *Administers the federal bureaucracy. ====In What Ways Does the Executive Branch Influence Policy making?==== # Propose legislation in an annual speech to Congress. This is the State of the Union Address. # Appeal directly to the people to push for legislation. # Approve or veto legislation. # Appoint officials who interpret and execute the laws. These appointed officials make up the [[ U. S. Government/U. S. Branches/Judicial Branch|Judicial Branch]], agencies, and regulatory groups. ===President's Roles=== ==== Chief of State ==== # Ceremonial head of the government. ==== Chief Executive ==== # Carries out laws # Issues executive orders # Appoint Officials who are then approved by the Senate # Head of large bureaucracy ==== Chief Legislature ==== # Ask Senators and Representatives to sponsor bills # Gives State of the Union Address # Sign/Veto Bills # Propose the annual budget # Calls special sessions of Congress ==== Commander-in-Chief ==== # Has final responsibility for the military # The War Act allows the President to send troops into combat for 60 days WITHOUT Congress approval ==== Chief Diplomat ==== # Deals with foreign countries # Appoints ambassadors. # Makes treaties which are then approved by the senate # Makes executive agreements with other countries that do NOT need Senate approval ==== Chief of Party ==== # Supports party members in Elections # Gives jobs to party supporters, also known as patronage. ==== Chief Citizen ==== # Representative of the people. ==See also== *For a vocab list, see '''[[U. S. Government/U. S. Branches/Executive Branch/Vocabulary|here]]''' *[[U. S. Government/U. S. Branches/Executive Branch/Separation of Powers]] *''[https://www.icslegal.co/ sponsor licence guidance]'' , research from the Executive Sponsor - ICS Legal [[Category:Executive Branch]] bcrm5zpz0csz9ezutuj6vctgvdra83x Haskell programming in plain view 0 203942 2683983 2683327 2024-11-11T21:05:41Z Young1lim 21186 /* Lambda Calculus */ 2683983 wikitext text/x-wiki ==Introduction== * Overview I ([[Media:HSKL.Overview.1.A.20160806.pdf |pdf]]) * Overview II ([[Media:HSKL.Overview.2.A.20160926.pdf |pdf]]) * Overview III ([[Media:HSKL.Overview.3.A.20161011.pdf |pdf]]) * Overview IV ([[Media:HSKL.Overview.4.A.20161104.pdf |pdf]]) * Overview V ([[Media:HSKL.Overview.5.A.20161108.pdf |pdf]]) </br> ==Applications== * Sudoku Background ([[Media:Sudoku.Background.0.A.20161108.pdf |pdf]]) * Bird's Implementation :- Specification ([[Media:Sudoku.1Bird.1.A.Spec.20170425.pdf |pdf]]) :- Rules ([[Media:Sudoku.1Bird.2.A.Rule.20170201.pdf |pdf]]) :- Pruning ([[Media:Sudoku.1Bird.3.A.Pruning.20170211.pdf |pdf]]) :- Expanding ([[Media:Sudoku.1Bird.4.A.Expand.20170506.pdf |pdf]]) </br> ==Using GHCi== * Getting started ([[Media:GHCi.Start.1.A.20170605.pdf |pdf]]) </br> ==Using Libraries== * Library ([[Media:Library.1.A.20170605.pdf |pdf]]) </br> </br> ==Types== * Constructors ([[Media:Background.1.A.Constructor.20180904.pdf |pdf]]) * TypeClasses ([[Media:Background.1.B.TypeClass.20180904.pdf |pdf]]) * Types ([[Media:MP3.1A.Mut.Type.20200721.pdf |pdf]]) * Primitive Types ([[Media:MP3.1B.Mut.PrimType.20200611.pdf |pdf]]) * Polymorphic Types ([[Media:MP3.1C.Mut.Polymorphic.20201212.pdf |pdf]]) ==Functions== * Functions ([[Media:Background.1.C.Function.20180712.pdf |pdf]]) * Operators ([[Media:Background.1.E.Operator.20180707.pdf |pdf]]) * Continuation Passing Style ([[Media:MP3.1D.Mut.Continuation.20220110.pdf |pdf]]) ==Expressions== * Expressions I ([[Media:Background.1.D.Expression.20180707.pdf |pdf]]) * Expressions II ([[Media:MP3.1E.Mut.Expression.20220628.pdf |pdf]]) * Non-terminating Expressions ([[Media:MP3.1F.Mut.Non-terminating.20220616.pdf |pdf]]) </br> </br> ==Lambda Calculus== * Lambda Calculus - informal description ([[Media:LCal.1A.informal.20220831.pdf |pdf]]) * Lambda Calculus - Formal definition ([[Media:LCal.2A.formal.20221015.pdf |pdf]]) * Expression Reduction ([[Media:LCal.3A.reduction.20220920.pdf |pdf]]) * Normal Forms ([[Media:LCal.4A.Normal.20220903.pdf |pdf]]) * Encoding Datatypes :- Church Numerals ([[Media:LCal.5A.Numeral.20230627.pdf |pdf]]) :- Church Booleans ([[Media:LCal.6A.Boolean.20230815.pdf |pdf]]) :- Functions ([[Media:LCal.7A.Function.20231230.pdf |pdf]]) :- Combinators ([[Media:LCal.8A.Combinator.20241112.pdf |pdf]]) :- Recursions ([[Media:LCal.9A.Recursion.20240418.pdf |pdf]]) </br> </br> ==Function Oriented Typeclasses== === Functors === * Functor Overview ([[Media:Functor.1.A.Overview.20180802.pdf |pdf]]) * Function Functor ([[Media:Functor.2.A.Function.20180804.pdf |pdf]]) * Functor Lifting ([[Media:Functor.2.B.Lifting.20180721.pdf |pdf]]) === Applicatives === * Applicatives Overview ([[Media:Applicative.3.A.Overview.20180606.pdf |pdf]]) * Applicatives Methods ([[Media:Applicative.3.B.Method.20180519.pdf |pdf]]) * Function Applicative ([[Media:Applicative.3.A.Function.20180804.pdf |pdf]]) * Applicatives Sequencing ([[Media:Applicative.3.C.Sequencing.20180606.pdf |pdf]]) === Monads I : Background === * Side Effects ([[Media:Monad.P1.1A.SideEffect.20190316.pdf |pdf]]) * Monad Overview ([[Media:Monad.P1.2A.Overview.20190308.pdf |pdf]]) * Monadic Operations ([[Media:Monad.P1.3A.Operations.20190308.pdf |pdf]]) * Maybe Monad ([[Media:Monad.P1.4A.Maybe.201900606.pdf |pdf]]) * IO Actions ([[Media:Monad.P1.5A.IOAction.20190606.pdf |pdf]]) * Several Monad Types ([[Media:Monad.P1.6A.Types.20191016.pdf |pdf]]) === Monads II : State Transformer Monads === * State Transformer : - State Transformer Basics ([[Media:MP2.1A.STrans.Basic.20191002.pdf |pdf]]) : - State Transformer Generic Monad ([[Media:MP2.1B.STrans.Generic.20191002.pdf |pdf]]) : - State Transformer Monads ([[Media:MP2.1C.STrans.Monad.20191022.pdf |pdf]]) * State Monad : - State Monad Basics ([[Media:MP2.2A.State.Basic.20190706.pdf |pdf]]) : - State Monad Methods ([[Media:MP2.2B.State.Method.20190706.pdf |pdf]]) : - State Monad Examples ([[Media:MP2.2C.State.Example.20190706.pdf |pdf]]) === Monads III : Mutable State Monads === * Mutability Background : - Inhabitedness ([[Media:MP3.1F.Mut.Inhabited.20220319.pdf |pdf]]) : - Existential Types ([[Media:MP3.1E.Mut.Existential.20220128.pdf |pdf]]) : - forall Keyword ([[Media:MP3.1E.Mut.forall.20210316.pdf |pdf]]) : - Mutability and Strictness ([[Media:MP3.1C.Mut.Strictness.20200613.pdf |pdf]]) : - Strict and Lazy Packages ([[Media:MP3.1D.Mut.Package.20200620.pdf |pdf]]) * Mutable Objects : - Mutable Variables ([[Media:MP3.1B.Mut.Variable.20200224.pdf |pdf]]) : - Mutable Data Structures ([[Media:MP3.1D.Mut.DataStruct.20191226.pdf |pdf]]) * IO Monad : - IO Monad Basics ([[Media:MP3.2A.IO.Basic.20191019.pdf |pdf]]) : - IO Monad Methods ([[Media:MP3.2B.IO.Method.20191022.pdf |pdf]]) : - IORef Mutable Variable ([[Media:MP3.2C.IO.IORef.20191019.pdf |pdf]]) * ST Monad : - ST Monad Basics ([[Media:MP3.3A.ST.Basic.20191031.pdf |pdf]]) : - ST Monad Methods ([[Media:MP3.3B.ST.Method.20191023.pdf |pdf]]) : - STRef Mutable Variable ([[Media:MP3.3C.ST.STRef.20191023.pdf |pdf]]) === Monads IV : Reader and Writer Monads === * Function Monad ([[Media:Monad.10.A.Function.20180806.pdf |pdf]]) * Monad Transformer ([[Media:Monad.3.I.Transformer.20180727.pdf |pdf]]) * MonadState Class :: - State & StateT Monads ([[Media:Monad.9.A.MonadState.Monad.20180920.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.9.B.MonadState.Class.20180920.pdf |pdf]]) * MonadReader Class :: - Reader & ReaderT Monads ([[Media:Monad.11.A.Reader.20180821.pdf |pdf]]) :: - MonadReader Class ([[Media:Monad.12.A.MonadReader.20180821.pdf |pdf]]) * Control Monad ([[Media:Monad.9.A.Control.20180908.pdf |pdf]]) === Monoid === * Monoids ([[Media:Monoid.4.A.20180508.pdf |pdf]]) === Arrow === * Arrows ([[Media:Arrow.1.A.20190504.pdf |pdf]]) </br> ==Polymorphism== * Polymorphism Overview ([[Media:Poly.1.A.20180220.pdf |pdf]]) </br> ==Concurrent Haskell == </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://learnyouahaskell.com/introduction Learn you Haskell] * [http://book.realworldhaskell.org/read/ Real World Haskell] * [http://www.scs.stanford.edu/14sp-cs240h/slides/ Standford Class Material] [[Category:Haskell|programming in plain view]] 7v0ggekia4xpaqekruay4c82mod2jhc Python programming in plain view 0 212733 2684112 2683404 2024-11-12T02:39:12Z Young1lim 21186 /* Using Libraries */ 2684112 wikitext text/x-wiki ==''' Part I '''== <!----------------------------------------------------------------------> === Introduction === * Overview * Memory * Number <!----------------------------------------------------------------------> === Python for C programmers === * Hello, World! ([[Media:CProg.Hello.1A.20230406.pdf |pdf]]) * Statement Level ([[Media:CProg.Statement.1A.20230509.pdf |pdf]]) * Output with print * Formatted output * File IO <!----------------------------------------------------------------------> === Using Libraries === * Scripts ([[Media:Python.Work2.Script.1A.20231129.pdf |pdf]]) * Modules ([[Media:Python.Work2.Module.1A.20231216.pdf |pdf]]) * Packages ([[Media:Python.Work2.Package.1A.20241112.pdf |pdf]]) * Libraries ([[Media:Python.Work2.Library.1A.20241109.pdf |pdf]]) * Namespaces ([[Media:Python.Work2.Scope.1A.20231021.pdf |pdf]]) <!----------------------------------------------------------------------> === Handling Repetition === * Control ([[Media:Python.Repeat1.Control.1.A.20230314.pdf |pdf]]) * Loop ([[Media:Repeat2.Loop.1A.20230401.pdf |pdf]]) <!----------------------------------------------------------------------> === Handling a Big Work === * Functions ([[Media:Python.Work1.Function.1A.20230529.pdf |pdf]]) * Lambda ([[Media:Python.Work2.Lambda.1A.20230705.pdf |pdf]]) * Type Annotations ([[Media:Python.Work2.AtypeAnnot.1A.20230817.pdf |pdf]]) <!----------------------------------------------------------------------> === Handling Series of Data === * Arrays ([[Media:Python.Series1.Array.1A.pdf |pdf]]) * Tuples ([[Media:Python.Series2.Tuple.1A.pdf |pdf]]) * Lists ([[Media:Python.Series3.List.1A.pdf |pdf]]) * Tuples ([[Media:Python.Series4.Tuple.1A.pdf |pdf]]) * Sets ([[Media:Python.Series5.Set.1A.pdf |pdf]]) * Dictionary ([[Media:Python.Series6.Dictionary.1A.pdf |pdf]]) <!----------------------------------------------------------------------> === Handling Various Kinds of Data === * Types * Operators ([[Media:Python.Data3.Operators.1.A.pdf |pdf]]) * Files ([[Media:Python.Data4.File.1.A.pdf |pdf]]) <!----------------------------------------------------------------------> === Class and Objects === * Classes & Objects ([[Media:Python.Work2.Class.1A.20230906.pdf |pdf]]) * Inheritance <!----------------------------------------------------------------------> </br> == Python in Numerical Analysis == </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] ==External links== * [http://www.southampton.ac.uk/~fangohr/training/python/pdfs/Python-for-Computational-Science-and-Engineering.pdf Python and Computational Science and Engineering] phvbfnu84n1ot9s9h5905ho8dmzjc4r The necessities in Microprocessor Based System Design 0 232469 2683991 2683334 2024-11-11T21:13:48Z Young1lim 21186 /* ARM Assembly Programming (II) */ 2683991 wikitext text/x-wiki == '''Background''' == '''Combinational and Sequential Circuits''' * [[Media:DD2.B.4..Adder.20131007.pdf |Adder]] * [[Media:DD3.A.1.LatchFF.20160308.pdf |Latches and Flipflops]] '''FSM''' * [[Media:DD3.A.3.FSM.20131030.pdf |FSM]] * [[Media:CArch.2.A.Bubble.20131021.pdf |FSM Example]] '''Tiny CPU Example''' * [[Media:CDsgn6.TinyCPU.2.A.ISA.20160511.pdf |Instruction Set]] * [[Media:CDsgn6.TinyCPU.2.B.DPath.20160502.pdf |Data Path]] * [[Media:CDsgn6.TinyCPU.2.C.CPath.20160427.pdf |Control Path]] * [[Media:CDsgn6.TinyCPU.2.D.Implement.20160513.pdf |FPGA Implementation]] </br> == '''Microprocessor Architecture''' == * ARM Architecture : - Programmer's Model ([[Media:ARM.1Arch.1A.Model.20180321.pdf |pdf]]) : - Pipelined Architecture ([[Media:ARM.1Arch.2A.Pipeline.20180419.pdf |pdf]]) * ARM Organization * ARM Cortex-M Processor Architecture * ARM Processor Cores </br> == '''Instruction Set Architecture''' == * ARM Instruction Set : - Overview ([[Media:ARM.2ISA.1A.Overview.20190611.pdf |pdf]]) : - Addressing Modes ([[Media:ARM.2ISA.2A.AddrMode.20191108.pdf |pdf]]) : - Multiple Transfer ([[Media:ARM.2ISA.3A.MTransfer.20190903.pdf |pdf]]) : - Assembler Format :: - Data Processing ([[Media:ARM.2ISA.4A.Proc.Format.20200204.pdf |pdf]]) :: - Data Transfer ([[Media:ARM.2ISA.4B.Trans.Format.20200205.pdf |pdf]]) :: - Coprocessor ([[Media:ARM.2ISA.4C.CoProc.Format.20191214.pdf |pdf]]) :: - Summary ([[Media:ARM.2ISA.4D.Summary.Format.20200205.pdf |pdf]]) : - Binary Encoding ([[Media:ARM.2ISA.5A.Encoding.201901105.pdf |pdf]]) * Thumb Instruction Set </br> == '''Assembly Programming''' == === ARM Assembly Programming (I) === * 1. Overview ([[Media:ARM.2ASM.1A.Overview.20200101.pdf |pdf]]) * 2. Example Programs ([[Media:ARM.2ASM.2A.Program.20200108.pdf |pdf]]) * 3. Addressing Modes ([[Media:ARM.2ASM.3A.Address.20200127.pdf |pdf]]) * 4. Data Transfer ([[Media:ARM.2ASM.4A.DTransfer.20230726.pdf |pdf]]) * 5. Data Processing ([[Media:ARM.2ASM.5A.DProcess.20200208.pdf |pdf]]) * 6. Control ([[Media:ARM.2ASM.6A.Control.20200215.pdf |pdf]]) * 7. Arrays ([[Media:ARM.2ASM.7A.Array.20200311.pdf |pdf]]) * 8. Data Structures ([[Media:ARM.2ASM.8A.DataStruct.20200718.pdf |pdf]]) * 9. Finite State Machines ([[Media:ARM.2ASM.9A.FSM.20200417.pdf |pdf]]) * 10. Functions ([[Media:ARM.2ASM.10A.Function.20210115.pdf |pdf]]) * 11. Parameter Passing ([[Media:ARM.2ASM.11A.Parameter.20210106.pdf |pdf]]) * 12. Stack Frames ([[Media:ARM.2ASM.12A.StackFrame.20210611.pdf |pdf]]) :: :: === ARM Assembly Programming (II) === :: * 1. Thumb instruction programming ([[Media:ARM.2ASM.Thumb.2024112.pdf |pdf]]) * 2. Exceptions ([[Media:ARM.2ASM.Exception.20220722.pdf |pdf]]) * 3. Exception Programming ([[Media:ARM.2ASM.ExceptionProg.20220311.pdf |pdf]]) * 4. Exception Handlers ([[Media:ARM.2ASM.ExceptionHandler.20220131.pdf |pdf]]) * 5. Interrupt Programming ([[Media:ARM.2ASM.InterruptProg.20211030.pdf |pdf]]) * 6. Interrupt Handlers ([[Media:ARM.2ASM.InterruptHandler.20211030.pdf |pdf]]) * 7. Vectored Interrupt Programming ([[Media:ARM.2ASM.VectorInt.20230610.pdf |pdf]]) * 8. Tail Chaining ([[Media:ARM.2ASM.TailChain.20230816.pdf |pdf]]) </br> * ARM Assembly Exercises ([[Media:ESys.3.A.ARM-ASM-Exercise.20160608.pdf |A.pdf]], [[Media:ESys.3.B.Assembly.20160716.pdf |B.pdf]]) :: === ARM Assembly Programming (III) === * 1. Fixed point arithmetic (integer division) * 2. Floating point arithmetic * 3. Matrix multiply === ARM Linking === * arm link ([[Media:arm_link.20211208.pdf |pdf]]) </br> === ARM Microcontroller Programming === * 1. Input / Output * 2. Serial / Parallel Port Interfacing * 3. Analog I/O Interfacing * 4. Communication </br> == '''Memory Architecture''' == </br> === '''Memory Hierarchy''' === </br> === '''System and Peripheral Buses''' === </br> === '''Architectural Support''' === * High Level Languages * System Development * Operating Systems </br> == '''Peripheral Architecture''' == </br> === '''Vectored Interrupt Controller ''' === </br> === '''Timers ''' === * Timer / Counter ([[Media:ARM.4ASM.Timer.20220801.pdf |pdf]]) * Real Time Clock * Watchdog Timer </br> === '''Serial Bus''' === * '''UART''' : Universal Asynchronous Receiver/Transmitter ([[Media:ARM.4ASM.UART.20220924.pdf |pdf]]) * '''I2C''' : Inter-Integrated Circuit * '''SPI''' : Serial Peripheral Interface * '''USB''' : Universal Serial Bus Device Controller </br> === '''I/Os ''' === * General Purpose Input/Output ports (GPIO) * Pulse Width Modulator * Analog-to-Digital Converter (ADC) * Digital-to-Analog Converter (DAC) </br> <!-- == '''Interrupts and Exceptions ''' == --> </br> == '''Synchrnoization'''== </br> === H/W and S/W Synchronization === * busy wait synchronization * handshake interface </br> === Interrupt Synchronization === * interrupt synchronization * reentrant programming * buffered IO * periodic interrupt * periodic polling </br> ==''' Interfacing '''== </br> === Time Interfacing === * input capture * output compare </br> === Serial Interfacing === * Programming UART * Programming SPI * Programming I2C * Programming USB </br> === Analog Interfacing === * OP Amp * Filters * ADC * DAC </br> == '''Old materials''' == === '''Instruction Set Architecture''' === * ARM Instruction Set :: - Overview ([[Media:ARM.2ISA.1A.Overview.20180528.pdf |pdf]]) :: - Binary Encoding ([[Media:ARM.2ISA.2A.Encoding.20180528.pdf |pdf]]) :: - Assembler Format ([[Media:ARM.2ISA.3A.Format.20180528.pdf |pdf]]) * Thumb Instruction Set * ARM Assembly Language ([[Media:ESys3.1A.Assembly.20160608.pdf |pdf]]) * ARM Machine Language ([[Media:ESys3.2A.Machine.20160615.pdf |pdf]]) </br> </br> go to [ [[Electrical_%26_Computer_Engineering_Studies]] ] lmau3tgk9fupnb1m2kvpa7lxi9ds0u3 User talk:Bnhassin 3 250786 2684052 2679928 2024-11-12T00:07:17Z MediaWiki message delivery 983498 /* Tech News: 2024-46 */ new section 2684052 wikitext text/x-wiki == First Message Posting == Update Talk on Wikiversity [[User:Bnhassin|Bnhassin]] ([[User talk:Bnhassin|discuss]] • [[Special:Contributions/Bnhassin|contribs]]) 21:04, 29 June 2019 (UTC) == Update Sandbox User == == Posting to sandbox == Update Sandbox on Wikiversity [[User:Bnhassin/sandbox]] ([[User talk:Bnhassin|discuss]] • [[Special:Contributions/Bnhassin|contribs]])[[User:Bnhassin|Bnhassin]] ([[User talk:Bnhassin|discuss]] • [[Special:Contributions/Bnhassin|contribs]]) 11:04, 25 October 2020 (UTC) == [[m:Special:MyLanguage/Tech/News/2020/50|Tech News: 2020-50]] == <section begin="technews-2020-W50"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2020/50|Translations]] are available. '''Recent changes''' * You can now put pages on your watchlist for a limited period of time. Some wikis already had this function. [https://meta.wikimedia.org/wiki/Community_Tech/Watchlist_Expiry][https://www.mediawiki.org/wiki/Help:Watchlist_expiry] '''Changes later this week''' * Information from Wikidata that is used on a wiki page can be shown in recent changes and watchlists on a Wikimedia wiki. To see this you need to turn on showing Wikidata edits in your watchlist in the preferences. Changes to the Wikidata description in the language of a Wikimedia wiki will then be shown in recent changes and watchlists. This will not show edits to languages that are not relevant to your wiki. [https://lists.wikimedia.org/pipermail/wikidata/2020-November/014402.html][https://phabricator.wikimedia.org/T191831] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2020-12-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2020-12-09|en}}. It will be on all wikis from {{#time:j xg|2020-12-10|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * You can vote on proposals in the [[m:Special:MyLanguage/Community Wishlist Survey 2021|Community Wishlist Survey]] between 8 December and 21 December. The survey decides what the [[m:Community Tech|Community Tech team]] will work on. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/50|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2020-W50"/> 16:15, 7 December 2020 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=20754641 --> == [[m:Special:MyLanguage/Tech/News/2020/51|Tech News: 2020-51]] == <section begin="technews-2020-W51"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2020/51|Translations]] are available. '''Recent changes''' * There is a [[mw:Wikipedia for KaiOS|Wikipedia app]] for [[:w:en:KaiOS|KaiOS]] phones. It was released in India in September. It can now be downloaded in other countries too. [https://diff.wikimedia.org/2020/12/10/growing-wikipedias-reach-with-an-app-for-kaios-feature-phones/] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2020-12-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2020-12-16|en}}. It will be on all wikis from {{#time:j xg|2020-12-17|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/51|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2020-W51"/> 21:34, 14 December 2020 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=20803489 --> == [[m:Special:MyLanguage/Tech/News/2020/52|Tech News: 2020-52]] == <section begin="technews-2020-W52"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2020/52|Translations]] are available. '''Tech News''' * Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 11 January 2021. '''Recent changes''' * The <code><nowiki>{{citation needed}}</nowiki></code> template shows when a statement in a Wikipedia article needs a source. If you click on it when you edit with the visual editor there is a popup that explains this. Now it can also show the reason and when it was added. [https://phabricator.wikimedia.org/T270107] '''Changes later this week''' * There is no new MediaWiki version this week or next week. '''Future changes''' * You can [[m:WMDE Technical Wishes/Geoinformation/Ideas|propose and discuss]] what technical improvements should be done for geographic information. This could be coordinates, maps or other related things. * Some wikis use [[mw:Writing systems/LanguageConverter|LanguageConverter]] to switch between writing systems or variants of a language. This can only be done for the entire page. There will be a <code><nowiki><langconvert></nowiki></code> tag that can convert a piece of text on a page. [https://phabricator.wikimedia.org/T263082] * Oversighters and stewards can hide entries in [[Special:AbuseLog|Special:AbuseLog]]. They can soon hide multiple entries at once using checkboxes. This works like hiding normal edits. It will happen in early January. [https://phabricator.wikimedia.org/T260904] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2020/52|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2020-W52"/> 20:54, 21 December 2020 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=20833836 --> == [[m:Special:MyLanguage/Tech/News/2021/02|Tech News: 2021-02]] == <section begin="technews-2021-W02"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/02|Translations]] are available. '''Recent changes''' * You can choose to be reminded when you have not added an edit summary. This can be done in your preferences. This could conflict with the [[:w:en:CAPTCHA|CAPTCHA]]. This has now been fixed. [https://phabricator.wikimedia.org/T12729] * You can link to specific log entries. You can get these links for example by clicking the timestamps in the log. Until now, such links to private log entries showed no entry even if you had permission to view private log entries. The links now show the entry. [https://phabricator.wikimedia.org/T269761] * Admins can use the [[:mw:Special:MyLanguage/Extension:AbuseFilter|abuse filter tool]] to automatically prevent bad edits. Three changes happened last week: ** The filter editing interface now shows syntax errors while you type. This is similar to JavaScript pages. It also shows a warning for regular expressions that match the empty string. New warnings will be added later. [https://phabricator.wikimedia.org/T187686] ** [[m:Special:MyLanguage/Meta:Oversighters|Oversighters]] can now hide multiple filter log entries at once using checkboxes on [[Special:AbuseLog]]. This is how the usual revision deletion works. [https://phabricator.wikimedia.org/T260904] ** When a filter matches too many actions after it has been changed it is "throttled". The most powerful actions are disabled. This is to avoid many editors getting blocked when an administrator made a mistake. The administrator will now get a notification about this "throttle". * [[File:Octicons-tools.svg|15px|link=|Advanced item]] There is a new tool to [https://skins.wmflabs.org/?#/add build new skins]. You can also [https://skins.wmflabs.org/?#/ see] existing [[mw:Special:MyLanguage/Manual:Skins|skins]]. You can [[mw:User talk:Jdlrobson|give feedback]]. [https://lists.wikimedia.org/pipermail/wikitech-l/2020-December/094130.html] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Bots using the API no longer watch pages automatically based on account preferences. Setting the <code>watchlist</code> to <code>watch</code> will still work. This is to reduce the size of the watchlist data in the database. [https://phabricator.wikimedia.org/T258108] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[mw:Special:MyLanguage/Extension:Scribunto|Scribunto's]] [[:mw:Extension:Scribunto/Lua reference manual#File metadata|file metadata]] now includes length. [https://phabricator.wikimedia.org/T209679] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:w:en:CSS|CSS]] and [[:w:en:JavaScript|JavaScript]] code pages now have link anchors to [https://patchdemo.wmflabs.org/wikis/40e4795d4448b55a6d8c46ff414bcf78/w/index.php/MediaWiki:En.js#L-125 line numbers]. You can use wikilinks like [[:w:en:MediaWiki:Common.js#L-50]]. [https://phabricator.wikimedia.org/T29531] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] There was a [[mw:MediaWiki 1.36/wmf.25|new version]] of MediaWiki last week. You can read [[mw:MediaWiki 1.36/wmf.25/Changelog|a detailed log]] of all 763 changes. Most of them are very small and will not affect you. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-13|en}}. It will be on all wikis from {{#time:j xg|2021-01-14|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/02|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W02"/> 15:42, 11 January 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=20950047 --> == [[m:Special:MyLanguage/Tech/News/2021/03|Tech News: 2021-03]] == <section begin="technews-2021-W03"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/03|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-20|en}}. It will be on all wikis from {{#time:j xg|2021-01-21|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * The [[mw:Special:MyLanguage/Growth|Growth team]] plans to add features to [[mw:Special:MyLanguage/Growth/Personalized first day/Newcomer tasks/Experiment analysis, November 2020|get more visitors to edit]] to more Wikipedias. You can help [https://translatewiki.net/w/i.php?title=Special:Translate&group=ext-growthexperiments&language=&filter=&action=translate translating the interface]. * You will be able to read but not to edit Wikimedia Commons for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210126T07 {{#time:j xg|2021-01-26|en}} at 07:00 (UTC)]. [https://phabricator.wikimedia.org/T271791] * [[m:Special:MyLanguage/MassMessage|MassMessage]] posts could be automatically timestamped in the future. This is because MassMessage senders can now send pages using MassMessage. Pages are more difficult to sign. If there are times when a MassMessage post should not be timestamped you can [[phab:T270435|let the developers know]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/03|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W03"/> 16:10, 18 January 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=20974628 --> == [[m:Special:MyLanguage/Tech/News/2021/04|Tech News: 2021-04]] == <section begin="technews-2021-W04"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/04|Translations]] are available. '''Problems''' * You will be able to read but not to edit Wikimedia Commons for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210126T07 {{#time:j xg|2021-01-26|en}} at 07:00 (UTC)]. You will not be able to read or edit [[:wikitech:Main Page|Wikitech]] for a short time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210128T09 {{#time:j xg|2021-01-28|en}} at 09:00 (UTC)]. [https://phabricator.wikimedia.org/T271791][https://phabricator.wikimedia.org/T272388] '''Changes later this week''' * [[m:WMDE Technical Wishes/Bracket Matching|Bracket matching]] will be added to the [[mw:Special:MyLanguage/Extension:CodeMirror|CodeMirror]] syntax highlighter on the first wikis. The first wikis are German and Catalan Wikipedia and maybe other Wikimedia wikis. This will happen on 27 January. [https://phabricator.wikimedia.org/T270238] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-01-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-01-27|en}}. It will be on all wikis from {{#time:j xg|2021-01-28|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/04|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W04"/> 18:31, 25 January 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21007423 --> == [[m:Special:MyLanguage/Tech/News/2021/05|Tech News: 2021-05]] == <section begin="technews-2021-W05"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/05|Translations]] are available. '''Problems''' * [[:w:en:IPv6|IPv6 addresses]] were written in lowercase letters in diffs. This caused dead links since [[Special:Contributions|Special:Contributions]] only accepted uppercase letters for the IPs. This has been fixed. [https://phabricator.wikimedia.org/T272225] '''Changes later this week''' * You can soon use Wikidata to link to pages on the multilingual Wikisource. [https://phabricator.wikimedia.org/T138332] * Often editors use a "non-breaking space" to make a gap between two items when reading but still show them together. This can be used to avoid a line break. You will now be able to add new ones via the special character tool in the 2010, 2017, and visual editors. The character will be shown in the visual editor as a space with a grey background. [https://phabricator.wikimedia.org/T70429][https://phabricator.wikimedia.org/T96666] * [[File:Octicons-tools.svg|15px|link=| Advanced item]] Wikis use [[mw:Special:MyLanguage/Extension:AbuseFilter|abuse filters]] to stop bad edits being made. Filter maintainers can now use syntax like <code>1.2.3.4 - 1.2.3.55</code> as well as the <code>1.2.3.4/27</code> syntax for IP ranges. [https://phabricator.wikimedia.org/T218074] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.29|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-03|en}}. It will be on all wikis from {{#time:j xg|2021-02-04|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * [[mw:Skin:Minerva Neue|Minerva]] is the skin Wikimedia wikis use for mobile traffic. When a page is protected and you can't edit it you can normally read the source wikicode. This doesn't work on Minerva on mobile devices. This is being fixed. Some text might overlap. This is because your community needs to update [[MediaWiki:Protectedpagetext|MediaWiki:Protectedpagetext]] to work on mobile. You can [[phab:T208827|read more]]. [https://www.mediawiki.org/wiki/Recommendations_for_mobile_friendly_articles_on_Wikimedia_wikis#Inline_styles_should_not_use_properties_that_impact_sizing_and_positioning][https://www.mediawiki.org/wiki/Recommendations_for_mobile_friendly_articles_on_Wikimedia_wikis#Avoid_tables_for_anything_except_data] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:wikitech:Portal:Cloud VPS|Cloud VPS]] and [[:wikitech:Portal:Toolforge|Toolforge]] will change the IP address they use to contact the wikis. The new IP address will be <code>185.15.56.1</code>. This will happen on February 8. You can [[:wikitech:News/CloudVPS NAT wikis|read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/05|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W05"/> 22:38, 1 February 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21033195 --> == [[m:Special:MyLanguage/Tech/News/2021/06|Tech News: 2021-06]] == <section begin="technews-2021-W06"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/06|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Wikimedia Apps|Wikipedia app]] for Android now has watchlists and talk pages in the app. [https://play.google.com/store/apps/details?id=org.wikipedia] '''Changes later this week''' * You can see edits to chosen pages on [[Special:Watchlist|Special:Watchlist]]. You can add pages to your watchlist on every wiki you like. The [[:mw:Special:MyLanguage/Extension:GlobalWatchlist|GlobalWatchlist]] extension will come to Meta on 11 February. There you can see entries on watched pages on different wikis on the same page. The new watchlist will be found on [[m:Special:GlobalWatchlist|Special:GlobalWatchlist]] on Meta. You can choose which wikis to watch and other preferences on [[m:Special:GlobalWatchlistSettings|Special:GlobalWatchlistSettings]] on Meta. You can watch up to five wikis. [https://phabricator.wikimedia.org/T260862] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.30|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-10|en}}. It will be on all wikis from {{#time:j xg|2021-02-11|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * When admins [[mw:Special:MyLanguage/Help:Protecting and unprotecting pages|protect]] pages the form will use the [[mw:UX standardization|OOUI look]]. [[Special:Import|Special:Import]] will also get the new look. This will make them easier to use on mobile phones. [https://phabricator.wikimedia.org/T235424][https://phabricator.wikimedia.org/T108792] * Some services will not work for a short period of time from 07:00 UTC on 17 February. There might be problems with new [[m:Special:MyLanguage/Wikimedia URL Shortener|short links]], new translations, new notifications, adding new items to your [[mw:Reading/Reading Lists|reading lists]] or recording [[:w:en:Email#Tracking of sent mail|email bounces]]. This is because of database maintenance. [https://phabricator.wikimedia.org/T273758] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[m:Tech/News/2021/05|Last week]] Tech News reported that the IP address [[:wikitech:Portal:Cloud VPS|Cloud VPS]] and [[:wikitech:Portal:Toolforge|Toolforge]] use to contact the wikis will change on 8 February. This is delayed. It will happen later instead. [https://wikitech.wikimedia.org/wiki/News/CloudVPS_NAT_wikis] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/06|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W06"/> 17:42, 8 February 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21082948 --> == [[m:Special:MyLanguage/Tech/News/2021/07|Tech News: 2021-07]] == <section begin="technews-2021-W07"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/07|Translations]] are available. '''Problems''' * There were problems with recent versions of MediaWiki. Because the updates caused problems the developers rolled back to an earlier version. Some updates and new functions will come later than planned. [https://lists.wikimedia.org/pipermail/wikitech-l/2021-February/094255.html][https://lists.wikimedia.org/pipermail/wikitech-l/2021-February/094271.html] * Some services will not work for a short period of time from 07:00 UTC on 17 February. There might be problems with new [[m:Special:MyLanguage/Wikimedia URL Shortener|short links]], new translations, new notifications, adding new items to your [[mw:Reading/Reading Lists|reading lists]] or recording [[:w:en:Email#Tracking of sent mail|email bounces]]. This is because of database maintenance. [https://phabricator.wikimedia.org/T273758] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.31|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-17|en}}. It will be on all wikis from {{#time:j xg|2021-02-18|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/07|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W07"/> 17:56, 15 February 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21105437 --> == [[m:Special:MyLanguage/Tech/News/2021/08|Tech News: 2021-08]] == <div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/08|Translations]] are available. '''Recent changes''' * The visual editor will now use [[:c:Commons:Structured data/Media search|MediaSearch]] to find images. You can search for images on Commons in the visual editor when you are looking for illustrations. This is to help editors find better images. [https://phabricator.wikimedia.org/T259896] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlighter]] now works with more languages: [[:w:en:Futhark (programming language)|Futhark]], [[:w:en:Graphviz|Graphviz]]/[[:w:en:DOT (graph description language)|DOT]], CDDL and AMDGPU. [https://phabricator.wikimedia.org/T274741] '''Problems''' * Editing a [[mw:Special:MyLanguage/Extension:EasyTimeline|timeline]] might have removed all text from it. This was because of a bug and has been fixed. You might need to edit the timeline again for it to show properly. [https://phabricator.wikimedia.org/T274822] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.32|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-02-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-02-24|en}}. It will be on all wikis from {{#time:j xg|2021-02-25|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] There is a [[:m:Wikimedia Rust developers user group|user group]] for developers and users interested in working on Wikimedia wikis with the [[:w:en:Rust (programming language)|Rust programming language]]. You can join or tell others who want to make your wiki better in the future. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div> ---- 00:17, 23 February 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21134058 --> == [[m:Special:MyLanguage/Tech/News/2021/09|Tech News: 2021-09]] == <div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/09|Translations]] are available. '''Recent changes''' * Wikis using the [[mw:Special:MyLanguage/Growth/Feature summary|Growth team tools]] can now show the name of a newcomer's mentor anywhere [[mw:Special:MyLanguage/Help:Growth/Mentorship/Integrating_mentorship|through a magic word]]. This can be used for welcome messages or userboxes. * A new version of the [[c:Special:MyLanguage/Commons:VideoCutTool|VideoCutTool]] is now available. It enables cropping, trimming, audio disabling, and rotating video content. It is being created as part of the developer outreach programs. '''Problems''' * There was a problem with the [[mw:Special:MyLanguage/Manual:Job queue|job queue]]. This meant some functions did not save changes and mass messages were delayed. This did not affect wiki edits. [https://phabricator.wikimedia.org/T275437] * Some editors may not be logged in to their accounts automatically in the latest versions of Firefox and Safari. [https://phabricator.wikimedia.org/T226797] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.33|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-03|en}}. It will be on all wikis from {{#time:j xg|2021-03-04|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div> ---- 19:08, 1 March 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21161722 --> == [[m:Special:MyLanguage/Tech/News/2021/10|Tech News: 2021-10]] == <section begin="technews-2021-W10"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/10|Translations]] are available. '''Recent changes''' * [[mw:Special:MyLanguage/Content translation/Section translation|Section translation]] now works on Bengali Wikipedia. It helps mobile editors translate sections of articles. It will come to more wikis later. The first focus is active wikis with a smaller number of articles. You can [https://sx.wmflabs.org/index.php/Main_Page test it] and [[mw:Talk:Content translation/Section translation|leave feedback]]. * [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs|Flagged revisions]] now give admins the review right. [https://phabricator.wikimedia.org/T275293] * When someone links to a Wikipedia article on Twitter this will now show a preview of the article. [https://phabricator.wikimedia.org/T276185] '''Problems''' * Many graphs have [[:w:en:JavaScript|JavaScript]] errors. Graph editors can check their graphs in their browser's developer console after editing. [https://phabricator.wikimedia.org/T275833] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.34|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-10|en}}. It will be on all wikis from {{#time:j xg|2021-03-11|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). * The [[mw:Talk pages project/New discussion|New Discussion]] tool will soon be a new [[mw:Special:MyLanguage/Extension:DiscussionTools|discussion tools]] beta feature for on most Wikipedias. The goal is to make it easier to start new discussions. [https://phabricator.wikimedia.org/T275257] '''Future changes''' * There will be a number of changes to make it easier to work with templates. Some will come to the first wikis in March. Other changes will come to the first wikis in June. This is both for those who use templates and those who create or maintain them. You can [[:m:WMDE Technical Wishes/Templates|read more]]. * [[m:WMDE Technical Wishes/ReferencePreviews|Reference Previews]] will become a default feature on some wikis on 17 March. They will share a setting with [[mw:Page Previews|Page Previews]]. If you prefer the Reference Tooltips or Navigation-Popups gadget you can keep using them. If so Reference Previews won't be shown. [https://phabricator.wikimedia.org/T271206][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/ReferencePreviews] * New JavaScript-based functions will not work in [[:w:en:Internet Explorer 11|Internet Explorer 11]]. This is because Internet Explorer is an old browser that doesn't work with how JavaScript is written today. Everything that works in Internet Explorer 11 today will continue working in Internet Explorer for now. You can [[mw:Compatibility/IE11|read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/10|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W10"/> 17:51, 8 March 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21175593 --> == [[m:Special:MyLanguage/Tech/News/2021/11|Tech News: 2021-11]] == <section begin="technews-2021-W11"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/11|Translations]] are available. '''Recent changes''' * Wikis that are part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|desktop improvements]] project can now use a new [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Search|search function]]. The desktop improvements and the new search will come to more wikis later. You can also [[mw:Reading/Web/Desktop Improvements#Deployment plan and timeline|test it early]]. * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Editors who put up banners or change site-wide [[:w:en:JavaScript|JavaScript]] code should use the [https://grafana.wikimedia.org/d/000000566/overview?viewPanel=16&orgId=1 client error graph] to see that their changes has not caused problems. You can [https://diff.wikimedia.org/2021/03/08/sailing-steady%e2%80%8a-%e2%80%8ahow-you-can-help-keep-wikimedia-sites-error-free read more]. [https://phabricator.wikimedia.org/T276296] '''Problems''' * Due to [[phab:T276968|database issues]] the [https://meta.wikimedia.beta.wmflabs.org Wikimedia Beta Cluster] was read-only for over a day. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.34|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-17|en}}. It will be on all wikis from {{#time:j xg|2021-03-18|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * You can add a [[:w:en:Newline|newline]] or [[:w:en:Carriage return|carriage return]] character to a custom signature if you use a template. There is a proposal to not allow them in the future. This is because they can cause formatting problems. [https://www.mediawiki.org/wiki/New_requirements_for_user_signatures#Additional_proposal_(2021)][https://phabricator.wikimedia.org/T272322] * You will be able to read but not edit [[phab:T276899|12 wikis]] for a short period of time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210323T06 {{#time:j xg|2021-03-23|en}} at 06:00 (UTC)]. This could take 30 minutes but will probably be much faster. * [[File:Octicons-tools.svg|15px|link=|Advanced item]] You can use [https://quarry.wmflabs.org/ Quarry] for [[:w:en:SQL|SQL]] queries to the [[wikitech:Wiki replicas|Wiki Replicas]]. Cross-database <code>JOINS</code> will no longer work from 23 March. There will be a new field to specify the database to connect to. If you think this affects you and you need help you can [[phab:T268498|post on Phabricator]] or on [[wikitech:Talk:News/Wiki Replicas 2020 Redesign|Wikitech]]. [https://wikitech.wikimedia.org/wiki/PAWS PAWS] and other ways to do [[:w:en:SQL|SQL]] queries to the Wiki Replicas will be affected later. [https://wikitech.wikimedia.org/wiki/News/Wiki_Replicas_2020_Redesign] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/11|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W11"/> 23:22, 15 March 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21226057 --> == [[m:Special:MyLanguage/Tech/News/2021/12|Tech News: 2021-12]] == <section begin="technews-2021-W12"/><div class="plainlinks mw-content-ltr" lang="en" dir="ltr"><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/12|Translations]] are available. '''Recent changes''' * There is a [[mw:Wikipedia for KaiOS|Wikipedia app]] for [[:w:en:KaiOS|KaiOS]] phones. They don't have a touch screen so readers navigate with the phone keys. There is now a [https://wikimedia.github.io/wikipedia-kaios/sim.html simulator] so you can see what it looks like. * The [[mw:Special:MyLanguage/Talk pages project/Replying|reply tool]] and [[mw:Special:MyLanguage/Talk pages project/New discussion|new discussion tool]] are now available as the "{{int:discussiontools-preference-label}}" [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] in almost all wikis except German Wikipedia. '''Problems''' * You will be able to read but not edit [[phab:T276899|twelve wikis]] for a short period of time on [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210323T06 {{#time:j xg|2021-03-23|{{PAGELANGUAGE}}}} at 06:00 (UTC)]. This can also affect password changes, logging in to new wikis, global renames and changing or confirming emails. This could take 30 minutes but will probably be much faster. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.36|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-24|en}}. It will be on all wikis from {{#time:j xg|2021-03-25|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). * [[:w:en:Syntax highlighting|Syntax highlighting]] colours will change to be easier to read. This will soon come to the [[phab:T276346|first wikis]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Improved_Color_Scheme_of_Syntax_Highlighting] '''Future changes''' * [[mw:Special:MyLanguage/Extension:FlaggedRevs|Flagged revisions]] will no longer have multiple tags like "tone" or "depth". It will also only have one tier. This was changed because very few wikis used these features and they make the tool difficult to maintain. [https://phabricator.wikimedia.org/T185664][https://phabricator.wikimedia.org/T277883] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets and user scripts can access variables about the current page in JavaScript. In 2015 this was moved from <code dir=ltr>wg*</code> to <code dir=ltr>mw.config</code>. <code dir=ltr>wg*</code> will soon no longer work. [https://phabricator.wikimedia.org/T72470] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]] • [[m:Special:MyLanguage/Tech/News#contribute|Contribute]] • [[m:Special:MyLanguage/Tech/News/2021/12|Translate]] • [[m:Tech|Get help]] • [[m:Talk:Tech/News|Give feedback]] • [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div></div> <section end="technews-2021-W12"/> 16:53, 22 March 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21244806 --> == [[m:Special:MyLanguage/Tech/News/2021/13|Tech News: 2021-13]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/13|Translations]] are available. '''Recent changes''' * Some very old [[:w:en:Web browser|web browsers]] [[:mw:Special:MyLanguage/Compatibility|don’t work]] well with the Wikimedia wikis. Some old code for browsers that used to be supported is being removed. This could cause issues in those browsers. [https://phabricator.wikimedia.org/T277803] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:m:IRC/Channels#Raw_feeds|IRC recent changes feeds]] have been moved to a new server. Make sure all tools automatically reconnect to <code>irc.wikimedia.org</code> and not to the name of any specific server. Users should also consider switching to the more modern [[:wikitech:Event Platform/EventStreams|EventStreams]]. [https://phabricator.wikimedia.org/T224579] '''Problems''' * When you move a page that many editors have on their watchlist the history can be split. It might also not be possible to move it again for a while. This is because of a [[:w:en:Job queue|job queue]] problem. [https://phabricator.wikimedia.org/T278350] * Some translatable pages on Meta could not be edited. This was because of a bug in the translation tool. The new MediaWiki version was delayed because of problems like this. [https://phabricator.wikimedia.org/T278429][https://phabricator.wikimedia.org/T274940] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.37|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-03-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-03-31|en}}. It will be on all wikis from {{#time:j xg|2021-04-01|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 17:30, 29 March 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21267131 --> == [[m:Special:MyLanguage/Tech/News/2021/14|Tech News: 2021-14]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/14|Translations]] are available. '''Recent changes''' * Editors can collapse part of an article so you have to click on it to see it. When you click a link to a section inside collapsed content it will now expand to show the section. The browser will scroll down to the section. Previously such links didn't work unless you manually expanded the content first. [https://phabricator.wikimedia.org/T276741] '''Changes later this week''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:Special:MyLanguage/Citoid|citoid]] [[:w:en:API|API]] will use for example <code>2010-12-XX</code> instead of <code>2010-12</code> for dates with a month but no days. This is because <code>2010-12</code> could be confused with <code>2010-2012</code> instead of <code>December 2010</code>. This is called level 1 instead of level 0 in the [https://www.loc.gov/standards/datetime/ Extended Date/Time Format]. [https://phabricator.wikimedia.org/T132308] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.36/wmf.38|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-04-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-04-07|en}}. It will be on all wikis from {{#time:j xg|2021-04-08|en}} ([[mw:MediaWiki 1.36/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[:wikitech:PAWS|PAWS]] can now connect to the new [[:wikitech:Wiki Replicas|Wiki Replicas]]. Cross-database <code>JOINS</code> will no longer work from 28 April. There is [[:wikitech:News/Wiki Replicas 2020 Redesign#How should I connect to databases in PAWS?|a new way to connect]] to the databases. Until 28 April both ways to connect to the databases will work. If you think this affects you and you need help you can post [[phab:T268498|on Phabricator]] or on [[wikitech:Talk:News/Wiki Replicas 2020 Redesign|Wikitech]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 19:41, 5 April 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21287348 --> == [[m:Special:MyLanguage/Tech/News/2021/16|Tech News: 2021-16]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/16|Translations]] are available. '''Recent changes''' * Email to the Wikimedia wikis are handled by groups of Wikimedia editors. These volunteer response teams now use [https://github.com/znuny/Znuny Znuny] instead of [[m:Special:MyLanguage/OTRS|OTRS]]. The functions and interface remain the same. The volunteer administrators will give more details about the next steps soon. [https://phabricator.wikimedia.org/T279303][https://phabricator.wikimedia.org/T275294] * If you use [[Mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighting]], you can see line numbers in the 2010 and 2017 wikitext editors when editing templates. This is to make it easier to see line breaks or talk about specific lines. Line numbers will soon come to all namespaces. [https://phabricator.wikimedia.org/T267911][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Line_Numbering][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/Line_Numbering] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Because of a technical change there could be problems with gadgets and scripts that have an edit summary area that looks [https://phab.wmfusercontent.org/file/data/llvdqqnb5zpsfzylbqcg/PHID-FILE-25vs4qowibmtysl7cbml/Screen_Shot_2021-04-06_at_2.34.04_PM.png similar to this one]. If they look strange they should use <code>mw.loader.using('mediawiki.action.edit.styles')</code> to go back to how they looked before. [https://phabricator.wikimedia.org/T278898] * The [[mw:MediaWiki 1.37/wmf.1|latest version]] of MediaWiki came to the Wikimedia wikis last week. There was no Tech News issue last week. '''Changes later this week''' * There is no new MediaWiki version this week. '''Future changes''' * The user group <code>oversight</code> will be renamed <code>suppress</code>. This is for [[phab:T109327|technical reasons]]. This is the technical name. It doesn't affect what you call the editors with this user right on your wiki. This is planned to happen in two weeks. You can comment [[phab:T112147|in Phabricator]] if you have objections. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 16:48, 19 April 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21356080 --> == [[m:Special:MyLanguage/Tech/News/2021/17|Tech News: 2021-17]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/17|Translations]] are available. '''Recent changes''' * Templates have parameters that can have specific values. It is possible to suggest values for editors with [[mw:Special:MyLanguage/Extension:TemplateData|TemplateData]]. You can soon see them as a drop-down list in the visual editor. This is to help template users find the right values faster. [https://phabricator.wikimedia.org/T273857][https://meta.wikimedia.org/wiki/Special:MyLanguage/WMDE_Technical_Wishes/Suggested_values_for_template_parameters][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/Suggested_values_for_template_parameters] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-04-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-04-28|en}}. It will be on all wikis from {{#time:j xg|2021-04-29|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 21:24, 26 April 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21391118 --> == [[m:Special:MyLanguage/Tech/News/2021/18|Tech News: 2021-18]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/18|Translations]] are available. '''Recent changes''' * [[w:en:Wikipedia:Twinkle|Twinkle]] is a gadget on English Wikipedia. It can help with maintenance and patrolling. It can [[m:Grants:Project/Rapid/SD0001/Twinkle localisation/Report|now be used on other wikis]]. You can get Twinkle on your wiki using the [https://github.com/wikimedia-gadgets/twinkle-starter twinkle-starter] GitHub repository. '''Problems''' * The [[mw:Special:MyLanguage/Content translation|content translation tool]] did not work for many articles for a little while. This was because of a bug. [https://phabricator.wikimedia.org/T281346] * Some things will not work for about a minute on 5 May. This will happen [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210505T0600 around 06:00 UTC]. This will affect the content translation tool and notifications among other things. This is because of an upgrade to avoid crashes. [https://phabricator.wikimedia.org/T281212] '''Changes later this week''' * [[mw:Special:MyLanguage/Help:Reference Previews|Reference Previews]] will become a default feature on a number of wikis on 5 May. This is later than planned because of some changes. You can use it without using [[mw:Special:MyLanguage/Page Previews|Page Previews]] if you want to. The earlier plan was to have the preference to use both or none. [https://phabricator.wikimedia.org/T271206][https://meta.wikimedia.org/wiki/Talk:WMDE_Technical_Wishes/ReferencePreviews] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-05|en}}. It will be on all wikis from {{#time:j xg|2021-05-06|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[:w:en:CSS|CSS]] classes <code dir=ltr>.error</code>, <code dir=ltr>.warning</code> and <code dir=ltr>.success</code> do not work for mobile readers if they have not been specifically defined on your wiki. From June they will not work for desktop readers. This can affect gadgets and templates. The classes can be defined in [[MediaWiki:Common.css]] or template styles instead. [https://phabricator.wikimedia.org/T280766] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:43, 3 May 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21418010 --> == [[m:Special:MyLanguage/Tech/News/2021/19|Tech News: 2021-19]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/19|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-12|en}}. It will be on all wikis from {{#time:j xg|2021-05-13|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * You can see what participants plan to work on at the online [[mw:Wikimedia Hackathon 2021|Wikimedia hackathon]] 22–23 May. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:10, 10 May 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21428676 --> == [[m:Special:MyLanguage/Tech/News/2021/20|Tech News: 2021-20]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/20|Translations]] are available. '''Recent changes''' * There is a new toolbar in [[mw:Talk pages project/Replying|the Reply tool]]. It works in the wikitext source mode. You can enable it in [[Special:Preferences#mw-htmlform-discussion|your preferences]]. [https://phabricator.wikimedia.org/T276608] [https://www.mediawiki.org/wiki/Talk_pages_project/Replying#13_May_2021] [https://www.mediawiki.org/wiki/Talk_pages_project/New_discussion#13_May_2021] * Wikimedia [https://lists.wikimedia.org/mailman/listinfo mailing lists] are being moved to [[:w:en:GNU Mailman|Mailman 3]]. This is a newer version. For the [[:w:en:Character encoding|character encoding]] to work it will change from <code>[[:w:en:UTF-8|UTF-8]]</code> to <code>utf8mb3</code>. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IEYQ2HS3LZF2P3DAYMNZYQDGHWPVMTPY/][https://phabricator.wikimedia.org/T282621] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] An [[m:Special:MyLanguage/Tech/News/2021/14|earlier issue]] of Tech News said that the [[mw:Special:MyLanguage/Citoid|citoid]] [[:w:en:API|API]] would handle dates with a month but no days in a new way. This has been reverted for now. There needs to be more discussion of how it affects different wikis first. [https://phabricator.wikimedia.org/T132308] '''Changes later this week''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] <code>MediaWiki:Pageimages-blacklist</code> will be renamed <code>MediaWiki:Pageimages-denylist</code>. The list can be copied to the new name. It will happen on 19 May for some wikis and 20 May for some wikis. Most wikis don't use it. It lists images that should never be used as thumbnails for articles. [https://phabricator.wikimedia.org/T282626] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-19|en}}. It will be on all wikis from {{#time:j xg|2021-05-20|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 13:49, 17 May 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21464279 --> == [[m:Special:MyLanguage/Tech/News/2021/21|Tech News: 2021-21]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/21|Translations]] are available. '''Recent changes''' * The Wikimedia movement has been using [[:m:Special:MyLanguage/IRC|IRC]] on a network called [[:w:en:Freenode|Freenode]]. There have been changes around who is in control of the network. The [[m:Special:MyLanguage/IRC/Group_Contacts|Wikimedia IRC Group Contacts]] have [[m:Special:Diff/21476411|decided]] to move to the new [[:w:en:Libera Chat|Libera Chat]] network instead. This is not a formal decision for the movement to move all channels but most Wikimedia IRC channels will probably leave Freenode. There is a [[:m:IRC/Migrating_to_Libera_Chat|migration guide]] and ongoing Wikimedia [[m:Wikimedia Forum#Freenode (IRC)|discussions about this]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-05-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-05-26|en}}. It will be on all wikis from {{#time:j xg|2021-05-27|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 17:07, 24 May 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21477606 --> == [[m:Special:MyLanguage/Tech/News/2021/22|Tech News: 2021-22]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/22|Translations]] are available. '''Problems''' * There was an issue on the Vector skin with the text size of categories and notices under the page title. It was fixed last Monday. [https://phabricator.wikimedia.org/T283206] '''Changes later this week''' * There is no new MediaWiki version this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 17:05, 31 May 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21516076 --> == [[m:Special:MyLanguage/Tech/News/2021/23|Tech News: 2021-23]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/23|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-09|en}}. It will be on all wikis from {{#time:j xg|2021-06-10|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * The Wikimedia movement uses [[:mw:Special:MyLanguage/Phabricator|Phabricator]] for technical tasks. This is where we collect technical suggestions, bugs and what developers are working on. The company behind Phabricator will stop working on it. This will not change anything for the Wikimedia movement now. It could lead to changes in the future. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/YAXOD46INJLAODYYIJUVQWOZFIV54VUI/][https://admin.phacility.com/phame/post/view/11/phacility_is_winding_down_operations/][https://phabricator.wikimedia.org/T283980] * Searching on Wikipedia will find more results in some languages. This is mainly true for when those who search do not use the correct [[:w:en:Diacritic|diacritics]] because they are not seen as necessary in that language. For example searching for <code>Bedusz</code> doesn't find <code>Będusz</code> on German Wikipedia. The character <code>ę</code> isn't used in German so many would write <code>e</code> instead. This will work better in the future in some languages. [https://phabricator.wikimedia.org/T219550] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[:w:en:Cross-site request forgery|CSRF token parameters]] in the [[:mw:Special:MyLanguage/API:Main page|action API]] were changed in 2014. The old parameters from before 2014 will stop working soon. This can affect bots, gadgets and user scripts that still use the old parameters. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IMP43BNCI32C524O5YCUWMQYP4WVBQ2B/][https://phabricator.wikimedia.org/T280806] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 20:02, 7 June 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21551759 --> == [[m:Special:MyLanguage/Tech/News/2021/24|Tech News: 2021-24]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/24|Translations]] are available. '''Recent changes''' * Logged-in users on the mobile web can choose to use the [[:mw:Special:MyLanguage/Reading/Web/Advanced mobile contributions|advanced mobile mode]]. They now see categories in a similar way as users on desktop do. This means that some gadgets that have just been for desktop users could work for users of the mobile site too. If your wiki has such gadgets you could decide to turn them on for the mobile site too. Some gadgets probably need to be fixed to look good on mobile. [https://phabricator.wikimedia.org/T284763] * Language links on Wikidata now works for [[:oldwikisource:Main Page|multilingual Wikisource]]. [https://phabricator.wikimedia.org/T275958] '''Changes later this week''' * There is no new MediaWiki version this week. '''Future changes''' * In the future we [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation|can't show the IP]] of unregistered editors to everyone. This is because privacy regulations and norms have changed. There is now a rough draft of how [[m:IP Editing: Privacy Enhancement and Abuse Mitigation#Updates|showing the IP to those who need to see it]] could work. * German Wikipedia, English Wikivoyage and 29 smaller wikis will be read-only for a few minutes on 22 June. This is planned between 5:00 and 5:30 UTC. [https://phabricator.wikimedia.org/T284530] * All wikis will be read-only for a few minutes in the week of 28 June. More information will be published in Tech News later. It will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T281515][https://phabricator.wikimedia.org/T281209] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 20:26, 14 June 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21587625 --> == [[m:Special:MyLanguage/Tech/News/2021/25|Tech News: 2021-25]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/25|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The <code>otrs-member</code> group name is now <code>vrt-permissions</code>. This could affect abuse filters. [https://phabricator.wikimedia.org/T280615] '''Problems''' * You will be able to read but not edit German Wikipedia, English Wikivoyage and 29 smaller wikis for a few minutes on 22 June. This is planned between [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210623T0500 5:00 and 5:30 UTC]. [https://phabricator.wikimedia.org/T284530] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-23|en}}. It will be on all wikis from {{#time:j xg|2021-06-24|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:49, 21 June 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21593987 --> == [[m:Special:MyLanguage/Tech/News/2021/26|Tech News: 2021-26]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/26|Translations]] are available. '''Recent changes''' * Wikis with the [[mw:Special:MyLanguage/Growth|Growth features]] now can [[mw:Special:MyLanguage/Growth/Community configuration|configure Growth features directly on their wiki]]. This uses the new special page <code>Special:EditGrowthConfig</code>. [https://phabricator.wikimedia.org/T285423] * Wikisources have a new [[m:Special:MyLanguage/Community Tech/OCR Improvements|OCR tool]]. If you don't want to see the "extract text" button on Wikisource you can add <code>.ext-wikisource-ExtractTextWidget { display: none; }</code> to your [[Special:MyPage/common.css|common.css page]]. [https://phabricator.wikimedia.org/T285311] '''Problems''' *You will be able to read but not edit the Wikimedia wikis for a few minutes on 29 June. This is planned at [https://www.timeanddate.com/worldclock/fixedtime.html?iso=20210629T1400 14:00 UTC]. [https://phabricator.wikimedia.org/T281515][https://phabricator.wikimedia.org/T281209] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-06-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-06-30|en}}. It will be on all wikis from {{#time:j xg|2021-07-01|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * <code>Threshold for stub link formatting</code>, <code>thumbnail size</code> and <code>auto-number headings</code> can be set in preferences. They are expensive to maintain and few editors use them. The developers are planning to remove them. Removing them will make pages load faster. You can [[mw:Special:MyLanguage/User:SKim (WMF)/Performance Dependent User Preferences|read more and give feedback]]. * A toolbar will be added to the [[mw:Talk pages project/Replying|Reply tool]]'s wikitext source mode. This will make it easier to link to pages and to ping other users. [https://phabricator.wikimedia.org/T276609][https://www.mediawiki.org/wiki/Talk_pages_project/Replying#Status_updates] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 16:32, 28 June 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21653312 --> == [[m:Special:MyLanguage/Tech/News/2021/27|Tech News: 2021-27]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/27|Translations]] are available. '''Tech News''' * The next issue of Tech News will be sent out on 19 July. '''Recent changes''' * [[:wikidata:Q4063270|AutoWikiBrowser]] is a tool to make repetitive tasks easier. It now uses [[:w:en:JSON|JSON]]. <code>Wikipedia:AutoWikiBrowser/CheckPage</code> has moved to <code>Wikipedia:AutoWikiBrowser/CheckPageJSON</code> and <code>Wikipedia:AutoWikiBrowser/Config</code>. <code>Wikipedia:AutoWikiBrowser/CheckPage/Version</code> has moved to <code>Wikipedia:AutoWikiBrowser/CheckPage/VersionJSON</code>. The tool will eventually be configured on the wiki so that you don't have to wait until the new version to add templates or regular expression fixes. [https://phabricator.wikimedia.org/T241196] '''Problems''' * [[m:Special:MyLanguage/InternetArchiveBot|InternetArchiveBot]] helps saving online sources on some wikis. It adds them to [[:w:en:Wayback Machine|Wayback Machine]] and links to them there. This is so they don't disappear if the page that was linked to is removed. It currently has a problem with linking to the wrong date when it moves pages from <code>archive.is</code> to <code>web.archive.org</code>. [https://phabricator.wikimedia.org/T283432] '''Changes later this week''' * The tool to [[m:WMDE Technical Wishes/Finding and inserting templates|find, add and remove templates]] will be updated. This is to make it easier to find and use the right templates. It will come to the first wikis on 7 July. It will come to more wikis later this year. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Removing_a_template_from_a_page_using_the_VisualEditor][https://phabricator.wikimedia.org/T284553] * There is no new MediaWiki version this week. '''Future changes''' * Some Wikimedia wikis use [[m:Special:MyLanguage/Flagged Revisions|Flagged Revisions]] or pending changes. It hides edits from new and unregistered accounts for readers until they have been patrolled. The auto review action in Flagged Revisions will no longer be logged. All old logs of auto-review will be removed. This is because it creates a lot of logs that are not very useful. [https://phabricator.wikimedia.org/T285608] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 17:33, 5 July 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21694636 --> == [[m:Special:MyLanguage/Tech/News/2021/29|Tech News: 2021-29]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/29|Translations]] are available. '''Recent changes''' * The tool to [[m:WMDE Technical Wishes/Finding and inserting templates|find, add and remove templates]] was updated. This is to make it easier to find and use the right templates. It was supposed to come to the first wikis on 7 July. It was delayed to 12 July instead. It will come to more wikis later this year. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Removing_a_template_from_a_page_using_the_VisualEditor][https://phabricator.wikimedia.org/T284553] * [[Special:UnconnectedPages|Special:UnconnectedPages]] lists pages that are not connected to Wikidata. This helps you find pages that can be connected to Wikidata items. Some pages should not be connected to Wikidata. You can use the magic word <code><nowiki>__EXPECTED_UNCONNECTED_PAGE__</nowiki></code> on pages that should not be listed on the special page. [https://phabricator.wikimedia.org/T97577] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-07-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-07-21|en}}. It will be on all wikis from {{#time:j xg|2021-07-22|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] How media is structured in the [[:w:en:Parsing|parser's]] HTML output will soon change. This can affect bots, gadgets, user scripts and extensions. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/L2UQJRHTFK5YG3IOZEC7JSLH2ZQNZRVU/ read more]. You can test it on [[:testwiki:Main Page|Testwiki]] or [[:test2wiki:Main Page|Testwiki 2]]. * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The parameters for how you obtain [[mw:API:Tokens|tokens]] in the MediaWiki API were changed in 2014. The old way will no longer work from 1 September. Scripts, bots and tools that use the parameters from before the 2014 change need to be updated. You can [[phab:T280806#7215377|read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:31, 19 July 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21755027 --> == [[m:Special:MyLanguage/Tech/News/2021/30|Tech News: 2021-30]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/30|Translations]] are available. '''Recent changes''' * A [[mw:MediaWiki 1.37/wmf.14|new version]] of MediaWiki came to the Wikimedia wikis the week before last week. This was not in Tech News because there was no newsletter that week. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-07-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-07-28|en}}. It will be on all wikis from {{#time:j xg|2021-07-29|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * If you use the [[mw:Special:MyLanguage/Skin:MonoBook|Monobook skin]] you can choose to switch off [[:w:en:Responsive web design|responsive design]] on mobile. This will now work for more skins. If <code>{{int:monobook-responsive-label}}</code> is unticked you need to also untick the new [[Special:Preferences#mw-prefsection-rendering|preference]] <code>{{int:prefs-skin-responsive}}</code>. Otherwise it will stop working. Interface admins can automate this process on your wiki. You can [[phab:T285991|read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 21:11, 26 July 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21771634 --> == [[m:Special:MyLanguage/Tech/News/2021/31|Tech News: 2021-31]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/31|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] If your wiki uses markup like <bdi lang="zxx" dir="ltr"><code><nowiki><div class="mw-content-ltr"></nowiki></code></bdi> or <bdi lang="zxx" dir="ltr"><code><nowiki><div class="mw-content-rtl"></nowiki></code></bdi> without the required <bdi lang="zxx" dir="ltr"><code>dir</code></bdi> attribute, then these will no longer work in 2 weeks. There is a short-term fix that can be added to your local wiki's Common.css page, which is explained at [[phab:T287701|T287701]]. From now on, all usages should include the full attributes, for example: <bdi lang="zxx" dir="ltr"><code><nowiki><div class="mw-content-ltr" dir="ltr" lang="en"></nowiki></code></bdi> or <bdi lang="zxx" dir="ltr"><code><nowiki><div class="mw-content-rtl" dir="rtl" lang="he"></nowiki></code></bdi>. This also applies to some other HTML tags, such as <code>span</code> or <code>code</code>. You can find existing examples on your wiki that need to be updated, using the instructions at [[phab:T287701|T287701]]. * Reminder: Wikimedia has [[m:Special:MyLanguage/IRC/Migrating to Libera Chat|migrated to the Libera Chat IRC network]], from the old Freenode network. Local documentation should be updated. '''Problems''' * Last week, all wikis had slow access or no access for 30 minutes. There was a problem with generating dynamic lists of articles on the Russian Wikinews, due to the bulk import of 200,000+ new articles over 3 days, which led to database problems. The problematic feature has been disabled on that wiki and developers are discussing if it can be fixed properly. [https://phabricator.wikimedia.org/T287380][https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-07-26_ruwikinews_DynamicPageList] '''Changes later this week''' * When adding links to a page using [[mw:VisualEditor|VisualEditor]] or the [[mw:Special:MyLanguage/2017 wikitext editor|2017 wikitext editor]], [[mw:Special:MyLanguage/Extension:Disambiguator|disambiguation pages]] will now only appear at the bottom of search results. This is because users do not often want to link to disambiguation pages. [https://phabricator.wikimedia.org/T285510] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-04|en}}. It will be on all wikis from {{#time:j xg|2021-08-05|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * The [[mw:Wikimedia Apps/Team/Android|team of the Wikipedia app for Android]] is working on communication in the app. The developers are working on how to talk to other editors and get notifications. You can [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication|read more]]. They are looking for users who want to [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication/UsertestingJuly2021|test the plans]]. Any editor who has an Android phone and is willing to download the app can do this. * The [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] for {{int:discussiontools-preference-label}} will be updated in the coming weeks. You will be able to [[mw:Talk pages project/Notifications|subscribe to individual sections]] on a talk page at more wikis. You can test this now by adding <code>?dtenable=1</code> to the end of the talk page's URL ([https://meta.wikimedia.org/wiki/Meta_talk:Sandbox?dtenable=1 example]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 20:47, 2 August 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21818289 --> == [[m:Special:MyLanguage/Tech/News/2021/32|Tech News: 2021-32]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/32|Translations]] are available. '''Problems''' * You can read but not edit 17 wikis for a few minutes on 10 August. This is planned at [https://zonestamp.toolforge.org/1628571650 05:00 UTC]. This is because of work on the database. [https://phabricator.wikimedia.org/T287449] '''Changes later this week''' * The [[wmania:Special:MyLanguage/2021:Hackathon|Wikimania Hackathon]] will take place remotely on 13 August, starting at 5:00 UTC, for 24 hours. You can participate in many ways. You can still propose projects and sessions. * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-11|en}}. It will be on all wikis from {{#time:j xg|2021-08-12|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The old CSS <bdi lang="zxx" dir="ltr"><code><nowiki><div class="visualClear"></div></nowiki></code></bdi> will not be supported after 12 August. Instead, templates and pages should use <bdi lang="zxx" dir="ltr"><code><nowiki><div style="clear:both;"></div></nowiki></code></bdi>. Please help to replace any existing uses on your wiki. There are global-search links available at [[phab:T287962|T287962]]. '''Future changes''' * [[m:Special:MyLanguage/The Wikipedia Library|The Wikipedia Library]] is a place for Wikipedia editors to get access to sources. There is an [[mw:Special:MyLanguage/Extension:TheWikipediaLibrary|extension]] which has a new function to tell users when they can take part in it. It will use notifications. It will start pinging the first users in September. It will ping more users later. [https://phabricator.wikimedia.org/T288070] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] [[w:en:Vue.js|Vue.js]] will be the [[w:en:JavaScript|JavaScript]] framework for MediaWiki in the future. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/SOZREBYR36PUNFZXMIUBVAIOQI4N7PDU/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 16:21, 9 August 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21856726 --> == [[m:Special:MyLanguage/Tech/News/2021/33|Tech News: 2021-33]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/33|Translations]] are available. '''Recent changes''' * You can add language links in the sidebar in the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|new Vector skin]] again. You do this by connecting the page to a Wikidata item. The new Vector skin has moved the language links but the new language selector cannot add language links yet. [https://phabricator.wikimedia.org/T287206] '''Problems''' * There was a problem on wikis which use the Translate extension. Translations were not updated or were replaced with the English text. The problems have been fixed. [https://phabricator.wikimedia.org/T288700][https://phabricator.wikimedia.org/T288683][https://phabricator.wikimedia.org/T288719] '''Changes later this week''' * A [[mw:Help:Tags|revision tag]] will soon be added to edits that add links to [[mw:Special:MyLanguage/Extension:Disambiguator|disambiguation pages]]. This is because these links are usually added by accident. The tag will allow editors to easily find the broken links and fix them. If your wiki does not like this feature, it can be [[mw:Help:Tags#Deleting a tag added by the software|hidden]]. [https://phabricator.wikimedia.org/T287549] *Would you like to help improve the information about tools? Would you like to attend or help organize a small virtual meetup for your community to discuss the list of tools? Please get in touch on the [[m:Toolhub/The Quality Signal Sessions|Toolhub Quality Signal Sessions]] talk page. We are also looking for feedback [[m:Talk:Toolhub/The Quality Signal Sessions#Discussion topic for "Quality Signal Sessions: The Tool Maintainers edition"|from tool maintainers]] on some specific questions. * In the past, edits to any page in your user talk space ignored your [[mw:Special:MyLanguage/Help:Notifications#mute|mute list]], e.g. sub-pages. Starting this week, this is only true for edits to your talk page. [https://phabricator.wikimedia.org/T288112] * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-18|en}}. It will be on all wikis from {{#time:j xg|2021-08-19|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 19:27, 16 August 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21889213 --> == [[m:Special:MyLanguage/Tech/News/2021/34|Tech News: 2021-34]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/34|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Extension:Score|Score]] extension (<bdi lang="zxx" dir="ltr"><code><nowiki><score></nowiki></code></bdi> notation) has been re-enabled on public wikis and upgraded to a newer version. Some musical score functionality may no longer work because the extension is only enabled in "safe mode". The security issue has been fixed and an [[mw:Special:MyLanguage/Extension:Score/2021 security advisory|advisory published]]. '''Problems''' * You will be able to read but not edit [[phab:T289130|some wikis]] for a few minutes on {{#time:j xg|2021-08-25|en}}. This will happen around [https://zonestamp.toolforge.org/1629871217 06:00 UTC]. This is for database maintenance. During this time, operations on the CentralAuth will also not be possible. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-08-25|en}}. It will be on all wikis from {{#time:j xg|2021-08-26|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 21:58, 23 August 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21923254 --> == Read-only reminder == <section begin="MassMessage"/> A maintenance operation will be performed on [https://zonestamp.toolforge.org/1629871231 {{#time: l F d H:i e|2021-08-25T06:00|en}}]. It should only last for a few minutes. This will affect your wiki as well as 11 other wikis. During this time, publishing edits will not be possible. Also during this time, operations on the CentralAuth will not be possible (GlobalRenames, changing/confirming e-mail addresses, logging into new wikis, password changes). For more details about the operation and on all impacted services, please check [[phab:T289130|on Phabricator]]. A banner will be displayed 30 minutes before the operation. Please help your community to be aware of this maintenance operation. {{Int:Feedback-thanks-title}}<section end="MassMessage"/> 20:35, 24 August 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21927201 --> == [[m:Special:MyLanguage/Tech/News/2021/35|Tech News: 2021-35]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/35|Translations]] are available. '''Recent changes''' * Some musical score syntax no longer works and may needed to be updated, you can check [[:Category:{{MediaWiki:score-error-category}}]] on your wiki for a list of pages with errors. '''Problems''' * Musical scores were unable to render lyrics in some languages because of missing fonts. This has been fixed now. If your language would prefer a different font, please file a request in Phabricator. [https://phabricator.wikimedia.org/T289554] '''Changes later this week''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The parameters for how you obtain [[mw:API:Tokens|tokens]] in the MediaWiki API were changed in 2014. The old way will no longer work from 1 September. Scripts, bots and tools that use the parameters from before the 2014 change need to be updated. You can [[phab:T280806#7215377|read more]] about this. * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-08-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-01|en}}. It will be on all wikis from {{#time:j xg|2021-09-02|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). '''Future changes''' * You will be able to read but not edit [[phab:T289660|Commons]] for a few minutes on {{#time:j xg|2021-09-06|en}}. This will happen around [https://zonestamp.toolforge.org/1630818058 05:00 UTC]. This is for database maintenance. * All wikis will be read-only for a few minutes in the week of 13 September. More information will be published in Tech News later. It will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T287539] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 16:01, 30 August 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21954810 --> == [[m:Special:MyLanguage/Tech/News/2021/36|Tech News: 2021-36]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/36|Translations]] are available. '''Recent changes''' * The wikis that have [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] deployed have been part of A/B testing since deployment, in which some newcomers did not receive the new features. Now, all of the newcomers on 21 of the smallest of those wikis will be receiving the features. [https://phabricator.wikimedia.org/T289786] '''Changes later this week''' * There is no new MediaWiki version this week. '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] In 2017, the provided jQuery library was upgraded from version 1 to 3, with a compatibility layer. The migration will soon finish, to make the site load faster for everyone. If you maintain a gadget or user script, check if you have any JQMIGRATE errors and fix them, or they will break. [https://phabricator.wikimedia.org/T280944][https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/6Z2BVLOBBEC2QP4VV4KOOVQVE52P3HOP/] * Last year, the Portuguese Wikipedia community embarked on an experiment to make log-in compulsory for editing.  The [[m:IP Editing: Privacy Enhancement and Abuse Mitigation/Impact report for Login Required Experiment on Portuguese Wikipedia|impact report of this trial]] is ready. Moving forward, the Anti-Harassment Tools team is looking for projects that are willing to experiment with restricting IP editing on their wiki for a short-term experiment. [[m:IP Editing: Privacy Enhancement and Abuse Mitigation/Login Required Experiment|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:20, 6 September 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=21981010 --> == [[m:Special:MyLanguage/Tech/News/2021/37|Tech News: 2021-37]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/37|Translations]] are available. '''Recent changes''' * 45 new Wikipedias now have access to the [[mw:Special:MyLanguage/Growth/Feature summary|Growth features]]. [https://phabricator.wikimedia.org/T289680] * [[mw:Special:MyLanguage/Growth/Deployment table|A majority of Wikipedias]] now have access to the Growth features. The Growth team [[mw:Special:MyLanguage/Growth/FAQ|has published an FAQ page]] about the features. This translatable FAQ covers the description of the features, how to use them, how to change the configuration, and more. '''Problems''' * [[m:Special:MyLanguage/Tech/Server switch|All wikis will be read-only]] for a few minutes on 14 September. This is planned at [https://zonestamp.toolforge.org/1631628002 14:00 UTC]. [https://phabricator.wikimedia.org/T287539] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.37/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-15|en}}. It will be on all wikis from {{#time:j xg|2021-09-16|en}} ([[mw:MediaWiki 1.37/Roadmap|calendar]]). * Starting this week, Wikipedia in Italian will receive weekly software updates on Wednesdays. It used to receive the updates on Thursdays. Due to this change, bugs will be noticed and fixed sooner. [https://phabricator.wikimedia.org/T286664] * You can add language links in the sidebar in [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|the new Vector skin]] again. You do this by connecting the page to a Wikidata item. The new Vector skin has moved the language links but the new language selector cannot add language links yet. [https://phabricator.wikimedia.org/T287206] * The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlight]] tool marks up code with different colours. It now can highlight 23 new code languages. Additionally, <bdi lang="zxx" dir="ltr"><code>golang</code></bdi> can now be used as an alias for the [[d:Q37227|Go programming language]], and a special <bdi lang="zxx" dir="ltr"><code>output</code></bdi> mode has been added to show a program's output. [https://phabricator.wikimedia.org/T280117][https://gerrit.wikimedia.org/r/c/mediawiki/extensions/SyntaxHighlight_GeSHi/+/715277/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 15:35, 13 September 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22009517 --> == [[m:Special:MyLanguage/Tech/News/2021/38|Tech News: 2021-38]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/38|Translations]] are available. '''Recent changes''' * Growth features are now deployed to almost all Wikipedias. [[phab:T290582|For the majority of small Wikipedias]], the features are only available for experienced users, to [[mw:Special:MyLanguage/Growth/FAQ#enable|test the features]] and [[mw:Special:MyLanguage/Growth/FAQ#config|configure them]]. Features will be available for newcomers starting on 20 September 2021. * MediaWiki had a feature that would highlight local links to short articles in a different style. Each user could pick the size at which "stubs" would be highlighted. This feature was very bad for performance, and following a consultation, has been removed. [https://phabricator.wikimedia.org/T284917] * A technical change was made to the MonoBook skin to allow for easier maintenance and upkeep. This has resulted in some minor changes to HTML that make MonoBook's HTML consistent with other skins. Efforts have been made to minimize the impact on editors, but please ping [[m:User:Jon (WMF)|Jon (WMF)]] on wiki or in [[phab:T290888|phabricator]] if any problems are reported. '''Problems''' * There was a problem with search last week. Many search requests did not work for 2 hours because of an accidental restart of the search servers. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-09-13_cirrussearch_restart] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-22|en}}. It will be on all wikis from {{#time:j xg|2021-09-23|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[s:Special:ApiHelp/query+proofreadinfo|meta=proofreadpage API]] has changed. The <bdi lang="zxx" dir="ltr"><code><nowiki>piprop</nowiki></code></bdi> parameter has been renamed to <bdi lang="zxx" dir="ltr"><code><nowiki>prpiprop</nowiki></code></bdi>. API users should update their code to avoid unrecognized parameter warnings. Pywikibot users should upgrade to 6.6.0. [https://phabricator.wikimedia.org/T290585] '''Future changes''' * The [[mw:Special:MyLanguage/Help:DiscussionTools#Replying|Reply tool]] will be deployed to the remaining wikis in the coming weeks. It is currently part of "{{int:discussiontools-preference-label}}" in [[Special:Preferences#mw-prefsection-betafeatures|Beta features]] at most wikis. You will be able to turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|Editing Preferences]]. [https://phabricator.wikimedia.org/T262331] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[mw:MediaWiki_1.37/Deprecation_of_legacy_API_token_parameters|previously announced]] change to how you obtain tokens from the API has been delayed to September 21 because of an incompatibility with Pywikibot. Bot operators using Pywikibot can follow [[phab:T291202|T291202]] for progress on a fix, and should plan to upgrade to 6.6.1 when it is released. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 18:32, 20 September 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22043415 --> == [[m:Special:MyLanguage/Tech/News/2021/39|Tech News: 2021-39]] == <section begin="technews-2021-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/39|Translations]] are available. '''Recent changes''' * [[w:en:IOS|iOS 15]] has a new function called [https://support.apple.com/en-us/HT212614 Private Relay] (Apple website). This can hide the user's IP when they use [[w:en:Safari (software)|Safari]] browser. This is like using a [[w:en:Virtual private network|VPN]] in that we see another IP address instead. It is opt-in and only for those who pay extra for [[w:en:ICloud|iCloud]]. It will come to Safari users on [[:w:en:OSX|OSX]] later. There is a [[phab:T289795|technical discussion]] about what this means for the Wikimedia wikis. '''Problems''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Some gadgets and user-scripts add items to the [[m:Customization:Explaining_skins#Portlets|portlets]] (article tools) part of the skin. A recent change to the HTML may have made those links a different font-size. This can be fixed by adding the CSS class <bdi lang="zxx" dir="ltr"><code>.vector-menu-dropdown-noicon</code></bdi>. [https://phabricator.wikimedia.org/T291438] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-09-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-09-29|en}}. It will be on all wikis from {{#time:j xg|2021-09-30|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * The [[mw:Special:MyLanguage/Onboarding_new_Wikipedians#New_experience|GettingStarted extension]] was built in 2013, and provides an onboarding process for new account holders in a few versions of Wikipedia. However, the recently developed [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] provide a better onboarding experience. Since the vast majority of Wikipedias now have access to the Growth features, GettingStarted will be deactivated starting on 4 October. [https://phabricator.wikimedia.org/T235752] * A small number of users will not be able to connect to the Wikimedia wikis after 30 September. This is because an old [[:w:en:root certificate|root certificate]] will no longer work. They will also have problems with many other websites. Users who have updated their software in the last five years are unlikely to have problems. Users in Europe, Africa and Asia are less likely to have immediate problems even if their software is too old. You can [[m:Special:MyLanguage/HTTPS/2021 Let's Encrypt root expiry|read more]]. * You can [[mw:Special:MyLanguage/Help:Notifications|receive notifications]] when someone leaves a comment on user talk page or mentions you in a talk page comment. Clicking the notification link will now bring you to the comment and highlight it. Previously, doing so brought you to the top of the section that contained the comment. You can find [[phab:T282029|more information in T282029.]] '''Future changes''' * The [[mw:Special:MyLanguage/Help:DiscussionTools#Replying|Reply tool]] will be deployed to the remaining wikis in the coming weeks. It is currently part of "{{int:discussiontools-preference-label}}" in [[Special:Preferences#mw-prefsection-betafeatures|Beta features]] at most wikis. You will be able to turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|Editing Preferences]]. [[phab:T288485|See the list of wikis.]] [https://phabricator.wikimedia.org/T262331] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W39"/> 22:23, 27 September 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22077885 --> == [[m:Special:MyLanguage/Tech/News/2021/40|Tech News: 2021-40]] == <section begin="tech-newsletter-content"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/40|Translations]] are available. '''Recent changes''' * A more efficient way of sending changes from Wikidata to Wikimedia wikis that show them has been enabled for the following 10 wikis: mediawiki.org, the Italian, Catalan, Hebrew and Vietnamese Wikipedias, French Wikisource, and English Wikivoygage, Wikibooks, Wiktionary and Wikinews. If you notice anything strange about how changes from Wikidata appear in recent changes or your watchlist on those wikis you can [[phab:T48643|let the developers know]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-06|en}}. It will be on all wikis from {{#time:j xg|2021-10-07|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Some gadgets and bots that use the API to read the AbuseFilter log might break. The <bdi lang="zxx" dir="ltr"><code>hidden</code></bdi> property will no longer say an entry is <bdi lang="zxx" dir="ltr"><code>implicit</code></bdi> for unsuppressed log entries about suppressed edits. If your bot needs to know this, do a separate revision query. Additionally, the property will have the value <bdi lang="zxx" dir="ltr"><code>false</code></bdi> for visible entries; previously, it wasn't included in the response. [https://phabricator.wikimedia.org/T291718] * A more efficient way of sending changes from Wikidata to Wikimedia wikis that show them will be enabled for ''all production wikis''. If you notice anything strange about how changes from Wikidata appear in recent changes or your watchlist you can [[phab:T48643|let the developers know]]. '''Future changes''' * You can soon get cross-wiki notifications in the [[mw:Wikimedia Apps/Team/iOS|iOS Wikipedia app]]. You can also get notifications as push notifications. More notification updates will follow in later versions. [https://www.mediawiki.org/wiki/Wikimedia_Apps/Team/iOS/Notifications#September_2021_update] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The JavaScript variables <bdi lang="zxx" dir="ltr"><code>wgExtraSignatureNamespaces</code></bdi>, <bdi lang="zxx" dir="ltr"><code>wgLegalTitleChars</code></bdi>, and <bdi lang="zxx" dir="ltr"><code>wgIllegalFileChars</code></bdi> will soon be removed from <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Manual:Interface/JavaScript#mw.config|mw.config]]</code></bdi>. These are not part of the "stable" variables available for use in wiki JavaScript. [https://phabricator.wikimedia.org/T292011] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The JavaScript variables <bdi lang="zxx" dir="ltr"><code>wgCookiePrefix</code></bdi>, <bdi lang="zxx" dir="ltr"><code>wgCookieDomain</code></bdi>, <bdi lang="zxx" dir="ltr"><code>wgCookiePath</code></bdi>, and <bdi lang="zxx" dir="ltr"><code>wgCookieExpiration</code></bdi> will soon be removed from mw.config. Scripts should instead use <bdi lang="zxx" dir="ltr"><code>mw.cookie</code></bdi> from the "<bdi lang="zxx" dir="ltr">[[mw:ResourceLoader/Core_modules#mediawiki.cookie|mediawiki.cookie]]</bdi>" module. [https://phabricator.wikimedia.org/T291760] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="tech-newsletter-content"/> 16:32, 4 October 2021 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22101208 --> == [[m:Special:MyLanguage/Tech/News/2021/41|Tech News: 2021-41]] == <section begin="technews-2021-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/41|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-13|en}}. It will be on all wikis from {{#time:j xg|2021-10-14|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * The [[mw:Manual:Table_of_contents#Auto-numbering|"auto-number headings" preference]] is being removed. You can read [[phab:T284921]] for the reasons and discussion. This change was [[m:Tech/News/2021/26|previously]] announced. [[mw:Snippets/Auto-number_headings|A JavaScript snippet]] is available which can be used to create a Gadget on wikis that still want to support auto-numbering. '''Meetings''' * You can join a meeting about the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]]. A demonstration version of the [[mw:Reading/Web/Desktop Improvements/Features/Sticky Header|newest feature]] will be shown. The event will take place on Tuesday, 12 October at 16:00 UTC. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web/12-10-2021|See how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W41"/> 15:30, 11 October 2021 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22152137 --> == [[m:Special:MyLanguage/Tech/News/2021/42|Tech News: 2021-42]] == <section begin="technews-2021-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/42|Translations]] are available. '''Recent changes''' *[[m:Toolhub|Toolhub]] is a catalogue to make it easier to find software tools that can be used for working on the Wikimedia projects. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/LF4SSR4QRCKV6NPRFGUAQWUFQISVIPTS/ read more]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-20|en}}. It will be on all wikis from {{#time:j xg|2021-10-21|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Future changes''' * The developers of the [[mw:Wikimedia Apps/Team/Android|Wikipedia Android app]] are working on [[mw:Wikimedia Apps/Team/Android/Communication|communication in the app]]. You can now answer questions in [[mw:Wikimedia Apps/Team/Android/Communication/UsertestingOctober2021|survey]] to help the development. * 3–5% of editors may be blocked in the next few months. This is because of a new service in Safari, which is similar to a [[w:en:Proxy server|proxy]] or a [[w:en:VPN|VPN]]. It is called iCloud Private Relay. There is a [[m:Special:MyLanguage/Apple iCloud Private Relay|discussion about this]] on Meta. The goal is to learn what iCloud Private Relay could mean for the communities. * [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] is a new [[w:en:API|API]] for those who use a lot of information from the Wikimedia projects on other sites. It is a way to get big commercial users to pay for the data. There will soon be a copy of the Wikimedia Enterprise dataset. You can [https://lists.wikimedia.org/hyperkitty/list/wikitech-ambassadors@lists.wikimedia.org/message/B2AX6PWH5MBKB4L63NFZY3ADBQG7MSBA/ read more]. You can also ask the team questions [https://wikimedia.zoom.us/j/88994018553 on Zoom] on [https://www.timeanddate.com/worldclock/fixedtime.html?hour=15&min=00&sec=0&day=22&month=10&year=2021 22 October 15:00 UTC]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W42"/> 20:53, 18 October 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22176877 --> == [[m:Special:MyLanguage/Tech/News/2021/43|Tech News: 2021-43]] == <section begin="technews-2021-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/43|Translations]] are available. '''Recent changes''' * The [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award 2021]] is looking for nominations. You can recommend tools until 27 October. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-10-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-10-27|en}}. It will be on all wikis from {{#time:j xg|2021-10-28|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Future changes''' *[[m:Special:MyLanguage/Help:Diff|Diff pages]] will have an improved copy and pasting experience. [[m:Special:MyLanguage/Community Wishlist Survey 2021/Copy paste diffs|The changes]] will allow the text in the diff for before and after to be treated as separate columns and will remove any unwanted syntax. [https://phabricator.wikimedia.org/T192526] * The version of the [[w:en:Liberation fonts|Liberation fonts]] used in SVG files will be upgraded. Only new thumbnails will be affected. Liberation Sans Narrow will not change. [https://phabricator.wikimedia.org/T253600] '''Meetings''' * You can join a meeting about the [[m:Special:MyLanguage/Community Wishlist Survey|Community Wishlist Survey]]. News about the [[m:Special:MyLanguage/Community Wishlist Survey 2021/Warn when linking to disambiguation pages|disambiguation]] and the [[m:Special:MyLanguage/Community Wishlist Survey 2021/Real Time Preview for Wikitext|real-time preview]] wishes will be shown. The event will take place on Wednesday, 27 October at 14:30 UTC. [[m:Special:MyLanguage/Community Wishlist Survey/Updates/Talk to Us|See how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W43"/> 20:08, 25 October 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22232718 --> == [[m:Special:MyLanguage/Tech/News/2021/44|Tech News: 2021-44]] == <section begin="technews-2021-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/44|Translations]] are available. '''Recent changes''' * There is a limit on the amount of emails a user can send each day. This limit is now global instead of per-wiki. This change is to prevent abuse. [https://phabricator.wikimedia.org/T293866] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-11-03|en}}. It will be on all wikis from {{#time:j xg|2021-11-04|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W44"/> 20:28, 1 November 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22269406 --> == [[m:Special:MyLanguage/Tech/News/2021/45|Tech News: 2021-45]] == <section begin="technews-2021-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/45|Translations]] are available. '''Recent changes''' * Mobile IP editors are now able to receive warning notices indicating they have a talk page message on the mobile website (similar to the orange banners available on desktop). These notices will be displayed on every page outside of the main namespace and every time the user attempts to edit. The notice on desktop now has a slightly different colour. [https://phabricator.wikimedia.org/T284642][https://phabricator.wikimedia.org/T278105] '''Changes later this week''' * [[phab:T294321|Wikidata will be read-only]] for a few minutes on 11 November. This will happen around [https://zonestamp.toolforge.org/1636610400 06:00 UTC]. This is for database maintenance. [https://phabricator.wikimedia.org/T294321] * There is no new MediaWiki version this week. '''Future changes''' * In the future, unregistered editors will be given an identity that is not their [[:w:en:IP address|IP address]]. This is for legal reasons. A new user right will let editors who need to know the IPs of unregistered accounts to fight vandalism, spam, and harassment, see the IP. You can read the [[m:IP Editing: Privacy Enhancement and Abuse Mitigation#IP Masking Implementation Approaches (FAQ)|suggestions for how that identity could work]] and [[m:Talk:IP Editing: Privacy Enhancement and Abuse Mitigation|discuss on the talk page]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W45"/> 20:36, 8 November 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22311003 --> == [[m:Special:MyLanguage/Tech/News/2021/46|Tech News: 2021-46]] == <section begin="technews-2021-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/46|Translations]] are available. '''Recent changes''' * Most [[c:Special:MyLanguage/Commons:Maximum_file_size#MAXTHUMB|large file uploads]] errors that had messages like "<bdi lang="zxx" dir="ltr"><code>stashfailed</code></bdi>" or "<bdi lang="zxx" dir="ltr"><code>DBQueryError</code></bdi>" have now been fixed. An [[wikitech:Incident documentation/2021-11-04 large file upload timeouts|incident report]] is available. '''Problems''' * Sometimes, edits made on iOS using the visual editor save groups of numbers as telephone number links, because of a feature in the operating system. This problem is under investigation. [https://phabricator.wikimedia.org/T116525] * There was a problem with search last week. Many search requests did not work for 2 hours because of a configuration error. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2021-11-10_cirrussearch_commonsfile_outage] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-11-17|en}}. It will be on all wikis from {{#time:j xg|2021-11-18|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W46"/> 22:06, 15 November 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22338097 --> == [[m:Special:MyLanguage/Tech/News/2021/47|Tech News: 2021-47]] == <section begin="technews-2021-W47"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/47|Translations]] are available. '''Changes later this week''' * There is no new MediaWiki version this week. *The template dialog in VisualEditor and in the [[Special:Preferences#mw-prefsection-betafeatures|new wikitext mode]] Beta feature will be [[m:WMDE Technical Wishes/VisualEditor template dialog improvements|heavily improved]] on [[phab:T286992|a few wikis]]. Your [[m:Talk:WMDE Technical Wishes/VisualEditor template dialog improvements|feedback is welcome]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/47|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W47"/> 20:02, 22 November 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22366010 --> == [[m:Special:MyLanguage/Tech/News/2021/48|Tech News: 2021-48]] == <section begin="technews-2021-W48"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/48|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-11-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-01|en}}. It will be on all wikis from {{#time:j xg|2021-12-02|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/48|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W48"/> 21:15, 29 November 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22375666 --> == [[m:Special:MyLanguage/Tech/News/2021/49|Tech News: 2021-49]] == <section begin="technews-2021-W49"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/49|Translations]] are available. '''Problems''' * MediaWiki 1.38-wmf.11 was scheduled to be deployed on some wikis last week. The deployment was delayed because of unexpected problems. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-12-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-08|en}}. It will be on all wikis from {{#time:j xg|2021-12-09|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * At all Wikipedias, a Mentor Dashboard is now available at <bdi lang="zxx" dir="ltr"><code><nowiki>Special:MentorDashboard</nowiki></code></bdi>. It allows registered mentors, who take care of newcomers' first steps, to monitor their assigned newcomers' activity. It is part of the [[mw:Special:MyLanguage/Growth/Feature summary|Growth features]]. You can learn more about [[mw:Special:MyLanguage/Growth/Communities/How_to_configure_the_mentors%27_list|activating the mentor list]] on your wiki and about [[mw:Special:MyLanguage/Growth/Mentor dashboard|the mentor dashboard project]]. * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The predecessor to the current [[mw:API|MediaWiki Action API]] (which was created in 2008), <bdi lang="zxx" dir="ltr"><code><nowiki>action=ajax</nowiki></code></bdi>, will be removed this week. Any scripts or bots using it will need to switch to the corresponding API module. [https://phabricator.wikimedia.org/T42786] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] An old ResourceLoader module, <bdi lang="zxx" dir="ltr"><code><nowiki>jquery.jStorage</nowiki></code></bdi>, which was deprecated in 2016, will be removed this week. Any scripts or bots using it will need to switch to <bdi lang="zxx" dir="ltr"><code><nowiki>mediawiki.storage</nowiki></code></bdi> instead. [https://phabricator.wikimedia.org/T143034] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/49|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W49"/> 21:59, 6 December 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22413926 --> == [[m:Special:MyLanguage/Tech/News/2021/50|Tech News: 2021-50]] == <section begin="technews-2021-W50"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/50|Translations]] are available. '''Recent changes''' * There are now default [[m:Special:MyLanguage/Help:Namespace#Other_namespace_aliases|short aliases]] for the "Project:" namespace on most wikis. E.g. On Wikibooks wikis, <bdi lang="zxx" dir="ltr"><code><nowiki>[[WB:]]</nowiki></code></bdi> will go to the local language default for the <bdi lang="zxx" dir="ltr"><code><nowiki>[[Project:]]</nowiki></code></bdi> namespace. This change is intended to help the smaller communities have easy access to this feature. Additional local aliases can still be requested via [[m:Special:MyLanguage/Requesting wiki configuration changes|the usual process]]. [https://phabricator.wikimedia.org/T293839] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2021-12-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2021-12-15|en}}. It will be on all wikis from {{#time:j xg|2021-12-16|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/50|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W50"/> 22:27, 13 December 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22441074 --> == [[m:Special:MyLanguage/Tech/News/2021/51|Tech News: 2021-51]] == <section begin="technews-2021-W51"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2021/51|Translations]] are available. '''Tech News''' * Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 10 January 2022. '''Recent changes''' * Queries made by the DynamicPageList extension (<bdi lang="zxx" dir="ltr"><code><nowiki><DynamicPageList></nowiki></code></bdi>) are now only allowed to run for 10 seconds and error if they take longer. This is in response to multiple outages where long-running queries caused an outage on all wikis. [https://phabricator.wikimedia.org/T287380#7575719] '''Changes later this week''' * There is no new MediaWiki version this week or next week. '''Future changes''' * The developers of the Wikipedia iOS app are looking for testers who edit in multiple languages. You can [[mw:Wikimedia Apps/Team/iOS/202112 testing|read more and let them know if you are interested]]. * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The Wikimedia [[wikitech:Portal:Cloud VPS|Cloud VPS]] hosts technical projects for the Wikimedia movement. Developers need to [[wikitech:News/Cloud VPS 2021 Purge|claim projects]] they use. This is because old and unused projects are removed once a year. Unclaimed projects can be shut down from February. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/2B7KYL5VLQNHGQQHMYLW7KTUKXKAYY3T/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2021/51|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2021-W51"/> 22:05, 20 December 2021 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22465395 --> == [[m:Special:MyLanguage/Tech/News/2022/02|Tech News: 2022-02]] == <section begin="technews-2022-W02"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/02|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] A <bdi lang="zxx" dir="ltr"><code>oauth_consumer</code></bdi> variable has been added to the [[mw:Special:MyLanguage/AbuseFilter|AbuseFilter]] to enable identifying changes made by specific tools. [https://phabricator.wikimedia.org/T298281] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets are [[mw:Special:MyLanguage/ResourceLoader/Migration_guide_(users)#Package_Gadgets|now able to directly include JSON pages]]. This means some gadgets can now be configured by administrators without needing the interface administrator permission, such as with the Geonotice gadget. [https://phabricator.wikimedia.org/T198758] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets [[mw:Extension:Gadgets#Options|can now specify page actions]] on which they are available. For example, <bdi lang="zxx" dir="ltr"><code>|actions=edit,history</code></bdi> will load a gadget only while editing and on history pages. [https://phabricator.wikimedia.org/T63007] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] Gadgets can now be loaded on demand with the <bdi lang="zxx" dir="ltr"><code>withgadget</code></bdi> URL parameter. This can be used to replace [[mw:Special:MyLanguage/Snippets/Load JS and CSS by URL|an earlier snippet]] that typically looks like <bdi lang="zxx" dir="ltr"><code>withJS</code></bdi> or <bdi lang="zxx" dir="ltr"><code>withCSS</code></bdi>. [https://phabricator.wikimedia.org/T29766] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] At wikis where [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list|the Mentorship system is configured]], you can now use the Action API to get a list of a [[mw:Special:MyLanguage/Growth/Mentor_dashboard|mentor's]] mentees. [https://phabricator.wikimedia.org/T291966] * The heading on the main page can now be configured using <span class="mw-content-ltr" lang="en" dir="ltr">[[MediaWiki:Mainpage-title-loggedin]]</span> for logged-in users and <span class="mw-content-ltr" lang="en" dir="ltr">[[MediaWiki:Mainpage-title]]</span> for logged-out users. Any CSS that was previously used to hide the heading should be removed. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Small_wiki_toolkits/Starter_kit/Main_page_customization#hide-heading] [https://phabricator.wikimedia.org/T298715] * Four special pages (and their API counterparts) now have a maximum database query execution time of 30 seconds. These special pages are: RecentChanges, Watchlist, Contributions, and Log. This change will help with site performance and stability. You can read [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/IPJNO75HYAQWIGTHI5LJHTDVLVOC4LJP/ more details about this change] including some possible solutions if this affects your workflows. [https://phabricator.wikimedia.org/T297708] * The [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Sticky Header|sticky header]] has been deployed for 50% of logged-in users on [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Frequently asked questions#pilot-wikis|more than 10 wikis]]. This is part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]]. See [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Participate|how to take part in the project]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-12|en}}. It will be on all wikis from {{#time:j xg|2022-01-13|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Events''' * [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey 2022]] begins. All contributors to the Wikimedia projects can propose for tools and platform improvements. The proposal phase takes place from {{#time:j xg|2022-01-10|en}} 18:00 UTC to {{#time:j xg|2022-01-23|en}} 18:00 UTC. [[m:Special:MyLanguage/Community_Wishlist_Survey/FAQ|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/02|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W02"/> 01:23, 11 January 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22562156 --> == [[m:Special:MyLanguage/Tech/News/2022/03|Tech News: 2022-03]] == <section begin="technews-2022-W03"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/03|Translations]] are available. '''Recent changes''' * When using [[mw:Special:MyLanguage/Extension:WikiEditor|WikiEditor]] (also known as the 2010 wikitext editor), people will now see a warning if they link to disambiguation pages. If you click "{{int:Disambiguator-review-link}}" in the warning, it will ask you to correct the link to a more specific term. You can [[m:Community Wishlist Survey 2021/Warn when linking to disambiguation pages#Jan 12, 2021: Turning on the changes for all Wikis|read more information]] about this completed 2021 Community Wishlist item. * You can [[mw:Special:MyLanguage/Help:DiscussionTools#subscribe|automatically subscribe to all of the talk page discussions]] that you start or comment in using [[mw:Special:MyLanguage/Talk pages project/Feature summary|DiscussionTools]]. You will receive [[mw:Special:MyLanguage/Notifications|notifications]] when another editor replies. This is available at most wikis. Go to your [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]] and turn on "{{int:discussiontools-preference-autotopicsub}}". [https://phabricator.wikimedia.org/T263819] * When asked to create a new page or talk page section, input fields can be [[mw:Special:MyLanguage/Manual:Creating_pages_with_preloaded_text|"preloaded" with some text]]. This feature is now limited to wikitext pages. This is so users can't be tricked into making malicious edits. There is a discussion about [[phab:T297725|if this feature should be re-enabled]] for some content types. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-19|en}}. It will be on all wikis from {{#time:j xg|2022-01-20|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Events''' * [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey 2022]] continues. All contributors to the Wikimedia projects can propose for tools and platform improvements. The proposal phase takes place from {{#time:j xg|2022-01-10|en}} 18:00 UTC to {{#time:j xg|2022-01-23|en}} 18:00 UTC. [[m:Special:MyLanguage/Community_Wishlist_Survey/FAQ|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/03|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W03"/> 19:55, 17 January 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22620285 --> == [[m:Special:MyLanguage/Tech/News/2022/04|Tech News: 2022-04]] == <section begin="technews-2022-W04"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/04|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-01-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-01-26|en}}. It will be on all wikis from {{#time:j xg|2022-01-27|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * The following languages can now be used with [[mw:Special:MyLanguage/Extension:SyntaxHighlight|syntax highlighting]]: BDD, Elpi, LilyPond, Maxima, Rita, Savi, Sed, Sophia, Spice, .SRCINFO. * You can now access your watchlist from outside of the user menu in the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|new Vector skin]]. The watchlist link appears next to the notification icons if you are at the top of the page. [https://phabricator.wikimedia.org/T289619] '''Events''' * You can see the results of the [[m:Special:MyLanguage/Coolest Tool Award|Coolest Tool Award 2021]] and learn more about 14 tools which were selected this year. * You can [[m:Special:MyLanguage/Community_Wishlist_Survey/Help_us|translate, promote]], or comment on [[m:Special:MyLanguage/Community Wishlist Survey 2022/Proposals|the proposals]] in the Community Wishlist Survey. Voting will begin on {{#time:j xg|2022-01-28|en}}. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/04|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W04"/> 21:38, 24 January 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22644148 --> == [[m:Special:MyLanguage/Tech/News/2022/05|Tech News: 2022-05]] == <section begin="technews-2022-W05"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/05|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] If a gadget should support the new <bdi lang="zxx" dir="ltr"><code>?withgadget</code></bdi> URL parameter that was [[m:Special:MyLanguage/Tech/News/2022/02|announced]] 3 weeks ago, then it must now also specify <bdi lang="zxx" dir="ltr"><code>supportsUrlLoad</code></bdi> in the gadget definition ([[mw:Special:MyLanguage/Extension:Gadgets#supportsUrlLoad|documentation]]). [https://phabricator.wikimedia.org/T29766] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-02|en}}. It will be on all wikis from {{#time:j xg|2022-02-03|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Future changes''' * A change that was [[m:Special:MyLanguage/Tech/News/2021/16|announced]] last year was delayed. It is now ready to move ahead: ** The user group <code>oversight</code> will be renamed <code>suppress</code>. This is for [[phab:T109327|technical reasons]]. This is the technical name. It doesn't affect what you call the editors with this user right on your wiki. This is planned to happen in three weeks. You can comment [[phab:T112147|in Phabricator]] if you have objections. As usual, these labels can be translated on translatewiki ([[phab:T112147|direct links are available]]) or by administrators on your wiki. '''Events''' * You can vote on proposals in the [[m:Special:MyLanguage/Community Wishlist Survey 2022|Community Wishlist Survey]] between 28 January and 11 February. The survey decides what the [[m:Special:MyLanguage/Community Tech|Community Tech team]] will work on. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/05|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W05"/> 17:42, 31 January 2022 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22721804 --> == [[m:Special:MyLanguage/Tech/News/2022/06|Tech News: 2022-06]] == <section begin="technews-2022-W06"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/06|Translations]] are available. '''Recent changes''' * English Wikipedia recently set up a gadget for dark mode. You can enable it there, or request help from an [[m:Special:MyLanguage/Interface administrators|interface administrator]] to set it up on your wiki ([[w:en:Wikipedia:Dark mode (gadget)|instructions and screenshot]]). * Category counts are sometimes wrong. They will now be completely recounted at the beginning of every month. [https://phabricator.wikimedia.org/T299823] '''Problems''' * A code-change last week to fix a bug with [[mw:Special:MyLanguage/Manual:Live preview|Live Preview]] may have caused problems with some local gadgets and user-scripts. Any code with skin-specific behaviour for <bdi lang="zxx" dir="ltr"><code>vector</code></bdi> should be updated to also check for <bdi lang="zxx" dir="ltr"><code>vector-2022</code></bdi>. [[phab:T300987|A code-snippet, global search, and example are available]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-09|en}}. It will be on all wikis from {{#time:j xg|2022-02-10|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/06|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W06"/> 21:15, 7 February 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22765948 --> == [[m:Special:MyLanguage/Tech/News/2022/07|Tech News: 2022-07]] == <section begin="technews-2022-W07"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/07|Translations]] are available. '''Recent changes''' * [[mw:Special:MyLanguage/Manual:Purge|Purging]] a category page with fewer than 5,000 members will now recount it completely. This will allow editors to fix incorrect counts when it is wrong. [https://phabricator.wikimedia.org/T85696] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-16|en}}. It will be on all wikis from {{#time:j xg|2022-02-17|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|Advanced item]] In the [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] extension, the <code dir=ltr>rmspecials()</code> function has been updated so that it does not remove the "space" character. Wikis are advised to wrap all the uses of <code dir=ltr>rmspecials()</code> with <code dir=ltr>rmwhitespace()</code> wherever necessary to keep filters' behavior unchanged. You can use the search function on [[Special:AbuseFilter]] to locate its usage. [https://phabricator.wikimedia.org/T263024] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/07|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W07"/> 19:18, 14 February 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22821788 --> == [[m:Special:MyLanguage/Tech/News/2022/08|Tech News: 2022-08]] == <section begin="technews-2022-W08"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/08|Translations]] are available. '''Recent changes''' * [[Special:Nuke|Special:Nuke]] will now provide the standard deletion reasons (editable at <bdi lang="en" dir="ltr">[[MediaWiki:Deletereason-dropdown]]</bdi>) to use when mass-deleting pages. This was [[m:Community Wishlist Survey 2022/Admins and patrollers/Mass-delete to offer drop-down of standard reasons, or templated reasons.|a request in the 2022 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T25020] * At Wikipedias, all new accounts now get the [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] by default when creating an account. Communities are encouraged to [[mw:Special:MyLanguage/Help:Growth/Tools/Account_creation|update their help resources]]. Previously, only 80% of new accounts would get the Growth features. A few Wikipedias remain unaffected by this change. [https://phabricator.wikimedia.org/T301820] * You can now prevent specific images that are used in a page from appearing in other locations, such as within PagePreviews or Search results. This is done with the markup <bdi lang="zxx" dir="ltr"><code><nowiki>class=notpageimage</nowiki></code></bdi>. For example, <code><nowiki>[[File:Example.png|class=notpageimage]]</nowiki></code>. [https://phabricator.wikimedia.org/T301588] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] There has been a change to the HTML of Special:Contributions, Special:MergeHistory, and History pages, to support the grouping of changes by date in [[mw:Special:MyLanguage/Skin:Minerva_Neue|the mobile skin]]. While unlikely, this may affect gadgets and user scripts. A [[phab:T298638|list of all the HTML changes]] is on Phabricator. '''Events''' * [[m:Special:MyLanguage/Community Wishlist Survey 2022/Results|Community Wishlist Survey results]] have been published. The [[m:Special:MyLanguage/Community Wishlist Survey/Updates/2022 results#leaderboard|ranking of prioritized proposals]] is also available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-02-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-02-23|en}}. It will be on all wikis from {{#time:j xg|2022-02-24|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Future changes''' * The software to play videos and audio files on pages will change soon on all wikis. The old player will be removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Toolforge's underlying operating system is being updated. If you maintain any tools there, there are two options for migrating your tools into the new system. There are [[wikitech:News/Toolforge Stretch deprecation|details, deadlines, and instructions]] on Wikitech. [https://lists.wikimedia.org/hyperkitty/list/cloud-announce@lists.wikimedia.org/thread/EPJFISC52T7OOEFH5YYMZNL57O4VGSPR/] * Administrators will soon have [[m:Special:MyLanguage/Community Wishlist Survey 2021/(Un)delete associated talk page|the option to delete/undelete]] the associated "talk" page when they are deleting a given page. An API endpoint with this option will also be available. This was [[m:Community Wishlist Survey 2021/Admins and patrollers/(Un)delete associated talk page|a request from the 2021 Wishlist Survey]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W08"/> 19:12, 21 February 2022 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22847768 --> == [[m:Special:MyLanguage/Tech/News/2022/09|Tech News: 2022-09]] == <section begin="technews-2022-W09"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/09|Translations]] are available. '''Recent changes''' * When searching for edits by [[mw:Special:MyLanguage/Help:Tags|change tags]], e.g. in page history or user contributions, there is now a dropdown list of possible tags. This was [[m:Community Wishlist Survey 2022/Miscellaneous/Improve plain-text change tag selector|a request in the 2022 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T27909] * Mentors using the [[mw:Special:MyLanguage/Growth/Mentor_dashboard|Growth Mentor dashboard]] will now see newcomers assigned to them who have made at least one edit, up to 200 edits. Previously, all newcomers assigned to the mentor were visible on the dashboard, even ones without any edit or ones who made hundred of edits. Mentors can still change these values using the filters on their dashboard. Also, the last choice of filters will now be saved. [https://phabricator.wikimedia.org/T301268][https://phabricator.wikimedia.org/T294460] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The user group <code>oversight</code> was renamed <code>suppress</code>. This is for [[phab:T109327|technical reasons]]. You may need to update any local references to the old name, e.g. gadgets, links to Special:Listusers, or uses of [[mw:Special:MyLanguage/Help:Magic_words|NUMBERINGROUP]]. '''Problems''' * The recent change to the HTML of [[mw:Special:MyLanguage/Help:Tracking changes|tracking changes]] pages caused some problems for screenreaders. This is being fixed. [https://phabricator.wikimedia.org/T298638] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-02|en}}. It will be on all wikis from {{#time:j xg|2022-03-03|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''Future changes''' * Working with templates will become easier. [[m:WMDE_Technical_Wishes/Templates|Several improvements]] are planned for March 9 on most wikis and on March 16 on English Wikipedia. The improvements include: Bracket matching, syntax highlighting colors, finding and inserting templates, and related visual editor features. * If you are a template developer or an interface administrator, and you are intentionally overriding or using the default CSS styles of user feedback boxes (the classes: <code dir=ltr>successbox, messagebox, errorbox, warningbox</code>), please note that these classes and associated CSS will soon be removed from MediaWiki core. This is to prevent problems when the same class-names are also used on a wiki. Please let us know by commenting at [[phab:T300314]] if you think you might be affected. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W09"/> 22:59, 28 February 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22902593 --> == [[m:Special:MyLanguage/Tech/News/2022/10|Tech News: 2022-10]] == <section begin="technews-2022-W10"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/10|Translations]] are available. '''Problems''' * There was a problem with some interface labels last week. It will be fixed this week. This change was part of ongoing work to simplify the support for skins which do not have active maintainers. [https://phabricator.wikimedia.org/T301203] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-08|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-09|en}}. It will be on all wikis from {{#time:j xg|2022-03-10|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/10|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W10"/> 21:16, 7 March 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22958074 --> == [[m:Special:MyLanguage/Tech/News/2022/11|Tech News: 2022-11]] == <section begin="technews-2022-W11"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/11|Translations]] are available. '''Recent changes''' * In the Wikipedia Android app [[mw:Special:MyLanguage/Wikimedia_Apps/Team/Android/Communication#Updates|it is now possible]] to change the toolbar at the bottom so the tools you use more often are easier to click on. The app now also has a focused reading mode. [https://phabricator.wikimedia.org/T296753][https://phabricator.wikimedia.org/T254771] '''Problems''' * There was a problem with the collection of some page-view data from June 2021 to January 2022 on all wikis. This means the statistics are incomplete. To help calculate which projects and regions were most affected, relevant datasets are being retained for 30 extra days. You can [[m:Talk:Data_retention_guidelines#Added_exception_for_page_views_investigation|read more on Meta-wiki]]. * There was a problem with the databases on March 10. All wikis were unreachable for logged-in users for 12 minutes. Logged-out users could read pages but could not edit or access uncached content then. [https://wikitech.wikimedia.org/wiki/Incident_documentation/2022-03-10_MediaWiki_availability] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.38/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-16|en}}. It will be on all wikis from {{#time:j xg|2022-03-17|en}} ([[mw:MediaWiki 1.38/Roadmap|calendar]]). * When [[mw:Special:MyLanguage/Help:System_message#Finding_messages_and_documentation|using <bdi lang="zxx" dir="ltr"><code>uselang=qqx</code></bdi> to find localisation messages]], it will now show all possible message keys for navigation tabs such as "{{int:vector-view-history}}". [https://phabricator.wikimedia.org/T300069] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Access to [[{{#special:RevisionDelete}}]] has been expanded to include users who have <code dir=ltr>deletelogentry</code> and <code dir=ltr>deletedhistory</code> rights through their group memberships. Before, only those with the <code dir=ltr>deleterevision</code> right could access this special page. [https://phabricator.wikimedia.org/T301928] * On the [[{{#special:Undelete}}]] pages for diffs and revisions, there will be a link back to the main Undelete page with the list of revisions. [https://phabricator.wikimedia.org/T284114] '''Future changes''' * The Wikimedia Foundation has announced the IP Masking implementation strategy and next steps. The [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation#feb25|announcement can be read here]]. * The [[mw:Special:MyLanguage/Wikimedia Apps/Android FAQ|Wikipedia Android app]] developers are working on [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Communication|new functions]] for user talk pages and article talk pages. [https://phabricator.wikimedia.org/T297617] '''Events''' * The [[mw:Wikimedia Hackathon 2022|Wikimedia Hackathon 2022]] will take place as a hybrid event on 20-22 May 2022. The Hackathon will be held online and there are grants available to support local in-person meetups around the world. Grants can be requested until 20 March. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/11|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W11"/> 22:07, 14 March 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=22993074 --> == [[m:Special:MyLanguage/Tech/News/2022/12|Tech News: 2022-12]] == <section begin="technews-2022-W12"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/12|Translations]] are available. '''New code release schedule for this week''' * There will be four MediaWiki releases this week, instead of just one. This is an experiment which should lead to fewer problems and to faster feature updates. The releases will be on all wikis, at different times, on Monday, Tuesday, and Wednesday. You can [[mw:Special:MyLanguage/Wikimedia Release Engineering Team/Trainsperiment week|read more about this project]]. '''Recent changes''' * You can now set how many search results to show by default in [[Special:Preferences#mw-prefsection-searchoptions|your Preferences]]. This was the 12th most popular wish in the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Results|Community Wishlist Survey 2022]]. [https://phabricator.wikimedia.org/T215716] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The Jupyter notebooks tool [[wikitech:PAWS|PAWS]] has been updated to a new interface. [https://phabricator.wikimedia.org/T295043] '''Future changes''' * Interactive maps via [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] will soon work on wikis using the [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevisions]] extension. [https://wikimedia.sslsurvey.de/Kartographer-Workflows-EN/ Please tell us] which improvements you want to see in Kartographer. You can take this survey in simple English. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/12|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W12"/> 16:01, 21 March 2022 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23034693 --> == [[m:Special:MyLanguage/Tech/News/2022/13|Tech News: 2022-13]] == <section begin="technews-2022-W13"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/13|Translations]] are available. '''Recent changes''' * There is a simple new Wikimedia Commons upload tool available for macOS users, [[c:Commons:Sunflower|Sunflower]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-03-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-03-30|en}}. It will be on all wikis from {{#time:j xg|2022-03-31|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * Some wikis will be in read-only for a few minutes because of regular database maintenance. It will be performed on {{#time:j xg|2022-03-29|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]) and on {{#time:j xg|2022-03-31|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]). [https://phabricator.wikimedia.org/T301850][https://phabricator.wikimedia.org/T303798] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W13"/> 19:54, 28 March 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23073711 --> == [[m:Special:MyLanguage/Tech/News/2022/14|Tech News: 2022-14]] == <section begin="technews-2022-W14"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/14|Translations]] are available. '''Problems''' * For a few days last week, edits that were suggested to newcomers were not tagged in the [[{{#special:recentchanges}}]] feed. This bug has been fixed. [https://phabricator.wikimedia.org/T304747] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-06|en}}. It will be on all wikis from {{#time:j xg|2022-04-07|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-07|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]). '''Future changes''' * Starting next week, Tech News' title will be translatable. When the newsletter is distributed, its title may not be <code dir=ltr>Tech News: 2022-14</code> anymore. It may affect some filters that have been set up by some communities. [https://phabricator.wikimedia.org/T302920] * Over the next few months, the "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" Growth feature [[phab:T304110|will become available to more Wikipedias]]. Each week, a few wikis will get the feature. You can test this tool at [[mw:Special:MyLanguage/Growth#deploymentstable|a few wikis where "Link recommendation" is already available]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W14"/> 21:01, 4 April 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23097604 --> == Tech News: 2022-15 == <section begin="technews-2022-W15"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/15|Translations]] are available. '''Recent changes''' * There is a new public status page at <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikimediastatus.net/ www.wikimediastatus.net]</span>. This site shows five automated high-level metrics where you can see the overall health and performance of our wikis' technical environment. It also contains manually-written updates for widespread incidents, which are written as quickly as the engineers are able to do so while also fixing the actual problem. The site is separated from our production infrastructure and hosted by an external service, so that it can be accessed even if the wikis are briefly unavailable. You can [https://diff.wikimedia.org/2022/03/31/announcing-www-wikimediastatus-net/ read more about this project]. * On Wiktionary wikis, the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-13|en}}. It will be on all wikis from {{#time:j xg|2022-04-14|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/15|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W15"/> 19:44, 11 April 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23124108 --> == Tech News: 2022-16 == <section begin="technews-2022-W16"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/16|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-20|en}}. It will be on all wikis from {{#time:j xg|2022-04-21|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-19|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]) and on {{#time:j xg|2022-04-21|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s8.dblist targeted wikis]). * Administrators will now have [[m:Community Wishlist Survey 2021/(Un)delete associated talk page|the option to delete/undelete the associated "Talk" page]] when they are deleting a given page. An API endpoint with this option is also available. This concludes the [[m:Community Wishlist Survey 2021/Admins and patrollers/(Un)delete associated talk page|11th wish of the 2021 Community Wishlist Survey]]. * On [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#test-wikis|selected wikis]], 50% of logged-in users will see the new [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Table of contents|table of contents]]. When scrolling up and down the page, the table of contents will stay in the same place on the screen. This is part of the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Desktop Improvements]] project. [https://phabricator.wikimedia.org/T304169] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Message boxes produced by MediaWiki code will no longer have these CSS classes: <code dir=ltr>successbox</code>, <code dir=ltr>errorbox</code>, <code dir=ltr>warningbox</code>. The styles for those classes and <code dir=ltr>messagebox</code> will be removed from MediaWiki core. This only affects wikis that use these classes in wikitext, or change their appearance within site-wide CSS. Please review any local usage and definitions for these classes you may have. This was previously announced in the [[m:Special:MyLanguage/Tech/News/2022/09|28 February issue of Tech News]]. '''Future changes''' * [[mw:Special:MyLanguage/Extension:Kartographer|Kartographer]] will become compatible with [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevisions page stabilization]]. Kartographer maps will also work on pages with [[mw:Special:MyLanguage/Help:Pending changes|pending changes]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Project_descriptions] The Kartographer documentation has been thoroughly updated. [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:Kartographer/Getting_started] [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:VisualEditor/Maps] [https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:Kartographer] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W16"/> 23:11, 18 April 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23167004 --> == Tech News: 2022-17 == <section begin="technews-2022-W17"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/17|Translations]] are available. '''Recent changes''' * On [https://noc.wikimedia.org/conf/dblists/group1.dblist many wikis] (group 1), the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-04-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-04-27|en}}. It will be on all wikis from {{#time:j xg|2022-04-28|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-04-26|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]). * Some very old browsers and operating systems are no longer supported. Some things on the wikis might look weird or not work in very old browsers like Internet Explorer 9 or 10, Android 4, or Firefox 38 or older. [https://phabricator.wikimedia.org/T306486] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W17"/> 22:56, 25 April 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23187115 --> == Tech News: 2022-18 == <section begin="technews-2022-W18"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/18|Translations]] are available. '''Recent changes''' * On [https://noc.wikimedia.org/conf/dblists/group2.dblist all remaining wikis] (group 2), the software to play videos and audio files on pages has now changed. The old player has been removed. Some audio players will become wider after this change. [[mw:Special:MyLanguage/Extension:TimedMediaHandler/VideoJS_Player|The new player]] has been a beta feature for over four years. [https://phabricator.wikimedia.org/T100106][https://phabricator.wikimedia.org/T248418] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-04|en}}. It will be on all wikis from {{#time:j xg|2022-05-05|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). '''Future changes''' * The developers are working on talk pages in the [[mw:Wikimedia Apps/Team/iOS|Wikipedia app for iOS]]. You can [https://wikimedia.qualtrics.com/jfe/form/SV_9GBcHczQGLbQWTY give feedback]. You can take the survey in English, German, Hebrew or Chinese. * [[m:WMDE_Technical_Wishes/VisualEditor_template_dialog_improvements#Status_and_next_steps|Most wikis]] will receive an [[m:WMDE_Technical_Wishes/VisualEditor_template_dialog_improvements|improved template dialog]] in VisualEditor and New Wikitext mode. [https://phabricator.wikimedia.org/T296759] [https://phabricator.wikimedia.org/T306967] * If you use syntax highlighting while editing wikitext, you can soon activate a [[m:WMDE_Technical_Wishes/Improved_Color_Scheme_of_Syntax_Highlighting#Color-blind_mode|colorblind-friendly color scheme]]. [https://phabricator.wikimedia.org/T306867] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Several CSS IDs related to MediaWiki interface messages will be removed. Technical editors should please [[phab:T304363|review the list of IDs and links to their existing uses]]. These include <code dir=ltr>#mw-anon-edit-warning</code>, <code dir=ltr>#mw-undelete-revision</code> and 3 others. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W18"/> 19:33, 2 May 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23232924 --> == Tech News: 2022-19 == <section begin="technews-2022-W19"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/19|Translations]] are available. '''Recent changes''' * You can now see categories in the [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android|Wikipedia app for Android]]. [https://phabricator.wikimedia.org/T73966] '''Problems''' * Last week, there was a problem with Wikidata's search autocomplete. This has now been fixed. [https://phabricator.wikimedia.org/T307586] * Last week, all wikis had slow access or no access for 20 minutes, for logged-in users and non-cached pages. This was caused by a problem with a database change. [https://phabricator.wikimedia.org/T307647] '''Changes later this week''' * There is no new MediaWiki version this week. [https://phabricator.wikimedia.org/T305217#7894966] * [[m:WMDE Technical Wishes/Geoinformation#Current issues|Incompatibility issues]] with [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] and the [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs|FlaggedRevs extension]] will be fixed: Deployment is planned for May 10 on all wikis. Kartographer will then be enabled on the [[phab:T307348|five wikis which have not yet enabled the extension]] on May 24. * The [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector (2022)]] skin will be set as the default on several more wikis, including Arabic and Catalan Wikipedias. Logged-in users will be able to switch back to the old Vector (2010). See the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2022-04 for the largest wikis|latest update]] about Vector (2022). '''Future meetings''' * The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place on 17 May. The following meetings are currently planned for: 7 June, 21 June, 5 July, 19 July. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W19"/> 15:22, 9 May 2022 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23256717 --> == Tech News: 2022-20 == <section begin="technews-2022-W20"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/20|Translations]] are available. '''Changes later this week''' * Some wikis can soon use the [[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|add a link]] feature. This will start on Wednesday. The wikis are {{int:project-localized-name-cawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-simplewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-svwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}. This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304542] * The [[mw:Special:MyLanguage/Wikimedia Hackathon 2022|Wikimedia Hackathon 2022]] will take place online on May 20–22. It will be in English. There are also local [[mw:Special:MyLanguage/Wikimedia Hackathon 2022/Meetups|hackathon meetups]] in Germany, Ghana, Greece, India, Nigeria and the United States. Technically interested Wikimedians can work on software projects and learn new skills. You can also host a session or post a project you want to work on. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-18|en}}. It will be on all wikis from {{#time:j xg|2022-05-19|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). '''Future changes''' * You can soon edit translatable pages in the visual editor. Translatable pages exist on for examples Meta and Commons. [https://diff.wikimedia.org/2022/05/12/mediawiki-1-38-brings-support-for-editing-translatable-pages-with-the-visual-editor/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W20"/> 18:58, 16 May 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23291515 --> == Tech News: 2022-21 == <section begin="technews-2022-W21"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/21|Translations]] are available. '''Recent changes''' * Administrators using the mobile web interface can now access Special:Block directly from user pages. [https://phabricator.wikimedia.org/T307341] * The <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wiktionary.org/ www.wiktionary.org]</span> portal page now uses an automated update system. Other [[m:Project_portals|project portals]] will be updated over the next few months. [https://phabricator.wikimedia.org/T304629] '''Problems''' * The Growth team maintains a mentorship program for newcomers. Previously, newcomers weren't able to opt out from the program. Starting May 19, 2022, newcomers are able to fully opt out from Growth mentorship, in case they do not wish to have any mentor at all. [https://phabricator.wikimedia.org/T287915] * Some editors cannot access the content translation tool if they load it by clicking from the contributions menu. This problem is being worked on. It should still work properly if accessed directly via Special:ContentTranslation. [https://phabricator.wikimedia.org/T308802] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-05-25|en}}. It will be on all wikis from {{#time:j xg|2022-05-26|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Gadget and user scripts developers are invited to give feedback on a [[mw:User:Jdlrobson/Extension:Gadget/Policy|proposed technical policy]] aiming to improve support from MediaWiki developers. [https://phabricator.wikimedia.org/T308686] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W21"/> 00:21, 24 May 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23317250 --> == Tech News: 2022-22 == <section begin="technews-2022-W22"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/22|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|Advanced item]] In the [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] extension, an <code dir=ltr>ip_in_ranges()</code> function has been introduced to check if an IP is in any of the ranges. Wikis are advised to combine multiple <code dir=ltr>ip_in_range()</code> expressions joined by <code>|</code> into a single expression for better performance. You can use the search function on [[Special:AbuseFilter|Special:AbuseFilter]] to locate its usage. [https://phabricator.wikimedia.org/T305017] * The [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature|IP Info feature]] which helps abuse fighters access information about IPs, [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#May 24, 2022|has been deployed]] to all wikis as a beta feature. This comes after weeks of beta testing on test.wikipedia.org. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-05-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-01|en}}. It will be on all wikis from {{#time:j xg|2022-06-02|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-05-31|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]). * The [[mw:Special:MyLanguage/Help:DiscussionTools#New topic tool|New Topic Tool]] will be deployed for all editors at most wikis soon. You will be able to opt out from within the tool and in [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/New_discussion][https://phabricator.wikimedia.org/T287804] * [[File:Octicons-tools.svg|15px|link=|Advanced item]] The [[:mw:Special:ApiHelp/query+usercontribs|list=usercontribs API]] will support fetching contributions from an [[mw:Special:MyLanguage/Help:Range blocks#Non-technical explanation|IP range]] soon. API users can set the <code>uciprange</code> parameter to get contributions from any IP range within [[:mw:Manual:$wgRangeContributionsCIDRLimit|the limit]]. [https://phabricator.wikimedia.org/T177150] * A new parser function will be introduced: <bdi lang="zxx" dir="ltr"><code><nowiki>{{=}}</nowiki></code></bdi>. It will replace existing templates named "=". It will insert an [[w:en:Equals sign|equal sign]]. This can be used to escape the equal sign in the parameter values of templates. [https://phabricator.wikimedia.org/T91154] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W22"/> 20:28, 30 May 2022 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23340178 --> == Tech News: 2022-23 == <section begin="technews-2022-W23"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/23|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-08|en}}. It will be on all wikis from {{#time:j xg|2022-06-09|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new <bdi lang="zxx" dir="ltr"><code>str_replace_regexp()</code></bdi> function can be used in [[Special:AbuseFilter|abuse filters]] to replace parts of text using a [[w:en:Regular expression|regular expression]]. [https://phabricator.wikimedia.org/T285468] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W23"/> 02:46, 7 June 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23366979 --> == Tech News: 2022-24 == <section begin="technews-2022-W24"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/24|Translations]] are available. '''Recent changes''' * All wikis can now use [[mw:Special:MyLanguage/Extension:Kartographer|Kartographer]] maps. Kartographer maps now also work on pages with [[mw:Special:MyLanguage/Help:Pending changes|pending changes]]. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Project_descriptions][https://phabricator.wikimedia.org/T307348] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-15|en}}. It will be on all wikis from {{#time:j xg|2022-06-16|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-14|en}} at 06:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]). [https://phabricator.wikimedia.org/T300471] * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-abwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-acewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-adywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-afwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-akwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-alswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-amwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-anwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-angwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-arcwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-arzwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-astwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-atjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-avwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-aywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-azbwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304548] * The [[mw:Special:MyLanguage/Help:DiscussionTools#New topic tool|New Topic Tool]] will be deployed for all editors at Commons, Wikidata, and some other wikis soon. You will be able to opt out from within the tool and in [[Special:Preferences#mw-prefsection-editing-discussion|Preferences]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/New_discussion][https://phabricator.wikimedia.org/T287804] '''Future meetings''' * The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place today (13 June). The following meetings will take place on: 28 June, 12 July, 26 July. '''Future changes''' * By the end of July, the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022]] skin should be ready to become the default across all wikis. Discussions on how to adjust it to the communities' needs will begin in the next weeks. It will always be possible to revert to the previous version on an individual basis. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2022-04 for the largest wikis|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W24"/> 16:58, 13 June 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23389956 --> == Tech News: 2022-25 == <section begin="technews-2022-W25"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/25|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android|Wikipedia App for Android]] now has an option for editing the whole page at once, located in the overflow menu (three-dots menu [[File:Ic more vert 36px.svg|15px|link=|alt=]]). [https://phabricator.wikimedia.org/T103622] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Some recent database changes may affect queries using the [[m:Research:Quarry|Quarry tool]]. Queries for <bdi lang="zxx" dir="ltr"><code>site_stats</code></bdi> at English Wikipedia, Commons, and Wikidata will need to be updated. [[phab:T306589|Read more]]. * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new <bdi lang="zxx" dir="ltr"><code>user_global_editcount</code></bdi> variable can be used in [[Special:AbuseFilter|abuse filters]] to avoid affecting globally active users. [https://phabricator.wikimedia.org/T130439] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-22|en}}. It will be on all wikis from {{#time:j xg|2022-06-23|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * Users of non-responsive skins (e.g. MonoBook or Vector) on mobile devices may notice a slight change in the default zoom level. This is intended to optimize zooming and ensure all interface elements are present on the page (for example the table of contents on Vector 2022). In the unlikely event this causes any problems with how you use the site, we'd love to understand better, please ping <span class="mw-content-ltr" lang="en" dir="ltr">[[m:User:Jon (WMF)|Jon (WMF)]]</span> to any on-wiki conversations. [https://phabricator.wikimedia.org/T306910] '''Future changes''' * The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July. Discussions will look different. You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Parsoid's HTML output will soon stop annotating file links with different <bdi lang="zxx" dir="ltr"><code>typeof</code></bdi> attribute values, and instead use <bdi lang="zxx" dir="ltr"><code>mw:File</code></bdi> for all types. Tool authors should adjust any code that expects: <bdi lang="zxx" dir="ltr"><code>mw:Image</code></bdi>, <bdi lang="zxx" dir="ltr"><code>mw:Audio</code></bdi>, or <bdi lang="zxx" dir="ltr"><code>mw:Video</code></bdi>. [https://phabricator.wikimedia.org/T273505] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W25"/> 20:18, 20 June 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23425855 --> == Tech News: 2022-26 == <section begin="technews-2022-W26"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/26|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] API service now has self-service accounts with free on-demand requests and monthly snapshots ([https://enterprise.wikimedia.com/docs/ API documentation]). Community access [[m:Special:MyLanguage/Wikimedia Enterprise/FAQ#community-access|via database dumps & Wikimedia Cloud Services]] continues. * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[d:Special:MyLanguage/Wikidata:Wiktionary#lua|All Wikimedia wikis can now use Wikidata Lexemes in Lua]] after creating local modules and templates. Discussions are welcome [[d:Wikidata_talk:Lexicographical_data#You_can_now_reuse_Wikidata_Lexemes_on_all_wikis|on the project talk page]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-06-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-06-29|en}}. It will be on all wikis from {{#time:j xg|2022-06-30|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-28|en}} at 06:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). [https://phabricator.wikimedia.org/T311033] * Some global and cross-wiki services will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-06-30|en}} at 06:00 UTC. This will impact ContentTranslation, Echo, StructuredDiscussions, Growth experiments and a few more services. [https://phabricator.wikimedia.org/T300472] * Users will be able to sort columns within sortable tables in the mobile skin. [https://phabricator.wikimedia.org/T233340] '''Future meetings''' * The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place tomorrow (28 June). The following meetings will take place on 12 July and 26 July. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W26"/> 20:02, 27 June 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23453785 --> == Tech News: 2022-27 == <section begin="technews-2022-W27"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/27|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-06|en}}. It will be on all wikis from {{#time:j xg|2022-07-07|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-07-05|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]) and on {{#time:j xg|2022-07-07|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]). * The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July. Discussions will look different. You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. * [[File:Octicons-tools.svg|15px|link=|alt=| Advanced item]] This change only affects pages in the main namespace in Wikisource. The Javascript config variable <bdi lang="zxx" dir="ltr"><code>proofreadpage_source_href</code></bdi> will be removed from <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Manual:Interface/JavaScript#mw.config|mw.config]]</code></bdi> and be replaced with the variable <bdi lang="zxx" dir="ltr"><code>prpSourceIndexPage</code></bdi>. [https://phabricator.wikimedia.org/T309490] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W27"/> 19:32, 4 July 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23466250 --> == Tech News: 2022-28 == <section begin="technews-2022-W28"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/28|Translations]] are available. '''Recent changes''' * In the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022 skin]], the page title is now displayed above the tabs such as Discussion, Read, Edit, View history, or More. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates#Page title/tabs switch|Learn more]]. [https://phabricator.wikimedia.org/T303549] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] It is now possible to easily view most of the configuration settings that apply to just one wiki, and to compare settings between two wikis if those settings are different. For example: [https://noc.wikimedia.org/wiki.php?wiki=jawiktionary Japanese Wiktionary settings], or [https://noc.wikimedia.org/wiki.php?wiki=eswiki&compare=eowiki settings that are different between the Spanish and Esperanto Wikipedias]. Local communities may want to [[m:Special:MyLanguage/Requesting_wiki_configuration_changes|discuss and propose changes]] to their local settings. Details about each of the named settings can be found by [[mw:Special:Search|searching MediaWiki.org]]. [https://phabricator.wikimedia.org/T308932] *The Anti-Harassment Tools team [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#May|recently deployed]] the IP Info Feature as a [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature at all wikis]]. This feature allows abuse fighters to access information about IP addresses. Please check our update on [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Info feature#April|how to find and use the tool]]. Please share your feedback using a link you will be given within the tool itself. '''Changes later this week''' * There is no new MediaWiki version this week. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-07-12|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]). '''Future changes''' * The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout July. Discussions will look different. You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/28|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W28"/> 19:24, 11 July 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23502519 --> == Tech News: 2022-29 == <section begin="technews-2022-W29"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/29|Translations]] are available. '''Problems''' * The feature on mobile web for [[mw:Special:MyLanguage/Extension:NearbyPages|Nearby Pages]] was missing last week. It will be fixed this week. [https://phabricator.wikimedia.org/T312864] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-20|en}}. It will be on all wikis from {{#time:j xg|2022-07-21|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). '''Future changes''' * The [[mw:Technical_decision_making/Forum|Technical Decision Forum]] is seeking [[mw:Technical_decision_making/Community_representation|community representatives]]. You can apply on wiki or by emailing <span class="mw-content-ltr" lang="en" dir="ltr">TDFSupport@wikimedia.org</span> before 12 August. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W29"/> 22:59, 18 July 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23517957 --> == Tech News: 2022-30 == <section begin="technews-2022-W30"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/30|Translations]] are available. '''Recent changes''' * The <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikibooks.org/ www.wikibooks.org]</span> and <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikiquote.org/ www.wikiquote.org]</span> portal pages now use an automated update system. Other [[m:Project_portals|project portals]] will be updated over the next few months. [https://phabricator.wikimedia.org/T273179] '''Problems''' * Last week, some wikis were in read-only mode for a few minutes because of an emergency switch of their main database ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). [https://phabricator.wikimedia.org/T313383] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-07-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-07-27|en}}. It will be on all wikis from {{#time:j xg|2022-07-28|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * The external link icon will change slightly in the skins Vector legacy and Vector 2022. The new icon uses simpler shapes to be more recognizable on low-fidelity screens. [https://phabricator.wikimedia.org/T261391] * Administrators will now see buttons on user pages for "{{int:changeblockip}}" and "{{int:unblockip}}" instead of just "{{int:blockip}}" if the user is already blocked. [https://phabricator.wikimedia.org/T308570] '''Future meetings''' * The next [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|open meeting with the Web team]] about Vector (2022) will take place tomorrow (26 July). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W30"/> 19:27, 25 July 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23545370 --> == Tech News: 2022-31 == <section begin="technews-2022-W31"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/31|Translations]] are available. '''Recent changes''' * Improved [[m:Special:MyLanguage/Help:Displaying_a_formula#Phantom|LaTeX capabilities for math rendering]] are now available in the wikis thanks to supporting <bdi lang="zxx" dir="ltr"><code>Phantom</code></bdi> tags. This completes part of [[m:Community_Wishlist_Survey_2022/Editing/Missing_LaTeX_capabilities_for_math_rendering|the #59 wish]] of the 2022 Community Wishlist Survey. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-03|en}}. It will be on all wikis from {{#time:j xg|2022-08-04|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] will be available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup0.dblist Group 0]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]]. '''Future changes''' * The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout August. Discussions will look different. You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. '''Future meetings''' * This week, three meetings about [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector (2022)]] with live interpretation will take place. On Tuesday, interpretation in Russian will be provided. On Thursday, meetings for Arabic and Spanish speakers will take place. [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/Talk to Web|See how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W31"/> 21:21, 1 August 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23615613 --> == Tech News: 2022-32 == <section begin="technews-2022-W32"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/32|Translations]] are available. '''Recent changes''' * [[:m:Special:MyLanguage/Meta:GUS2Wiki/Script|GUS2Wiki]] copies the information from [[{{#special:GadgetUsage}}]] to an on-wiki page so you can review its history. If your project isn't already listed on the [[d:Q113143828|Wikidata entry for Project:GUS2Wiki]] you can either run GUS2Wiki yourself or [[:m:Special:MyLanguage/Meta:GUS2Wiki/Script#Opting|make a request to receive updates]]. [https://phabricator.wikimedia.org/T121049] '''Changes later this week''' * There is no new MediaWiki version this week. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-09|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2022-08-11|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]). '''Future meetings''' * The [[wmania:Special:MyLanguage/Hackathon|Wikimania Hackathon]] will take place online from August 12–14. Don't miss [[wmania:Special:MyLanguage/Hackathon/Schedule|the pre-hacking showcase]] to learn about projects and find collaborators. Anyone can [[phab:/project/board/6030/|propose a project]] or [[wmania:Special:MyLanguage/Hackathon/Schedule|host a session]]. [[wmania:Special:MyLanguage/Hackathon/Newcomers|Newcomers are welcome]]! '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W32"/> 19:50, 8 August 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23627807 --> == Tech News: 2022-33 == <section begin="technews-2022-W33"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/33|Translations]] are available. '''Recent changes''' * The Persian (Farsi) Wikipedia community decided to block IP editing from October 2021 to April 2022. The Wikimedia Foundation's Product Analytics team tracked the impact of this change. [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/IP Editing Restriction Study/Farsi Wikipedia|An impact report]] is now available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-17|en}}. It will be on all wikis from {{#time:j xg|2022-08-18|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-16|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]) and on {{#time:j xg|2022-08-18|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s8.dblist targeted wikis]). * The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] will be available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup1.dblist Group 1]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]]. '''Future changes''' * The Beta Feature for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated throughout August. Discussions will look different. You can see [[mw:Special:MyLanguage/Talk pages project/Usability/Prototype|some of the proposed changes]]. [https://www.mediawiki.org/wiki/Talk_pages_project/Usability#4_August_2022][https://www.mediawiki.org/wiki/Talk_pages_project/Usability#Phase_1:_Topic_containers][https://phabricator.wikimedia.org/T312672] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W33"/> 21:08, 15 August 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23658001 --> == Tech News: 2022-34 == <section begin="technews-2022-W34"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/34|Translations]] are available. '''Recent changes''' * Two problems with [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps have been fixed. Maps are no longer shown as empty when a geoline was created via VisualEditor. Geolines consisting of points with QIDs (e.g., subway lines) are no longer shown with pushpins. [https://phabricator.wikimedia.org/T292613][https://phabricator.wikimedia.org/T308560] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-24|en}}. It will be on all wikis from {{#time:j xg|2022-08-25|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-25|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]). * The colours of links and visited links will change. This is to make the difference between links and other text more clear. [https://phabricator.wikimedia.org/T213778] '''Future changes''' * The new [{{int:discussiontools-topicsubscription-button-subscribe}}] button [[mw:Talk pages project/Notifications#12 August 2022|helps newcomers get answers]]. The Editing team is enabling this tool everywhere. You can turn it off in [[Special:Preferences#mw-prefsection-editing-discussion|your preferences]]. [https://phabricator.wikimedia.org/T284489] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W34"/> 00:12, 23 August 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23675501 --> == Tech News: 2022-35 == <section begin="technews-2022-W35"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/35|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Help:Extension:WikiEditor/Realtime_Preview|Realtime Preview]] is available as a Beta Feature on wikis in [https://noc.wikimedia.org/conf/highlight.php?file=dblists%2Fgroup2.dblist Group 2]. This feature was built in order to fulfill [[m:Special:MyLanguage/Community_Wishlist_Survey_2021/Real_Time_Preview_for_Wikitext|one of the Community Wishlist Survey proposals]]. Please note that when this Beta feature is enabled, it may cause conflicts with some wiki-specific Gadgets. '''Problems''' * In recent months, there have been inaccurate numbers shown for various [[{{#special:statistics}}]] at Commons, Wikidata, and English Wikipedia. This has now been fixed. [https://phabricator.wikimedia.org/T315693] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-08-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-08-31|en}}. It will be on all wikis from {{#time:j xg|2022-09-01|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-08-30|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]) and on {{#time:j xg|2022-09-01|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). '''Future changes''' * The Wikimedia Foundation wants to improve how Wikimedia communities report harmful incidents by building the [[m:Special:MyLanguage/Private Incident Reporting System|Private Incident Reporting System (PIRS)]] to make it easy and safe for users to make reports. You can leave comments on the talk page, by answering the [[m:Special:MyLanguage/Private Incident Reporting System#Phase 1|questions provided]]. If you have ever faced a harmful situation that you wanted to report/reported, join a PIRS interview to share your experience. To sign up [[m:Special:EmailUser/MAna_(WMF)|please email]] <span class="mw-content-ltr" lang="en" dir="ltr">[[m:User:MAna (WMF)|Madalina Ana]]</span>. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W35"/> 23:05, 29 August 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23725814 --> == Tech News: 2022-36 == <section begin="technews-2022-W36"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/36|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.39/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-07|en}}. It will be on all wikis from {{#time:j xg|2022-09-08|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-09-06|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]) and on {{#time:j xg|2022-09-08|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]). * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] On Special pages that only have one tab, the tab-bar's row will be hidden in the Vector-2022 skin to save space. The row will still show if Gadgets use it. Gadgets that currently append directly to the CSS id of <bdi lang="zxx" dir="ltr"><code>#p-namespaces</code></bdi> should be updated to use the <bdi lang="zxx" dir="ltr"><code>[[mw:ResourceLoader/Core_modules#addPortletLink|mw.util.addPortletLink]]</code></bdi> function instead. Gadgets that style this id should consider also targeting <bdi lang="zxx" dir="ltr"><code>#p-associated-pages</code></bdi>, the new id for this row. [[phab:T316908|Examples are available]]. [https://phabricator.wikimedia.org/T316908][https://phabricator.wikimedia.org/T313409] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W36"/> 23:22, 5 September 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23757743 --> == Tech News: 2022-37 == <section begin="technews-2022-W37"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/37|Translations]] are available. '''Recent changes''' * The search servers have been upgraded to a new major version. If you notice any issues with searching, please report them on [[phab:project/view/1849/|Phabricator]]. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/XPCTYYTN67FVFKN6XOHULJVGUO44J662] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-14|en}}. It will be on all wikis from {{#time:j xg|2022-09-15|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[mw:Special:MyLanguage/Extension:SyntaxHighlight|Syntax highlighting]] is now tracked as an [[mw:Special:MyLanguage/Manual:$wgExpensiveParserFunctionLimit|expensive parser function]]. Only 500 expensive function calls can be used on a single page. Pages that exceed the limit are added to a [[:Category:{{MediaWiki:expensive-parserfunction-category}}|tracking category]]. [https://phabricator.wikimedia.org/T316858] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W37"/> 01:50, 13 September 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23787318 --> == Tech News: 2022-38 == <section begin="technews-2022-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/38|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Two database fields in the <bdi lang="zxx" dir="ltr"><code><nowiki>templatelinks</nowiki></code></bdi> table are now being dropped: <bdi lang="zxx" dir="ltr"><code><nowiki>tl_namespace</nowiki></code></bdi> and <bdi lang="zxx" dir="ltr"><code><nowiki>tl_title</nowiki></code></bdi>. Any queries that rely on these fields need to be changed to use the new normalization field called <bdi lang="zxx" dir="ltr"><code><nowiki>tl_target_id</nowiki></code></bdi>. See <span class="mw-content-ltr" lang="en" dir="ltr">[[phab:T299417|T299417]]</span> for more information. This is part of [[w:Database normalization|normalization]] of links tables. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/message/U2U6TXIBABU3KDCVUOITIGI5OJ4COBSW/][https://www.mediawiki.org/wiki/User:ASarabadani_(WMF)/Database_for_devs_toolkit/Concepts/Normalization] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-21|en}}. It will be on all wikis from {{#time:j xg|2022-09-22|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * In [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps, you can use icons on markers for common points of interest. On Tuesday, the [[mw:Special:MyLanguage/Help:Extension:Kartographer/Icons|previous icon set]] will be updated to [https://de.wikipedia.beta.wmflabs.org/wiki/Hilfe:Extension:Kartographer/Icons version maki 7.2]. That means, around 100 new icons will be available. Additionally, all existing icons were updated for clarity and to make them work better in international contexts. [https://phabricator.wikimedia.org/T302861][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation#Update_maki_icons] '''Future changes''' * In a [[m:Content_Partnerships_Hub/Software/Volunteer_developers_discussion_at_Wikimania_2022|group discussion at Wikimania]], more than 30 people talked about how to make content partnership software in the Wikimedia movement more sustainable. What kind of support is acceptable for volunteer developers? Read the summary and [[m:Talk:Content Partnerships Hub/Software/Volunteer developers discussion at Wikimania 2022|leave your feedback]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W38"/> <span class="mw-content-ltr" lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</span> 22:16, 19 September 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23826293 --> == Tech News: 2022-39 == <section begin="technews-2022-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/39|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Parsoid clients should be updated to allow for space-separated multi-values in the <bdi lang="en" dir="ltr"><code>rel</code></bdi> attribute of links. Further details are in <bdi lang="en" dir="ltr">[[phab:T315209|T315209]]</bdi>. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-09-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-09-28|en}}. It will be on all wikis from {{#time:j xg|2022-09-29|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[mw:Special:MyLanguage/VisualEditor/Diffs|Visual diffs]] will become available to all users, except at the Wiktionaries and Wikipedias. [https://phabricator.wikimedia.org/T314588] * [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|Talk pages on the mobile site]] will change at the Arabic, Bangla, Chinese, French, Haitian Creole, Hebrew, Korean, and Vietnamese Wikipedias. They should be easier to use and provide more information. [https://phabricator.wikimedia.org/T318302] [https://www.mediawiki.org/wiki/Talk_pages_project/Mobile] * In the [[mw:Lua/Scripting|{{ns:828}}]] namespace, pages ending with <bdi lang="en" dir="ltr"><code>.json</code></bdi> will be treated as JSON, just like they already are in the {{ns:2}} and {{ns:8}} namespaces. [https://phabricator.wikimedia.org/T144475] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W39"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:30, 27 September 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23860085 --> == Tech News: 2022-40 == <section begin="technews-2022-W40"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/40|Translations]] are available. '''Recent changes''' * [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps can now show geopoints from Wikidata, via QID or SPARQL query. Previously, this was only possible for geoshapes and geolines. [https://phabricator.wikimedia.org/T307695] [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Geopoints_via_QID] * The [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award 2022]] is looking for nominations. You can recommend tools until 12 October. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-05|en}}. It will be on all wikis from {{#time:j xg|2022-10-06|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|Talk pages on the mobile site]] will change at the Arabic, Bangla, Chinese, French, Haitian Creole, Hebrew, Korean, and Vietnamese Wikipedias. They should be easier to use and provide more information. (Last week's release was delayed) [https://phabricator.wikimedia.org/T318302] [https://www.mediawiki.org/wiki/Talk_pages_project/Mobile] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The <bdi lang="zxx" dir="ltr"><code>scribunto-console</code></bdi> API module will require a [[mw:Special:MyLanguage/API:Tokens|CSRF token]]. This module is documented as internal and use of it is not supported. [[phab:T212071|[5]]] * The Vector 2022 skin will become the default across the smallest Wikimedia projects. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#Deployment_plan_and_timeline|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W40"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:23, 4 October 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23885489 --> == Tech News: 2022-41 == <section begin="technews-2022-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/41|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-12|en}}. It will be on all wikis from {{#time:j xg|2022-10-13|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * On some wikis, [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps in full size view will be able to display nearby articles. After a feedback period, more wikis will follow. [https://phabricator.wikimedia.org/T316782][https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Nearby_articles] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W41"/> 14:08, 10 October 2022 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23912412 --> == Tech News: 2022-42 == <section begin="technews-2022-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/42|Translations]] are available. '''Recent changes''' * The recently implemented feature of [[phab:T306883|article thumbnails in Special:Search]] will be limited to Wikipedia projects only. Further details are in [[phab:T320510|T320510]]. [https://www.mediawiki.org/wiki/Special:MyLanguage/Structured_Data_Across_Wikimedia/Search_Improvements] * A bug that caused problems in loading article thumbnails in Special:Search has been fixed. Further details are in [[phab:T320406|T320406]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-19|en}}. It will be on all wikis from {{#time:j xg|2022-10-20|en}} ([[mw:MediaWiki 1.39/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Lua module authors can use <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Extension:Scribunto/Lua_reference_manual#mw.loadJsonData|mw.loadJsonData()]]</code></bdi> to load data from JSON pages. [https://phabricator.wikimedia.org/T217500] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Lua module authors can enable <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Extension:Scribunto/Lua_reference_manual#Strict_library|require( "strict" )]]</code></bdi> to add errors for some possible code problems. This replaces "[[wikidata:Q16748603|Module:No globals]]" on most wikis. [https://phabricator.wikimedia.org/T209310] '''Future changes''' * The [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] for [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] will be updated at most wikis. The "{{int:discussiontools-replylink}}" button will look different after this change. [https://phabricator.wikimedia.org/T320683] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W42"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:46, 17 October 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23943992 --> == Tech News: 2022-43 == <section begin="technews-2022-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/43|Translations]] are available. '''Recent changes''' * There have been some minor visual fixes in Special:Search, regarding audio player alignment and image placeholder height. Further details are in [[phab:T319230|T319230]]. * On Wikipedias, a new [[Special:Preferences#mw-prefsection-searchoptions|preference]] has been added to hide article thumbnails in Special:Search. Full details are in [[phab:T320337|T320337]]. '''Problems''' * Last week, three wikis ({{int:project-localized-name-frwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ruwiki/en}}) had read-only access for 25 minutes. This was caused by a hardware problem. [https://phabricator.wikimedia.org/T320990] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-10-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-10-26|en}}. It will be on all wikis from {{#time:j xg|2022-10-27|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-10-25|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2022-10-27|en}} at 7:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s4.dblist targeted wikis]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-aswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-banwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-barwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bat smgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bclwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-be x oldwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-biwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bjnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bpywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-brwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bugwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bxrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304549] * Starting on Wednesday October 26, 2022, the list of mentors will be upgraded [[d:Q14339834 | at wikis where Growth mentorship is available]]. The mentorship system will continue to work as it does now. The signup process [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list#add|will be replaced]], and a new management option will be provided. Also, this change simplifies [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list#create|the creation of mentorship systems at Wikipedias]]. [https://phabricator.wikimedia.org/T314858][https://phabricator.wikimedia.org/T310905][https://www.mediawiki.org/wiki/Special:MyLanguage/Growth/Structured_mentor_list] * Pages with titles that start with a lower-case letter according to Unicode 11 will be renamed or deleted. There is a list of affected pages at <bdi lang="en" dir="ltr">[[m:Unicode 11 case map migration]]</bdi>. More information can be found at [[phab:T292552|T292552]]. * The Vector 2022 skin will become the default across the smallest Wikipedias. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements#smallest-1|Learn more]]. '''Future changes''' * The [[mw:Special:MyLanguage/Talk pages project/Replying|Reply tool]] and [[mw:Special:MyLanguage/Talk pages project/New discussion|New Topic tool]] will soon get a [[mw:Special:MyLanguage/VisualEditor/Special characters|special characters menu]]. [https://phabricator.wikimedia.org/T249072] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W43"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:22, 24 October 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23975411 --> == Tech News: 2022-44 == <section begin="technews-2022-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/44|Translations]] are available. '''Recent changes''' * When using keyboard navigation on a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map, the focus will become more visible. [https://phabricator.wikimedia.org/T315997] * In {{#special:RecentChanges}}, you can now hide the log entries for new user creations with the filter for "{{int:rcfilters-filter-newuserlogactions-label}}". [https://phabricator.wikimedia.org/T321155] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-02|en}}. It will be on all wikis from {{#time:j xg|2022-11-03|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * The [[mw:Special:MyLanguage/Help:Extension:Kartographer|maps dialog]] in VisualEditor now has some help texts. [https://phabricator.wikimedia.org/T318818] * It is now possible to select the language of a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor via a dropdown menu. [https://phabricator.wikimedia.org/T318817] * It is now possible to add a caption to a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor. [https://phabricator.wikimedia.org/T318815] * It is now possible to hide the frame of a [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] map in VisualEditor. [https://phabricator.wikimedia.org/T318813] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W44"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:15, 31 October 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=23977539 --> == Tech News: 2022-45 == <section begin="technews-2022-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/45|Translations]] are available. '''Recent changes''' * An updated version of the [[m:Special:MyLanguage/EventCenter/Registration|Event Registration]] tool is now available for testing at [[testwiki:|testwiki]] and [[test2wiki:| test2wiki]]. The tool provides features for event organizers and participants. Your feedback is welcome at our [[m:Talk:Campaigns/Foundation Product Team/Registration|project talkpage]]. More information about [[m:Campaigns/Foundation Product Team/Registration|the project]] is available. [https://phabricator.wikimedia.org/T318592] '''Problems''' * Twice last week, for about 45 minutes, some files and thumbnails failed to load and uploads failed, mostly for logged-in users. The cause is being investigated and an incident report will be available soon. '''Changes later this week''' * There is no new MediaWiki version this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W45"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:32, 8 November 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24001035 --> == Tech News: 2022-46 == <section begin="technews-2022-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/46|Translations]] are available. '''Recent changes''' * At Wikidata, an interwiki link can now point to a redirect page if certain conditions are met. This new feature is called [[wikidata:Special:MyLanguage/Wikidata:Sitelinks_to_redirects|sitelinks to redirects]]. It is needed when one wiki uses one page to cover multiple concepts but another wiki uses more pages to cover the same concepts. Your [[wikidata:Special:MyLanguage/Wikidata talk:Sitelinks to redirects|feedback on the talkpage]] of the new proposed guideline is welcome. [https://phabricator.wikimedia.org/T278962] * The <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikinews.org/ www.wikinews.org]</span>, <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikiversity.org/ www.wikiversity.org]</span>, and <span class="mw-content-ltr" lang="en" dir="ltr">[https://www.wikivoyage.org/ www.wikivoyage.org]</span> portal pages now use an automated update system. [https://phabricator.wikimedia.org/T273179] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-16|en}}. It will be on all wikis from {{#time:j xg|2022-11-17|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * There will be a new link to directly "Edit template data" on Template pages. [https://phabricator.wikimedia.org/T316759] '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Wikis where mobile [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] are enabled ([[mw:Special:MyLanguage/Talk pages project/Deployment Status|these ones]]) will soon use full CSS styling to display any templates that are placed at the top of talk pages. To adapt these “talk page boxes” for narrow mobile devices you can use media queries, such as in [https://en.wikipedia.org/w/index.php?title=Module:Message_box/tmbox.css&oldid=1097618699#L-69 this example]. [https://phabricator.wikimedia.org/T312309] * Starting in January 2023, [[m:Special:MyLanguage/Community Tech|Community Tech]] will be [[m:Special:MyLanguage/Community Wishlist Survey/Updates/2023 Changes Update|running the Community Wishlist Survey (CWS) every two years]]. This means that in 2024, there will be no new proposals or voting. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W46"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:54, 14 November 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24071290 --> == Tech News: 2022-47 == <section begin="technews-2022-W47"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/47|Translations]] are available. '''Recent changes''' * The display of non-free media in the search bar and for article thumbnails in Special:Search has been deactivated. Further details are in [[phab:T320661|T320661]]. '''Changes later this week''' * There is no new MediaWiki version this week. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-11-22|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s2.dblist targeted wikis]) and on {{#time:j xg|2022-11-24|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s7.dblist targeted wikis]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/47|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W47"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:22, 21 November 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24071290 --> == Tech News: 2022-48 == <section begin="technews-2022-W48"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/48|Translations]] are available. '''Recent changes''' * A new preference, “Enable limited width mode”, has been added to the [[Special:Preferences#mw-prefsection-rendering|Vector 2022 skin]]. The preference is also available as a toggle on every page if your monitor is 1600 pixels or wider. It allows for increasing the width of the page for logged-out and logged-in users. [https://phabricator.wikimedia.org/T319449] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-11-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-11-30|en}}. It will be on all wikis from {{#time:j xg|2022-12-01|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2022-11-29|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s3.dblist targeted wikis]) and on {{#time:j xg|2022-12-01|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s1.dblist targeted wikis]). * Mathematical formulas shown in SVG image format will no longer have PNG fall-backs for browsers that don't support them. This is part of work to modernise the generation system. Showing only PNG versions was the default option until in February 2018. [https://lists.wikimedia.org/hyperkitty/list/wikimedia-l@lists.wikimedia.org/message/3BGOKWJIZGL4TC4HJ22ICRU2SEPWGCR4/][https://phabricator.wikimedia.org/T311620][https://phabricator.wikimedia.org/T186327] * On [[phab:P40224|some wikis]] that use flagged revisions, [[mw:Special:MyLanguage/Help:Extension:FlaggedRevs#Special:Contributions|a new checkbox will be added]] to Special:Contributions that enables you to see only the [[mw:Special:MyLanguage/Help:Pending changes|pending changes]] by a user. [https://phabricator.wikimedia.org/T321445] '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] How media is structured in the parser's HTML output will change early next week at [https://wikitech.wikimedia.org/wiki/Deployments/Train#Wednesday group1 wikis] (but not Wikimedia Commons or Meta-Wiki). This change improves the accessibility of content, and makes it easier to write related CSS. You may need to update your site-CSS, or userscripts and gadgets. There are [[mw:Special:MyLanguage/Parsoid/Parser_Unification/Media_structure/FAQ|details on what code to check, how to update the code, and where to report any related problems]]. [https://phabricator.wikimedia.org/T314318] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/48|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W48"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:03, 28 November 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24114342 --> == Tech News: 2022-49 == <section begin="technews-2022-W49"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/49|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The Wikisources use a tool called ProofreadPage. ProofreadPage uses OpenSeadragon which is an open source tool. The OpenSeadragon JavaScript API has been significantly re-written to support dynamically loading images. The functionality provided by the older version of the API should still work but it is no longer supported. User scripts and gadgets should migrate over to the newer version of the API. The functionality provided by the newer version of the API is [[mw:Extension:Proofread_Page/Page_viewer#JS_API|documented on MediaWiki]]. [https://phabricator.wikimedia.org/T308098][https://www.mediawiki.org/wiki/Extension:Proofread_Page/Edit-in-Sequence] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-12-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-12-07|en}}. It will be on all wikis from {{#time:j xg|2022-12-08|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/49|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W49"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:41, 6 December 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24151590 --> == Tech News: 2022-50 == <section begin="technews-2022-W50"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/50|Translations]] are available. '''Recent changes''' * An [[mw:Special:MyLanguage/Talk pages project/Mobile|A/B test has begun]] at 15 Wikipedias for [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|DiscussionTools on mobile]]. Half of the editors on the [[mw:Reading/Web/Mobile|mobile web site]] will have access to the {{int:discussiontools-replybutton}} tool and other features. [https://phabricator.wikimedia.org/T321961] * The character <code>=</code> cannot be used in new usernames, to make usernames work better with templates. Existing usernames are not affected. [https://phabricator.wikimedia.org/T254045] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2022-12-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2022-12-14|en}}. It will be on all wikis from {{#time:j xg|2022-12-15|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The HTML markup used by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] to [[mw:Special:MyLanguage/Talk_pages_project/Usability#Phase_1:_Topic_containers|show discussion metadata below section headings]] will be inserted after these headings, not inside of them. This change improves the accessibility of discussion pages for screen reader software. [https://phabricator.wikimedia.org/T314714] '''Events''' * The fourth edition of the [[m:Special:MyLanguage/Coolest_Tool_Award|Coolest Tool Award]] will happen online on [https://zonestamp.toolforge.org/1671210002 Friday 16 December 2022 at 17:00 UTC]! The event will be live-streamed on YouTube in the [https://www.youtube.com/user/watchmediawiki MediaWiki channel] and added to Commons afterwards. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/50|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W50"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:34, 12 December 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24216570 --> == Tech News: 2022-51 == <section begin="technews-2022-W51"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2022/51|Translations]] are available. '''Tech News''' * Because of the [[w:en:Christmas and holiday season|holidays]] the next issue of Tech News will be sent out on 9 January 2023. '''Recent changes''' * On a user's contributions page, you can filter it for edits with a tag like 'reverted'. Now, you can also filter for all edits that are not tagged like that. This was part of a Community Wishlist 2022 request. [https://phabricator.wikimedia.org/T119072] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] A new function has been used for gadget developers to add content underneath the title on article pages. This is considered a stable API that should work across all skins. [[mw:Special:MyLanguage/ResourceLoader/Core_modules#addSubtitle|Documentation is available]]. [https://phabricator.wikimedia.org/T316830] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] [[test2wiki:|One of our test wikis]] is now being served from a new infrastructure powered by [[w:Kubernetes|Kubernetes]] ([[wikitech:MediaWiki On Kubernetes|read more]]). More Wikis will switch to this new infrastructure in early 2023. Please test and let us know of any issues. [https://phabricator.wikimedia.org/T290536] '''Problems''' * Last week, all wikis had no edit access for 9 minutes. This was caused by a database problem. [https://wikitech.wikimedia.org/wiki/Incidents/2022-12-13_sessionstore] '''Changes later this week''' * There is no new MediaWiki version this week or next week. * The word "{{int:discussiontools-replybutton}}" is very short in some languages, such as Arabic ("<bdi lang="ar">ردّ</bdi>"). This makes the {{int:discussiontools-preference-label}} button on talk pages difficult to use. An arrow icon will be added to those languages. This will only be visible to editors who have the [[Special:Preferences#mw-prefsection-betafeatures|Beta Feature]] turned on. [https://www.mediawiki.org/wiki/Talk_pages_project/Usability#Status] [https://phabricator.wikimedia.org/T323537] '''Future changes''' * Edits can be automatically "tagged" by the system software or the {{int:Abusefilter}} system. Those tags link to a help page about the tags. Soon they will also link to Recent Changes to let you see other edits tagged this way. This was a Community Wishlist 2022 request. [https://phabricator.wikimedia.org/T301063] * The Trust & Safety tools team [[m:Special:MyLanguage/Private Incident Reporting System/Timeline and Updates|have shared new plans]] for building the Private Incident Reporting System. The system will make it easier for editors to ask for help if they are harassed or abused. * [[m:Special:MyLanguage/Community Wishlist Survey 2021/Real Time Preview for Wikitext|Realtime Preview for Wikitext]] is coming out of beta as an enabled feature for every user of the 2010 Wikitext [[mw:Special:MyLanguage/Editor|editor]] in the week of January 9, 2023. It will be available to use via the toolbar in the 2010 Wikitext editor. The feature was the 4th most popular wish of the Community Wishlist Survey 2021. '''Events''' * You can now [[mw:Special:MyLanguage/Wikimedia Hackathon 2023/Participate|register for the Wikimedia Hackathon 2023]], taking place on May 19–21 in Athens, Greece. You can also apply for a scholarship until January 14th. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2022/51|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2022-W51"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:00, 20 December 2022 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24258101 --> == Tech News: 2023-02 == <section begin="technews-2023-W02"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/02|Translations]] are available. '''Recent changes''' * You can use tags to filter edits in the recent changes feed or on your watchlist. You can now use tags to filter out edits you don't want to see. Previously you could only use tags to focus on the edits with those tags. [https://phabricator.wikimedia.org/T174349] * [[Special:WhatLinksHere|Special:WhatLinksHere]] shows all pages that link to a specific page. There is now a [https://wlh.toolforge.org prototype] for how to sort those pages alphabetically. You can see the discussion in the [[phab:T4306|Phabricator ticket]]. * You can now use the [[mw:Special:MyLanguage/Extension:Thanks|thanks]] function on your watchlist and the user contribution page. [https://phabricator.wikimedia.org/T51541] * A wiki page can be moved to give it a new name. You can now get a dropdown menu with common reasons when you move a page. This is so you don't have to write the explanation every time. [https://phabricator.wikimedia.org/T325257] * [[m:Special:MyLanguage/Matrix.org|Matrix]] is a chat tool. You can now use <code>matrix:</code> to create Matrix links on wiki pages. [https://phabricator.wikimedia.org/T326021] * You can filter out translations when you look at the recent changes on multilingual wikis. This didn't hide translation pages. You can now also hide subpages which are translation pages. [https://phabricator.wikimedia.org/T233493] '''Changes later this week''' * [[m:Special:MyLanguage/Real Time Preview for Wikitext|Realtime preview for wikitext]] is a tool which lets editors preview the page when they edit wikitext. It will be enabled for all users of the 2010 wikitext editor. You will find it in the editor toolbar. * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] Some wikis will be in read-only for a few minutes because of a switch of their main database. It will be performed on {{#time:j xg|2023-01-10|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist targeted wikis]) and on {{#time:j xg|2023-01-12|en}} at 07:00 UTC ([https://noc.wikimedia.org/conf/highlight.php?file=dblists/s6.dblist targeted wikis]). * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-11|en}}. It will be on all wikis from {{#time:j xg|2023-01-12|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/02|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W02"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:07, 10 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24342971 --> == Tech News: 2023-03 == <section begin="technews-2023-W03"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/03|Translations]] are available. '''Problems''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The URLs in "{{int:last}}" links on page history now contain <bdi lang="zxx" dir="ltr"><code><nowiki>diff=prev&oldid=[revision ID]</nowiki></code></bdi> in place of <bdi lang="zxx" dir="ltr"><code><nowiki>diff=[revision ID]&oldid=[revision ID]</nowiki></code></bdi>. This is to fix a problem with links pointing to incorrect diffs when history was filtered by a tag. Some user scripts may break as a result of this change. [https://phabricator.wikimedia.org/T243569] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-18|en}}. It will be on all wikis from {{#time:j xg|2023-01-19|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Some [[mw:Special:MyLanguage/Talk pages project/Usability|changes to the appearance of talk pages]] have only been available on <code>{{ns:1}}:</code> and <code>{{ns:3}}:</code> namespaces. These will be extended to other talk namespaces, such as <code>{{ns:5}}:</code>. They will continue to be unavailable in non-talk namespaces, including <code>{{ns:4}}:</code> pages (e.g., at the Village Pump). You can [[Special:Preferences#mw-prefsection-editing-discussion|change your preferences]] ([[Special:Preferences#mw-prefsection-betafeatures|beta feature]]). [https://phabricator.wikimedia.org/T325417] *On Wikisources, when an image is zoomed or panned in the Page: namespace, the same zoom and pan settings will be remembered for all Page: namespace pages that are linked to a particular Index: namespace page. [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/ProofreadPage/+/868841] * The Vector 2022 skin will become the default for the English Wikipedia desktop users. The change will take place on January 18 at 15:00 UTC. [[:en:w:Wikipedia:Vector 2022|Learn more]]. '''Future changes''' * The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]], which invites contributors to make technical proposals and vote for tools and improvements, starts next week on 23 January 2023 at 18:00 UTC. You can start drafting your proposals in [[m:Community Wishlist Survey/Sandbox|the CWS sandbox]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/03|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W03"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:10, 17 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24381020 --> == Tech News: 2023-04 == <section begin="technews-2023-W04"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/04|Translations]] are available. '''Problems''' * Last week, for ~15 minutes, all wikis were unreachable for logged-in users and non-cached pages. This was caused by a timing issue. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-17_MediaWiki] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-01-25|en}}. It will be on all wikis from {{#time:j xg|2023-01-26|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * If you have the Beta Feature for [[mw:Special:MyLanguage/Talk pages project|DiscussionTools]] enabled, the appearance of talk pages will add more information about discussion activity. [https://www.mediawiki.org/wiki/Special:MyLanguage/Talk_pages_project/Usability#Status][https://phabricator.wikimedia.org/T317907] * The 2023 edition of the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey]] (CWS), which invites contributors to make technical proposals and vote for tools and improvements, starts on Monday 23 January 2023 at [https://zonestamp.toolforge.org/1674496814 18:00 UTC]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/04|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W04"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:46, 23 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24418874 --> == Tech News: 2023-05 == <section begin="technews-2023-W05"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/05|Translations]] are available. '''Problems''' * Last week, for ~15 minutes, some users were unable to log in or edit pages. This was caused by a problem with session storage. [https://wikitech.wikimedia.org/wiki/Incidents/2023-01-24_sessionstore_quorum_issues] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-01-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-01|en}}. It will be on all wikis from {{#time:j xg|2023-02-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Wikis that use localized numbering schemes for references need to add new CSS. This will help to show citation numbers the same way in all reading and editing modes. If your wiki would prefer to do it yourselves, please see the [[mw:Special:MyLanguage/Parsoid/Parser Unification/Cite CSS|details and example CSS to copy from]], and also add your wiki to the list. Otherwise, the developers will directly help out starting the week of February 5. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/05|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W05"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:05, 31 January 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24455949 --> == Tech News: 2023-06 == <section begin="technews-2023-W06"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/06|Translations]] are available. '''Recent changes''' * In the [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements|Vector 2022 skin]], logged-out users using the full-width toggle will be able to see the setting of their choice even after refreshing pages or opening new ones. This only applies to wikis where Vector 2022 is the default. [https://phabricator.wikimedia.org/T321498] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-08|en}}. It will be on all wikis from {{#time:j xg|2023-02-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Previously, we announced when some wikis would be in read-only for a few minutes because of a switch of their main database. These switches will not be announced any more, as the read-only time has become non-significant. Switches will continue to happen at 7AM UTC on Tuesdays and Thursdays. [https://phabricator.wikimedia.org/T292543#8568433] * Across all the wikis, in the Vector 2022 skin, logged-in users will see the page-related links such as "What links here" in a [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Features/Page_tools|new side menu]]. It will be displayed on the other side of the screen. This change had previously been made on Czech, English, and Vietnamese Wikipedias. [https://phabricator.wikimedia.org/T328692] *[[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] will stop receiving new proposals on [https://zonestamp.toolforge.org/1675706431 Monday, 6 February 2023, at 18:00 UTC]. Proposers should complete any edits by then, to give time for [[m:Special:MyLanguage/Community_Wishlist_Survey/Help_us|translations]] and review. Voting will begin on Friday, 10 February. '''Future changes''' * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] Gadgets and user scripts will be changing to load on desktop and mobile sites. Previously they would only load on the desktop site. It is recommended that wiki administrators audit the [[MediaWiki:Gadgets-definition|gadget definitions]] prior to this change, and add <bdi lang="zxx" dir="ltr"><code>skins=…</code></bdi> for any gadgets which should not load on mobile. [https://phabricator.wikimedia.org/T328610 More details are available]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/06|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W06"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 10:21, 6 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24491749 --> == Tech News: 2023-07 == <section begin="technews-2023-W07"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/07|Translations]] are available. '''Problems''' * On wikis where patrolled edits are enabled, changes made to the [[mw:Special:MyLanguage/Growth/Communities/How to configure the mentors' list|mentor list]] by autopatrolled mentors are not correctly marked as patrolled. It will be fixed later this week. [https://phabricator.wikimedia.org/T328444] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-15|en}}. It will be on all wikis from {{#time:j xg|2023-02-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * The Reply tool and other parts of [[mw:Special:MyLanguage/Help:DiscussionTools#Mobile|DiscussionTools]] will be deployed for all editors using the mobile site. You can [[mw:Special:MyLanguage/Talk_pages_project/Mobile#Status_Updates|read more about this decision]]. [https://phabricator.wikimedia.org/T298060] '''Future changes''' * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/07|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W07"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:48, 14 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24540832 --> == Tech News: 2023-08 == <section begin="technews-2023-W08"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/08|Translations]] are available. '''Problems''' * Last week, during planned maintenance of Cloud Services, unforeseen complications forced the team to turn off all tools for 2–3 hours to prevent data corruption. Work is ongoing to prevent similar problems in the future. [https://phabricator.wikimedia.org/T329535] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-02-22|en}}. It will be on all wikis from {{#time:j xg|2023-02-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). *The voting phase for the [[m:Special:MyLanguage/Community Wishlist Survey 2023|Community Wishlist Survey 2023]] ends on [https://zonestamp.toolforge.org/1677261621 24 February at 18:00 UTC]. The results of the survey will be announced on 28 February. '''Future changes''' * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T328287][https://phabricator.wikimedia.org/T327920][https://wikitech.wikimedia.org/wiki/Deployments] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W08"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:57, 21 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24570514 --> == Tech News: 2023-09 == <section begin="technews-2023-W09"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/09|Translations]] are available. '''Problems''' * Last week, in some areas of the world, there were problems with loading pages for 20 minutes and saving edits for 55 minutes. These issues were caused by a problem with our caching servers due to unforseen events during a routine maintenance task. [https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_wiki_outage][https://wikitech.wikimedia.org/wiki/Incidents/2023-02-22_read_only] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-02-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-01|en}}. It will be on all wikis from {{#time:j xg|2023-03-02|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * All wikis will be read-only for a few minutes on March 1. This is planned for [https://zonestamp.toolforge.org/1677679222 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W09"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:47, 27 February 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24634242 --> == Tech News: 2023-10 == <section begin="technews-2023-W10"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/10|Translations]] are available. '''Recent changes''' * The Community Wishlist Survey 2023 edition has been concluded. Community Tech has [[m:Special:MyLanguage/Community Wishlist Survey 2023/Results|published the results]] of the survey and will provide an update on what is next in April 2023. * On wikis which use [[mw:Special:MyLanguage/Writing_systems|LanguageConverter]] to handle multiple writing systems, articles which used custom conversion rules in the wikitext (primarily on Chinese Wikipedia) would have these rules applied inconsistently in the table of contents, especially in the Vector 2022 skin. This has now been fixed. [https://phabricator.wikimedia.org/T306862] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-08|en}}. It will be on all wikis from {{#time:j xg|2023-03-09|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * A search system has been added to the [[Special:Preferences|Preferences screen]]. This will let you find different options more easily. Making it work on mobile devices will happen soon. [https://phabricator.wikimedia.org/T313804] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/10|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W10"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:49, 6 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24676916 --> == Tech News: 2023-11 == <section begin="technews-2023-W11"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/11|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.40/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-15|en}}. It will be on all wikis from {{#time:j xg|2023-03-16|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-cbk_zamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cdowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cebwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-chywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ckbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-csbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-cywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-itwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304542][https://phabricator.wikimedia.org/T304550] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/11|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W11"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:20, 13 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24700189 --> == Tech News: 2023-12 == <section begin="technews-2023-W12"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/12|Translations]] are available. '''Problems''' * Last week, some users experienced issues loading image thumbnails. This was due to incorrectly cached images. [https://phabricator.wikimedia.org/T331820] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-22|en}}. It will be on all wikis from {{#time:j xg|2023-03-23|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A link to the user's [[{{#special:CentralAuth}}]] page will appear on [[{{#special:Contributions}}]] — some user scripts which previously added this link may cause conflicts. This feature request was [[:m:Community Wishlist Survey 2023/Admins and patrollers/Add link to CentralAuth on Special:Contributions|voted #17 in the 2023 Community Wishlist Survey]]. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[{{#special:AbuseFilter}}]] edit window will be resizable and larger by default. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Make the AbuseFilter edit window resizable and larger by default|voted #80 in the 2023 Community Wishlist Survey]]. * There will be a new option for Administrators when they are unblocking a user, to add the unblocked user’s user page to their watchlist. This will work both via [[{{#special:Unblock}}]] and via the API. [https://phabricator.wikimedia.org/T257662] '''Meetings''' * You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1679677204 24 March at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia Apps/Office Hours|details and how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/12|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W12"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:25, 21 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24732558 --> == Tech News: 2023-13 == <section begin="technews-2023-W13"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/13|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] condition limit was increased from 1000 to 2000. [https://phabricator.wikimedia.org/T309609] * [[:m:Special:MyLanguage/Global AbuseFilter#Locally disabled actions|Some Global AbuseFilter]] actions will no longer apply to local projects. [https://phabricator.wikimedia.org/T332521] * Desktop users are now able to subscribe to talk pages by clicking on the {{int:discussiontools-newtopicssubscription-button-subscribe-label}} link in the {{int:toolbox}} menu. If you subscribe to a talk page, you receive [[mw:Special:MyLanguage/Notifications|notifications]] when new topics are started on that talk page. This is separate from putting the page on your watchlist or subscribing to a single discussion. [https://phabricator.wikimedia.org/T263821] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-03-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-03-29|en}}. It will be on all wikis from {{#time:j xg|2023-03-30|en}} ([[mw:MediaWiki 1.40/Roadmap|calendar]]). '''Future changes''' * You will be able to choose [[mw:Special:MyLanguage/VisualEditor/Diffs|visual diffs]] on all [[m:Special:MyLanguage/Help:Page history|history pages]] at the Wiktionaries and Wikipedias. [https://phabricator.wikimedia.org/T314588] * [[File:Octicons-tools.svg|15px|link=|alt=|Advanced item]] The legacy [[mw:Mobile Content Service|Mobile Content Service]] is going away in July 2023. Developers are encouraged to switch to Parsoid or another API before then to ensure service continuity. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/4MVQQTONJT7FJAXNVOFV3WWVVMCHRINE/] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W13"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:13, 28 March 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24780854 --> == Tech News: 2023-14 == <section begin="technews-2023-W14"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/14|Translations]] are available. '''Recent changes''' * The system for automatically creating categories for the [[mw:Special:MyLanguage/Extension:Babel|Babel]] extension has had several important changes and fixes. One of them allows you to insert templates for automatic category descriptions on creation, allowing you to categorize the new categories. [https://phabricator.wikimedia.org/T211665][https://phabricator.wikimedia.org/T64714][https://phabricator.wikimedia.org/T170654][https://phabricator.wikimedia.org/T184941][https://phabricator.wikimedia.org/T33074] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-05|en}}. It will be on all wikis from {{#time:j xg|2023-04-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Some older [[w:en:Web browser|Web browsers]] will stop being able to use [[w:en:JavaScript|JavaScript]] on Wikimedia wikis from this week. This mainly affects users of Internet Explorer 11. If you have an old web browser on your computer you can try to upgrade to a newer version. [https://phabricator.wikimedia.org/T178356] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The deprecated <bdi lang="zxx" dir="ltr"><code>jquery.hoverIntent</code></bdi> module has been removed. This module could be used by gadgets and user scripts, to create an artificial delay in how JavaScript responds to a hover event. Gadgets and user scripts should now use jQuery <bdi lang="zxx" dir="ltr"><code>hover()</code></bdi> or <bdi lang="zxx" dir="ltr"><code>on()</code></bdi> instead. Examples can be found in the [[mw:Special:MyLanguage/ResourceLoader/Migration_guide_(users)#jquery.hoverIntent|migration guide]]. [https://phabricator.wikimedia.org/T311194] * Some of the links in [[{{#special:SpecialPages}}]] will be re-arranged. There will be a clearer separation between links that relate to all users, and links related to your own user account. [https://phabricator.wikimedia.org/T333242] * You will be able to hide the [[mw:Special:MyLanguage/Talk pages project/Replying|Reply button]] in archived discussion pages with a new <bdi lang="zxx" dir="ltr"><code><nowiki>__ARCHIVEDTALK__</nowiki></code></bdi> magic word. There will also be a new <bdi lang="zxx" dir="ltr"><code>.mw-archivedtalk</code></bdi> CSS class for hiding the Reply button in individual sections on a page. [https://phabricator.wikimedia.org/T249293][https://phabricator.wikimedia.org/T295553][https://gerrit.wikimedia.org/r/c/mediawiki/extensions/DiscussionTools/+/738221] '''Future changes''' * The Vega software that creates data visualizations in pages, such as graphs, will be upgraded to the newest version in the future. Graphs that still use the very old version 1.5 syntax may stop working properly. Most existing uses have been found and updated, but you can help to check, and to update any local documentation. [[phab:T260542|Examples of how to find and fix these graphs are available]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W14"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:39, 3 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24820268 --> == Tech News: 2023-15 == <section begin="technews-2023-W15"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/15|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] In the visual editor, it is now possible to edit captions of images in galleries without opening the gallery dialog. This feature request was [[:m:Community Wishlist Survey 2023/Editing/Editable gallery captions in Visual Editor|voted #61 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T190224] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] You can now receive notifications when another user edits your user page. See the "{{int:Echo-category-title-edit-user-page}}" option in [[Special:Preferences#mw-prefsection-echo|your Preferences]]. This feature request was [[:m:Community Wishlist Survey 2023/Anti-harassment/Notifications for user page edits|voted #3 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T3876] '''Problems''' * There was a problem with all types of CentralNotice banners still being shown to logged-in users even if they had [[Special:Preferences#mw-prefsection-centralnotice-banners|turned off]] specific banner types. This has now been fixed. [https://phabricator.wikimedia.org/T331671] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-12|en}}. It will be on all wikis from {{#time:j xg|2023-04-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-arywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dinwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-elwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-emlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-eowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-etwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-euwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-extwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tumwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ffwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fiu_vrowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-frrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-furwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gcrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-glkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gomwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gotwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-guwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-gvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T304551][https://phabricator.wikimedia.org/T308133] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/15|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W15"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:05, 10 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24851886 --> == Tech News: 2023-16 == <section begin="technews-2023-W16"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/16|Translations]] are available. '''Recent changes''' * You can now see [[mw:Special:MyLanguage/Help:Extension:Kartographer#Show_nearby_articles|nearby articles on a Kartographer map]] with the button for the new feature "{{int:Kartographer-sidebar-nearbybutton}}". Six wikis have been testing this feature since October. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/Geoinformation/Nearby_articles#Implementation][https://phabricator.wikimedia.org/T334079] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The [[m:Special:GlobalWatchlist|Special:GlobalWatchlist]] page now has links for "{{int:globalwatchlist-markpageseen}}" for each entry. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Button to mark a single change as read in the global watch list|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334246] '''Problems''' * At Wikimedia Commons, some thumbnails have not been getting replaced correctly after a new version of the image is uploaded. This should be fixed later this week. [https://phabricator.wikimedia.org/T331138][https://phabricator.wikimedia.org/T333042] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] For the last few weeks, some external tools had inconsistent problems with logging-in with OAuth. This has now been fixed. [https://phabricator.wikimedia.org/T332650] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-19|en}}. It will be on all wikis from {{#time:j xg|2023-04-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W16"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:54, 18 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24881071 --> == Tech News: 2023-17 == <section begin="technews-2023-W17"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/17|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The date-selection menu on pages such as [[{{#special:Contributions}}]] will now show year-ranges that are in the current and past decade, instead of the current and future decade. This feature request was [[m:Community Wishlist Survey 2023/Miscellaneous/Change year range shown in date selection popup|voted #145 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334316] '''Problems''' * Due to security issues with the [[mw:Special:MyLanguage/Extension:Graph|Graph extension]], graphs have been disabled in all Wikimedia projects. Wikimedia Foundation teams are working to respond to these vulnerabilities. [https://phabricator.wikimedia.org/T334940] * For a few days, it was not possible to save some kinds of edits on the mobile version of a wiki. This has been fixed. [https://phabricator.wikimedia.org/T334797][https://phabricator.wikimedia.org/T334799][https://phabricator.wikimedia.org/T334794] '''Changes later this week''' * All wikis will be read-only for a few minutes on April 26. This is planned for [https://zonestamp.toolforge.org/1682517653 14:00 UTC]. [https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-04-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-04-26|en}}. It will be on all wikis from {{#time:j xg|2023-04-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * The Editing team plans an A/B test for [[mw:Special:MyLanguage/Talk pages project/Usability|a usability analysis of the Talk page project]]. The [[mw:Special:MyLanguage/Talk pages project/Usability/Analysis|planned measurements are available]]. Your wiki [[phab:T332946|may be invited to participate]]. Please suggest improvements to the measurement plan at [[mw:Talk:Talk pages project/Usability|the discussion page]]. * [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2023-2024|The Wikimedia Foundation annual plan 2023-2024 draft is open for comment and input]] until May 19. The final plan will be published in July 2023 on Meta-wiki. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W17"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:03, 24 April 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24933592 --> == Tech News: 2023-18 == <section begin="technews-2023-W18"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/18|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the French and Italian Wikipedias. More languages will be added in the near future. This is part of the [[m:Community Wishlist Survey 2023/Reading/Extend "Who Wrote That?" tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T243711][https://phabricator.wikimedia.org/T270490][https://phabricator.wikimedia.org/T334891] * The [[:commons:Special:MyLanguage/Commons:Video2commons|Video2commons]] tool has been updated. This fixed several bugs related to YouTube uploads. [https://github.com/toolforge/video2commons/pull/162/commits] * The [[{{#special:Preferences}}]] page has been redesigned on mobile web. The new design makes it easier to browse the different categories and settings at low screen widths. You can also now access the page via a link in the Settings menu in the mobile web sidebar. [https://www.mediawiki.org/wiki/Moderator_Tools/Content_moderation_on_mobile_web/Preferences] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-03|en}}. It will be on all wikis from {{#time:j xg|2023-05-04|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W18"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:45, 2 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24966974 --> == Tech News: 2023-19 == <section begin="technews-2023-W19"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/19|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] Last week, Community Tech released the first update for providing [[m:Special:MyLanguage/Community Wishlist Survey 2022/Better diff handling of paragraph splits|better diffs]], the #1 request in the 2022 Community Wishlist Survey. [[phab:T324759|This update]] adds legends and tooltips to inline diffs so that users unfamiliar with the blue and yellow highlights can better understand the type of edits made. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] When you close an image that is displayed via MediaViewer, it will now return to the wiki page instead of going back in your browser history. This feature request was [[m:Community Wishlist Survey 2023/Reading/Return to the article when closing the MediaViewer|voted #65 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T236591] * The [[mw:Special:MyLanguage/Extension:SyntaxHighlight|SyntaxHighlight]] extension now supports <bdi lang="en" dir="ltr"><code>wikitext</code></bdi> as a selected language. Old alternatives that were used to highlight wikitext, such as <bdi lang="en" dir="ltr"><code>html5</code></bdi>, <bdi lang="en" dir="ltr"><code>moin</code></bdi>, and <bdi lang="en" dir="ltr"><code>html+handlebars</code></bdi>, can now be replaced. [https://phabricator.wikimedia.org/T29828] * [[mw:Special:MyLanguage/Manual:Creating pages with preloaded text|Preloading text to new pages/sections]] now supports preloading from localized MediaWiki interface messages. [https://cs.wikipedia.org/wiki/User_talk:Martin_Urbanec_(WMF)?action=edit&section=new&preload=MediaWiki:July Here is an example] at the {{int:project-localized-name-cswiki/en}} that uses <bdi lang="zxx" dir="ltr"><code><nowiki>preload=MediaWiki:July</nowiki></code></bdi>. [https://phabricator.wikimedia.org/T330337] '''Problems''' * Graph Extension update: Foundation developers have completed upgrading the visualization software to Vega5. Existing community graphs based on Vega2 are no longer compatible. Communities need to update local graphs and templates, and shared lua modules like <bdi lang="de" dir="ltr">[[:de:Modul:Graph]]</bdi>. The [https://vega.github.io/vega/docs/porting-guide/ Vega Porting guide] provides the most comprehensive detail on migration from Vega2 and [https://www.mediawiki.org/w/index.php?title=Template:Graph:PageViews&action=history here is an example migration]. Vega5 has currently just been enabled on mediawiki.org to provide a test environment for communities. [https://phabricator.wikimedia.org/T334940#8813922] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-10|en}}. It will be on all wikis from {{#time:j xg|2023-05-11|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Until now, all new OAuth apps went through manual review. Starting this week, apps using identification-only or basic authorizations will not require review. [https://phabricator.wikimedia.org/T67750] '''Future changes''' * During the next year, MediaWiki will stop using IP addresses to identify logged-out users, and will start automatically assigning unique temporary usernames. Read more at [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates|IP Editing: Privacy Enhancement and Abuse Mitigation/Updates]]. You can [[m:Talk:IP Editing: Privacy Enhancement and Abuse Mitigation#What should it look like?|join the discussion]] about the [[m:Special:MyLanguage/IP Editing: Privacy Enhancement and Abuse Mitigation/Updates#What will temporary usernames look like?|format of the temporary usernames]]. [https://phabricator.wikimedia.org/T332805] * There will be an [[:w:en:A/B testing|A/B test]] on 10 Wikipedias where the Vector 2022 skin is the default skin. Half of logged-in desktop users will see an interface where the different parts of the page are more clearly separated. You can [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Updates/2023-05 Zebra9 A/B test|read more]]. [https://phabricator.wikimedia.org/T333180][https://phabricator.wikimedia.org/T335972] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] <code>jquery.tipsy</code> will be removed from the MediaWiki core. This will affect some user scripts. Many lines with <code>.tipsy(</code> can be commented out. <code>OO.ui.PopupWidget</code> can be used to keep things working like they are now. You can [[phab:T336019|read more]] and [[:mw:Help:Locating broken scripts|read about how to find broken scripts]]. [https://phabricator.wikimedia.org/T336019] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W19"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:36, 9 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=24998636 --> == Tech News: 2023-20 == <section begin="technews-2023-W20"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/20|Translations]] are available. '''Problems''' * Citations that are automatically generated based on [[d:Q33057|ISBN]] are currently broken. This affects citations made with the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]], and the use of the citoid API in gadgets and user scripts. Work is ongoing to restore this feature. [https://phabricator.wikimedia.org/T336298] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-17|en}}. It will be on all wikis from {{#time:j xg|2023-05-18|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-gorwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hakwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hawwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hifwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hsbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-htwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-igwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ilowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-inhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-iuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-jvwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308134] '''Future changes''' * There is a recently formed team at the Wikimedia Foundation which will be focusing on experimenting with new tools. Currently they are building [[m:Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI|a prototype ChatGPT plugin that allows information generated by ChatGPT to be properly attributed]] to the Wikimedia projects. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget and userscript developers should replace <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> with <bdi lang="zxx" dir="ltr"><code>mediawiki.cookie</code></bdi>. The <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> library will be removed in ~1 month, and staff developers will run a script to replace any remaining uses at that time. [https://phabricator.wikimedia.org/T336018] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W20"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:45, 15 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25011501 --> == Tech News: 2023-21 == <section begin="technews-2023-W21"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/21|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The "recent edits" time period for page watchers is now 30 days. It used to be 180 days. This was a [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Change information about the number of watchers on a page|Community Wishlist Survey proposal]]. [https://phabricator.wikimedia.org/T336250] '''Changes later this week''' * An [[mw:special:MyLanguage/Growth/Positive reinforcement#Impact|improved impact module]] will be available at Wikipedias. The impact module is a feature available to newcomers [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer homepage|at their personal homepage]]. It will show their number of edits, how many readers their edited pages have, how many thanks they have received and similar things. It is also accessible by accessing Special:Impact. [https://phabricator.wikimedia.org/T336203] * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-24|en}}. It will be on all wikis from {{#time:j xg|2023-05-25|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W21"/> 16:55, 22 May 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25028325 --> == Tech News: 2023-22 == <section begin="technews-2023-W22"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/22|Translations]] are available. '''Recent changes''' * Citations can once again be added automatically from ISBNs, thanks to Zotero's ISBN searches. The current data sources are the Library of Congress (United States), the Bibliothèque nationale de France (French National Library), and K10plus ISBN (German repository). Additional data source searches can be [[mw:Citoid/Creating Zotero translators|proposed to Zotero]]. The ISBN labels in the [[mw:Special:MyLanguage/Help:VisualEditor/User_guide/Citations-Full#Automatic|VisualEditor Automatic tab]] will reappear later this week. [https://phabricator.wikimedia.org/T336298#8859917] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The page [[{{#special:EditWatchlist}}]] now has "{{int:watchlistedit-normal-check-all}}" options to select all the pages within a namespace. This feature request was [[m:Community Wishlist Survey 2023/Notifications, Watchlists and Talk Pages/Watchlist edit - "check all" checkbox|voted #161 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334252] '''Problems''' * For a few days earlier this month, the "Add interlanguage link" item in the Tools menu did not work properly. This has now been fixed. [https://phabricator.wikimedia.org/T337081] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-05-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-05-31|en}}. It will be on all wikis from {{#time:j xg|2023-06-01|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * VisualEditor will be switched to a new backend on [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/small.dblist small] and [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/medium.dblist medium] wikis this week. Large wikis will follow in the coming weeks. This is part of the effort to move Parsoid into MediaWiki core. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W22"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:03, 29 May 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25079963 --> == Tech News: 2023-23 == <section begin="technews-2023-W23"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/23|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Help:Extension:RealMe|RealMe]] extension allows you to mark URLs on your user page as verified for Mastodon and similar software. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] Citation and footnote editing can now be started from the reference list when using the visual editor. This feature request was [[m:Community Wishlist Survey 2023/Citations/Allow citations to be edited in the references section with VisualEditor|voted #2 in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T54750] * Previously, clicking on someone else's link to Recent Changes with filters applied within the URL could unintentionally change your preference for "{{int:Rcfilters-group-results-by-page}}". This has now been fixed. [https://phabricator.wikimedia.org/T202916#8874081] '''Problems''' * For a few days last week, some tools and bots returned outdated information due to database replication problems, and may have been down entirely while it was being fixed. These issues have now been fixed. [https://phabricator.wikimedia.org/T337446] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.12|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-07|en}}. It will be on all wikis from {{#time:j xg|2023-06-08|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Bots will no longer be prevented from making edits because of URLs that match the [[mw:Special:MyLanguage/Extension:SpamBlacklist|spam blacklist]]. [https://phabricator.wikimedia.org/T313107] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W23"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:52, 5 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25114640 --> == Tech News: 2023-24 == <section begin="technews-2023-W24"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/24|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] The content attribution tools [[mw:Special:MyLanguage/Who Wrote That?|Who Wrote That?]], [[xtools:authorship|XTools Authorship]], and [[xtools:blame|XTools Blame]] now support the Dutch, German, Hungarian, Indonesian, Japanese, Polish and Portuguese Wikipedias. This was the [[m:Community Wishlist Survey 2023/Reading/Extend "Who Wrote That?" tool to more wikis|#7 wish in the 2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T334891] * The [[mw:Special:MyLanguage/Structured Data Across Wikimedia/Search Improvements#Search Preview panel|Search Preview panel]] has been deployed on four Wikipedias (Catalan, Dutch, Hungarian and Norwegian). The panel will show an image related to the article (if existing), the top sections of the article, related images (coming from MediaSearch on Commons), and eventually the sister projects associated with the article. [https://phabricator.wikimedia.org/T306341] * The [[:mw:Special:MyLanguage/Help:Extension:RealMe#Verifying_a_link_on_non-user_pages|RealMe]] extension now allows administrators to verify URLs for any page, for Mastodon and similar software. [https://phabricator.wikimedia.org/T324937] * The default project license [https://lists.wikimedia.org/hyperkitty/list/wikimediaannounce-l@lists.wikimedia.org/thread/7G6XPWZPQFLZ2JANN3ZX6RT4DVUI3HZQ/ has been officially upgraded] to CC BY-SA 4.0. The software interface messages have been updated. Communities should feel free to start updating any mentions of the old CC BY-SA 3.0 licensing within policies and related documentation pages. [https://phabricator.wikimedia.org/T319064] '''Problems''' * For three days last month, some Wikipedia pages edited with VisualEditor or DiscussionTools had an unintended <code><nowiki>__TOC__</nowiki></code> (or its localized form) added during an edit. There is [[mw:Parsoid/Deployments/T336101_followup|a listing of affected pages sorted by wiki]], that may still need to be fixed. [https://phabricator.wikimedia.org/T336101] * Currently, the "{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}" feature in VisualEditor is broken. Existing <code><nowiki>{{DEFAULTSORT:...}}</nowiki></code> keywords incorrectly appear as missing templates in VisualEditor. Developers are exploring how to fix this. In the meantime, those wishing to edit the default sortkey of a page are advised to switch to source editing. [https://phabricator.wikimedia.org/T337398] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Last week, an update to the delete form may have broken some gadgets or user scripts. If you need to manipulate (empty) the reason field, replace <bdi lang="zxx" dir="ltr"><code>#wpReason</code></bdi> with <bdi lang="zxx" dir="ltr" style="white-space: nowrap;"><code>#wpReason > input</code></bdi>. See [https://cs.wikipedia.org/w/index.php?title=MediaWiki%3AGadget-CleanDeleteReasons.js&diff=22859956&oldid=12794189 an example fix]. [https://phabricator.wikimedia.org/T337809] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-14|en}}. It will be on all wikis from {{#time:j xg|2023-06-15|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * VisualEditor will be switched to a new backend on English Wikipedia on Monday, and all other [https://phabricator.wikimedia.org/source/mediawiki-config/browse/master/dblists/large.dblist large] wikis on Thursday. The change should have no noticeable effect on users, but if you experience any slow loading or other strangeness when using VisualEditor, please report it on the phabricator ticket linked here. [https://phabricator.wikimedia.org/T320529] '''Future changes''' * From 5 June to 17 July, the Foundation's [[:mw:Wikimedia Security Team|Security team]] is holding a consultation with contributors regarding a draft policy to govern the use of third-party resources in volunteer-developed gadgets and scripts. Feedback and suggestions are warmly welcome at [[m:Special:MyLanguage/Third-party resources policy|Third-party resources policy]] on meta-wiki. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W24"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:51, 12 June 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25133779 --> == Tech News: 2023-25 == <section begin="technews-2023-W25"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/25|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Flame graphs are now available in WikimediaDebug. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/JXNQD3EHG5V5QW5UXFDPSHQG4MJ3FWJQ/][https://techblog.wikimedia.org/2023/06/08/flame-graphs-arrive-in-wikimediadebug/] '''Changes later this week''' * There is no new MediaWiki version this week. * There is now a toolbar search popup in the visual editor. You can trigger it by typing <code>\</code> or pressing <code>ctrl + shift + p</code>. It can help you quickly access most tools in the editor. [https://commons.wikimedia.org/wiki/File:Visual_editor_toolbar_search_feature.png][https://phabricator.wikimedia.org/T66905] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W25"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:08, 19 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25159510 --> == Tech News: 2023-26 == <section begin="technews-2023-W26"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/26|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Action API modules and Special:LinkSearch will now add a trailing <bdi lang="zxx" dir="ltr"><code>/</code></bdi> to all <bdi lang="zxx" dir="ltr"><code>prop=extlinks</code></bdi> responses for bare domains. This is part of the work to remove duplication in the <code>externallinks</code> database table. [https://phabricator.wikimedia.org/T337994] '''Problems''' * Last week, search was broken on Commons and Wikidata for 23 hours. [https://phabricator.wikimedia.org/T339810][https://wikitech.wikimedia.org/wiki/Incidents/2023-06-18_search_broken_on_wikidata_and_commons] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-06-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-06-28|en}}. It will be on all wikis from {{#time:j xg|2023-06-29|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Minerva skin now applies more predefined styles to the <bdi lang="zxx" dir="ltr"><code>.mbox-text</code></bdi> CSS class. This enables support for mbox templates that use divs instead of tables. Please make sure that the new styles won't affect other templates in your wiki. [https://gerrit.wikimedia.org/r/c/mediawiki/skins/MinervaNeue/+/930901/][https://phabricator.wikimedia.org/T339040] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadgets will now load on both desktop and mobile by default. Previously, gadgets loaded only on desktop by default. Changing this default using the <bdi lang="zxx" dir="ltr"><code>|targets=</code></bdi> parameter is also deprecated and should not be used. You should make gadgets work on mobile or disable them based on the skin (with the <bdi lang="zxx" dir="ltr"><code>|skins=</code></bdi> parameter in <bdi lang="en" dir="ltr">MediaWiki:Gadgets-definition</bdi>) rather than whether the user uses the mobile or the desktop website. Popular gadgets that create errors on mobile will be disabled by developers on the Minerva skin as a temporary solution. [https://phabricator.wikimedia.org/T127268] * All namespace tabs now have the same browser [[m:Special:MyLanguage/Help:Keyboard_shortcuts|access key]] by default. Previously, custom and extension-defined namespaces would have to have their access keys set manually on-wiki, but that is no longer necessary. [https://phabricator.wikimedia.org/T22126] * The review form of the Flagged Revisions extension now uses the standardized [[mw:Special:MyLanguage/Codex|user interface components]]. [https://phabricator.wikimedia.org/T191156] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] How media is structured in the parser's HTML output will change in the coming weeks at [[:wikitech:Deployments/Train#Thursday|group2 wikis]]. This change improves the accessibility of content. You may need to update your site-CSS, or userscripts and gadgets. There are [[mw:Special:MyLanguage/Parsoid/Parser_Unification/Media_structure/FAQ|details on what code to check, how to update the code, and where to report any related problems]]. [https://phabricator.wikimedia.org/T314318] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W26"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:18, 26 June 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25202311 --> == Tech News: 2023-27 == <section begin="technews-2023-W27"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/27|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the rolling out of the [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|audio links that play on click]] wishlist proposal, [https://noc.wikimedia.org/conf/highlight.php?file=dblists/small.dblist small wikis] will now be able to use the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline audio player mode|inline audio player]] that is implemented by the [[mw:Extension:Phonos|Phonos]] extension. [https://phabricator.wikimedia.org/T336763] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] From this week all gadgets automatically load on mobile and desktop sites. If you see any problems with gadgets on your wikis, please adjust the [[mw:Special:MyLanguage/Extension:Gadgets#Options|gadget options]] in your gadget definitions file. [https://phabricator.wikimedia.org/T328610] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-05|en}}. It will be on all wikis from {{#time:j xg|2023-07-06|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W27"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:51, 3 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25231546 --> == Tech News: 2023-28 == <section begin="technews-2023-W28"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/28|Translations]] are available. '''Recent changes''' * The [[:mw:Special:MyLanguage/Structured Data Across Wikimedia/Section-level Image Suggestions|Section-level Image Suggestions feature]] has been deployed on seven Wikipedias (Portuguese, Russian, Indonesian, Catalan, Hungarian, Finnish and Norwegian Bokmål). The feature recommends images for articles on contributors' watchlists that are a good match for individual sections of those articles. * [[:m:Special:MyLanguage/Global AbuseFilter|Global abuse filters]] have been enabled on all Wikimedia projects, except English and Japanese Wikipedias (who opted out). This change was made following a [[:m:Requests for comment/Make global abuse filters opt-out|global request for comments]]. [https://phabricator.wikimedia.org/T341159] * [[{{#special:BlockedExternalDomains}}]] is a new tool for administrators to help fight spam. It provides a clearer interface for blocking plain domains (and their subdomains), is more easily searchable, and is faster for the software to process for each edit on the wiki. It does not support regex (for complex cases), nor URL path-matching, nor the [[MediaWiki:Spam-whitelist|MediaWiki:Spam-whitelist]], but otherwise it replaces most of the functionalities of the existing [[MediaWiki:Spam-blacklist|MediaWiki:Spam-blacklist]]. There is a Python script to help migrate all simple domains into this tool, and more feature details, within [[mw:Special:MyLanguage/Manual:BlockedExternalDomains|the tool's documentation]]. It is available at all wikis except for Meta-wiki, Commons, and Wikidata. [https://phabricator.wikimedia.org/T337431] * The WikiEditor extension was updated. It includes some of the most frequently used features of wikitext editing. In the past, many of its messages could only be translated by administrators, but now all regular translators on translatewiki can translate them. Please check [https://translatewiki.net/wiki/Special:MessageGroupStats?group=ext-wikieditor&messages=&x=D#sortable:0=asc the state of WikiEditor localization into your language], and if the "Completion" for your language shows anything less than 100%, please complete the translation. See [https://lists.wikimedia.org/hyperkitty/list/wikitech-ambassadors@lists.wikimedia.org/thread/D4YELU2DXMZ75PGELUOKXXMFF3FH45XA/ a more detailed explanation]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-12|en}}. It will be on all wikis from {{#time:j xg|2023-07-13|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * The default protocol of [[{{#special:LinkSearch}}]] and API counterparts has changed from http to both http and https. [https://phabricator.wikimedia.org/T14810] * [[{{#special:LinkSearch}}]] and its API counterparts will now search for all of the URL provided in the query. It used to be only the first 60 characters. This feature was requested fifteen years ago. [https://phabricator.wikimedia.org/T17218] '''Future changes''' * There is an experiment with a [[:w:en:ChatGPT|ChatGPT]] plugin. This is to show users where the information is coming from when they read information from Wikipedia. It has been tested by Wikimedia Foundation staff and other Wikimedians. Soon all ChatGPT plugin users can use the Wikipedia plugin. This is the same plugin which was mentioned in [[m:Special:MyLanguage/Tech/News/2023/20|Tech News 2023/20]]. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI] * There is an ongoing discussion on a [[m:Special:MyLanguage/Third-party resources policy|proposed Third-party resources policy]]. The proposal will impact the use of third-party resources in gadgets and userscripts. Based on the ideas received so far, policy includes some of the risks related to user scripts and gadgets loading third-party resources, some best practices and exemption requirements such as code transparency and inspectability. Your feedback and suggestions are warmly welcome until July 17, 2023 on [[m:Talk:Third-party resources policy|on the policy talk page]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/28|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W28"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:54, 10 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25278797 --> == Tech News: 2023-29 == <section begin="technews-2023-W29"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/29|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] We are now serving 1% of all global user traffic from [[w:en:Kubernetes|Kubernetes]] (you can [[wikitech:MediaWiki On Kubernetes|read more technical details]]). We are planning to increment this percentage regularly. You can [[phab:T290536|follow the progress of this work]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-19|en}}. It will be on all wikis from {{#time:j xg|2023-07-20|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki [[mw:Special:MyLanguage/Help:System_message|system messages]] will now look for available local fallbacks, instead of always using the default fallback defined by software. This means wikis no longer need to override each language on the [[mw:Special:MyLanguage/Manual:Language#Fallback_languages|fallback chain]] separately. For example, English Wikipedia doesn't have to create <bdi lang="zxx" dir="ltr"><code>en-ca</code></bdi> and <bdi lang="zxx" dir="ltr"><code>en-gb</code></bdi> subpages with a transclusion of the base pages anymore. This makes it easier to maintain local overrides. [https://phabricator.wikimedia.org/T229992] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The <bdi lang="zxx" dir="ltr"><code>action=growthsetmentorstatus</code></bdi> API will be deprecated with the new MediaWiki version. Bots or scripts calling that API should use the <bdi lang="zxx" dir="ltr"><code>action=growthmanagementorlist</code></bdi> API now. [https://phabricator.wikimedia.org/T321503] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W29"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:08, 17 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25289122 --> == Tech News: 2023-30 == <section begin="technews-2023-W30"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/30|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] On July 18, the Wikimedia Foundation launched a survey about the [[:mw:Technical_decision_making|technical decision making process]] for people who do technical work that relies on software that is maintained by the Foundation or affiliates. If this applies to you, [https://wikimediafoundation.limesurvey.net/885471 please take part in the survey]. The survey will be open for three weeks, until August 7. You can find more information in [[listarchive:list/wikitech-l@lists.wikimedia.org/thread/Q7DUCFA75DXG3G2KHTO7CEWMLCYTSDB2/|the announcement e-mail on wikitech-l]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-07-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-07-26|en}}. It will be on all wikis from {{#time:j xg|2023-07-27|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W30"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 02:20, 25 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25332248 --> == Tech News: 2023-31 == <section begin="technews-2023-W31"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/31|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Synchronizer|Synchronizer]] tool is now available to keep Lua modules synced across Wikimedia wikis, along with [[mw:Multilingual Templates and Modules|updated documentation]] to develop global Lua modules and templates. * The tag filter on [[{{#special:NewPages}}]] and revision history pages can now be inverted. For example, you can hide edits that were made using an automated tool. [https://phabricator.wikimedia.org/T334337][https://phabricator.wikimedia.org/T334338] * The Wikipedia [[:w:en:ChatGPT|ChatGPT]] plugin experiment can now be used by ChatGPT users who can use plugins. You can participate in a [[:m:Talk:Wikimedia Foundation Annual Plan/2023-2024/Draft/Future Audiences#Announcing monthly Future Audiences open "office hours"|video call]] if you want to talk about this experiment or similar work. [https://meta.wikimedia.org/wiki/Wikimedia_Foundation_Annual_Plan/2023-2024/Draft/Future_Audiences#FA2.2_Conversational_AI] '''Problems''' * It was not possible to generate a PDF for pages with non-Latin characters in the title, for the last two weeks. This has now been fixed. [https://phabricator.wikimedia.org/T342442] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-01|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-02|en}}. It will be on all wikis from {{#time:j xg|2023-08-03|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Tuesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-kawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kaawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kabwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kbpwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-knwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kshwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kuwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kwwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308135] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W31"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:54, 31 July 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25362228 --> == Tech News: 2023-32 == <section begin="technews-2023-W32"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/32|Translations]] are available. '''Recent changes''' * Mobile Web editors can now [[mw:Special:MyLanguage/Reading/Web/Advanced_mobile_contributions#August_1,_2023_-_Full-page_editing_added_on_mobile|edit a whole page at once]]. To use this feature, turn on "{{int:Mobile-frontend-mobile-option-amc}}" in your settings and use the "{{int:Minerva-page-actions-editfull}}" button in the "{{int:Minerva-page-actions-overflow}}" menu. [https://phabricator.wikimedia.org/T203151] '''Changes later this week''' * There is no new MediaWiki version this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W32"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:20, 7 August 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25420038 --> == Tech News: 2023-33 == <section begin="technews-2023-W33"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/33|Translations]] are available. '''Recent changes''' * The Content translation system is no longer using Youdao's [[mw:Special:MyLanguage/Help:Content_translation/Translating/Initial_machine_translation|machine translation service]]. The service was in place for several years, but due to no usage, and availability of alternatives, it was deprecated to reduce maintenance overheads. Other services which cover the same languages are still available. [https://phabricator.wikimedia.org/T329137] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-15|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-16|en}}. It will be on all wikis from {{#time:j xg|2023-08-17|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-lawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ladwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lbewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lezwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lfnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-liwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lijwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lmowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ltgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-lvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-maiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-map_bmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mdfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kywiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308136] <!-- TODO replace wiki codes --> '''Future changes''' * A few gadgets/user scripts which add icons to the Minerva skin need to have their CSS updated. There are more details available including a [[phab:T344067|search for all existing instances and how to update them]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W33"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 05:59, 15 August 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25428668 --> == Tech News: 2023-34 == <section begin="technews-2023-W34"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/34|Translations]] are available. '''Recent changes''' * The [https://gdrive-to-commons.toolforge.org/ GDrive to Commons Uploader] tool is now available. It enables [[m:Special:MyLanguage/GDrive to Commons Uploader|securely selecting and uploading files]] from your Google Drive directly to Wikimedia Commons. [https://phabricator.wikimedia.org/T267868] * From now on, we will announce new Wikimedia wikis in Tech News, so you can update any tools or pages. ** Since the last edition, two new wikis have been created: *** a Wiktionary in [[d:Q7121294|Pa'O]] ([[wikt:blk:|<code>wikt:blk:</code>]]) [https://phabricator.wikimedia.org/T343540] *** a Wikisource in [[d:Q34002|Sundanese]] ([[s:su:|<code>s:su:</code>]]) [https://phabricator.wikimedia.org/T343539] ** To catch up, the next most recent six wikis are: *** Wikifunctions ([[f:|<code>f:</code>]]) [https://phabricator.wikimedia.org/T275945] *** a Wiktionary in [[d:Q2891049|Mandailing]] ([[wikt:btm:|<code>wikt:btm:</code>]]) [https://phabricator.wikimedia.org/T335216] *** a Wikipedia in [[d:Q5555465|Ghanaian Pidgin]] ([[w:gpe:|<code>w:gpe:</code>]]) [https://phabricator.wikimedia.org/T335969] *** a Wikinews in [[d:Q3111668|Gungbe]] ([[n:guw:|<code>n:guw:</code>]]) [https://phabricator.wikimedia.org/T334394] *** a Wiktionary in [[d:Q33522|Kabardian]] ([[wikt:kbd:|<code>wikt:kbd:</code>]]) [https://phabricator.wikimedia.org/T333266] *** a Wikipedia in [[d:Q35570|Fante]] ([[w:fat:|<code>w:fat:</code>]]) [https://phabricator.wikimedia.org/T335016] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-22|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-23|en}}. It will be on all wikis from {{#time:j xg|2023-08-24|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There is an existing [[mw:Stable interface policy|stable interface policy]] for MediaWiki backend code. There is a [[mw:User:Jdlrobson/Stable interface policy/frontend|proposed stable interface policy for frontend code]]. This is relevant for anyone who works on gadgets or Wikimedia frontend code. You can read it, discuss it, and let the proposer know if there are any problems. [https://phabricator.wikimedia.org/T344079] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W34"/> 15:25, 21 August 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25497111 --> == Tech News: 2023-35 == <section begin="technews-2023-W35"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/35|Translations]] are available. '''Recent changes''' * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Community Wishlist Survey 2022/Better diff handling of paragraph splits|better diff handling of paragraph splits]], improved detection of splits is being rolled out. Over the last two weeks, we deployed this support to [[wikitech:Deployments/Train#Groups|group0]] and group1 wikis. This week it will be deployed to group2 wikis. [https://phabricator.wikimedia.org/T341754] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] All [[{{#special:Contributions}}]] pages now show the user's local edit count and the account's creation date. [https://phabricator.wikimedia.org/T324166] * Wikisource users can now use the <bdi lang="zxx" dir="ltr"><code>prpbengalicurrency</code></bdi> label to denote Bengali currency characters as page numbers inside the <bdi lang="zxx" dir="ltr"><code><nowiki><pagelist></nowiki></code></bdi> tag. [https://phabricator.wikimedia.org/T268932] * Two preferences have been relocated. The preference "{{int:visualeditor-preference-visualeditor}}" is now shown on the [[Special:Preferences#mw-prefsection-editing|"{{int:prefs-editing}}" tab]] at all wikis. Previously it was shown on the "{{int:prefs-betafeatures}}" tab at some wikis. The preference "{{int:visualeditor-preference-newwikitexteditor-enable}}" is now also shown on the "{{int:prefs-editing}}" tab at all wikis, instead of the "{{int:prefs-betafeatures}}" tab. [https://phabricator.wikimedia.org/T335056][https://phabricator.wikimedia.org/T344158] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-08-29|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-08-30|en}}. It will be on all wikis from {{#time:j xg|2023-08-31|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] New signups for a Wikimedia developer account will start being pushed towards <bdi lang="en" dir="ltr">[https://idm.wikimedia.org/ idm.wikimedia.org]</bdi>, rather than going via Wikitech. [[wikitech:IDM|Further information about the new system is available]]. * All right-to-left language wikis, plus Korean, Armenian, Ukrainian, Russian, and Bulgarian Wikipedias, will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. This feature will come to more wikis in future weeks. [https://phabricator.wikimedia.org/T267921] '''Future changes''' * The removal of the [[mw:Special:MyLanguage/Extension:DoubleWiki|DoubleWiki extension]] is being discussed. This extension currently allows Wikisource users to view articles from multiple language versions side by side when the <bdi lang="zxx" dir="ltr"><code><=></code></bdi> symbol next to a specific language edition is selected. Comments on this are welcomed at [[phab:T344544|the phabricator task]]. * A proposal has been made to merge the second hidden-categories list (which appears below the wikitext editing form) with the main list of categories (which is further down the page). [[phab:T340606|More information is available on Phabricator]]; feedback is welcome! '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W35"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:00, 28 August 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25510866 --> == Tech News: 2023-36 == <section begin="technews-2023-W36"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/36|Translations]] are available. '''Recent changes''' * [[m:Wikisource_EditInSequence|EditInSequence]], a feature that allows users to edit pages faster on Wikisource has been moved to a Beta Feature based on community feedback. To enable it, you can navigate to the [[Special:Preferences#mw-prefsection-betafeatures|beta features tab in Preferences]]. [https://phabricator.wikimedia.org/T308098] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Generate Audio for IPA|Generate Audio for IPA]] and [[m:Community Wishlist Survey 2022/Multimedia and Commons/Audio links that play on click|Audio links that play on click]] wishlist proposals, the [[mw:Special:MyLanguage/Help:Extension:Phonos#Inline_audio_player_mode|inline audio player mode]] of [[mw:Extension:Phonos|Phonos]] has been deployed to all projects. [https://phabricator.wikimedia.org/T336763] * There is a new option for Administrators when they are changing the usergroups for a user, to add the user’s user page to their watchlist. This works both via [[{{#special:UserRights}}]] and via the API. [https://phabricator.wikimedia.org/T272294] * One new wiki has been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q34318|Talysh]] ([[w:tly:|<code>w:tly:</code>]]) [https://phabricator.wikimedia.org/T345166] '''Problems''' * The [[mw:Special:MyLanguage/Extension:LoginNotify|LoginNotify extension]] was not sending notifications since January. It has now been fixed, so going forward, you may see notifications for failed login attempts, and successful login attempts from a new device. [https://phabricator.wikimedia.org/T344785] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-06|en}}. It will be on all wikis from {{#time:j xg|2023-09-07|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-mhrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-miwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-minwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mrjwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mtwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mwlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-myvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-mznwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-napwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ndswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nds_nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-newwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-novwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nqowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nrmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nsowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ocwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-olowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-omwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-orwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-oswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pagwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pamwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-papwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pcdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pdcwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pflwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pihwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pmswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pnbwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pntwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-pswiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308137][https://phabricator.wikimedia.org/T308138] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W36"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:33, 4 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25566983 --> == Tech News: 2023-37 == <section begin="technews-2023-W37"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/37|Translations]] are available. '''Recent changes''' * [[mw:Special:MyLanguage/ORES|ORES]], the revision evaluation service, is now using a new open-source infrastructure on all wikis except for English Wikipedia and Wikidata. These two will follow this week. If you notice any unusual results from the Recent Changes filters that are related to ORES (for example, "{{int:ores-rcfilters-damaging-title}}" and "{{int:ores-rcfilters-goodfaith-title}}"), please [[mw:Talk:Machine Learning|report them]]. [https://phabricator.wikimedia.org/T342115] * When you are logged in on one Wikimedia wiki and visit a different Wikimedia wiki, the system tries to log you in there automatically. This has been unreliable for a long time. You can now visit the login page to make the system try extra hard. If you feel that made logging in better or worse than it used to be, your feedback is appreciated. [https://phabricator.wikimedia.org/T326281] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-13|en}}. It will be on all wikis from {{#time:j xg|2023-09-14|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/Technical decision making|Technical Decision-Making Forum Retrospective]] team invites anyone involved in the technical field of Wikimedia projects to signup to and join [[mw:Technical decision making/Listening Sessions|one of their listening sessions]] on 13 September. Another date will be scheduled later. The goal is to improve the technical decision-making processes. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] As part of the changes for the [[m:Special:MyLanguage/Community Wishlist Survey 2022/Better diff handling of paragraph splits|Better diff handling of paragraph splits]] wishlist proposal, the inline switch widget in diff pages is being rolled out this week to all wikis. The inline switch will allow viewers to toggle between a unified inline or two-column diff wikitext format. [https://phabricator.wikimedia.org/T336716] '''Future changes''' * All wikis will be read-only for a few minutes on 20 September. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T345263] * The Enterprise API is launching a new feature called "[http://breakingnews-beta.enterprise.wikimedia.com/ breaking news]". Currently in BETA, this attempts to identify likely "newsworthy" topics as they are currently being written about in any Wikipedia. Your help is requested to improve the accuracy of its detection model, especially on smaller language editions, by recommending templates or identifiable editing patterns. See more information at [[mw:Special:MyLanguage/Wikimedia Enterprise/Breaking news|the documentation page]] on MediaWiki or [[m:Special:MyLanguage/Wikimedia Enterprise/FAQ#What is Breaking News|the FAQ]] on Meta. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W37"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:07, 11 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25589064 --> == Tech News: 2023-38 == <section begin="technews-2023-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/38|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki now has a [[mw:Stable interface policy/frontend|stable interface policy for frontend code]] that more clearly defines how we deprecate MediaWiki code and wiki-based code (e.g. gadgets and user scripts). Thank you to everyone who contributed to the content and discussions. [https://phabricator.wikimedia.org/T346467][https://phabricator.wikimedia.org/T344079] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.27|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-20|en}}. It will be on all wikis from {{#time:j xg|2023-09-21|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * All wikis will be read-only for a few minutes on September 20. [[m:Special:MyLanguage/Tech/Server switch|This is planned at 14:00 UTC.]] [https://phabricator.wikimedia.org/T345263] * All wikis will have a link in the sidebar that provides a short URL of that page, using the [[m:Special:MyLanguage/Wikimedia URL Shortener|Wikimedia URL Shortener]]. [https://phabricator.wikimedia.org/T267921] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The team investigating the Graph Extension posted [[mw:Extension:Graph/Plans#Proposal|a proposal for reenabling it]] and they need your input. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W38"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:19, 18 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25623533 --> == Tech News: 2023-39 == <section begin="technews-2023-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/39|Translations]] are available. '''Recent changes''' * The Vector 2022 skin will now remember the pinned/unpinned status for the Table of Contents for all logged-out users. [https://phabricator.wikimedia.org/T316060] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.28|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-09-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-09-27|en}}. It will be on all wikis from {{#time:j xg|2023-09-28|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The ResourceLoader <bdi lang="zxx" dir="ltr"><code><nowiki>mediawiki.ui</nowiki></code></bdi> modules are now deprecated as part of the move to Vue.js and Codex. There is a [[mw:Codex/Migrating_from_MediaWiki_UI|guide for migrating from MediaWiki UI to Codex]] for any tools that use it. More [[phab:T346468|details are available in the task]] and your questions are welcome there. * Gadget definitions will have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new "namespaces" option]]. The option takes a list of namespace IDs. Gadgets that use this option will only load on pages in the given namespaces. '''Future changes''' * New variables will be added to [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]]: <code><bdi lang="zxx" dir="ltr">global_account_groups</bdi></code> and <code><bdi lang="zxx" dir="ltr">global_account_editcount</bdi></code>. They are available only when an account is being created. You can use them to prevent blocking automatic creation of accounts when users with many edits elsewhere visit your wiki for the first time. [https://phabricator.wikimedia.org/T345632][https://www.mediawiki.org/wiki/Special:MyLanguage/Extension:AbuseFilter/Rules_format] '''Meetings''' * You can join the next meeting with the Wikipedia mobile apps teams. During the meeting, we will discuss the current features and future roadmap. The meeting will be on [https://zonestamp.toolforge.org/1698426015 27 October at 17:00 (UTC)]. See [[mw:Special:MyLanguage/Wikimedia_Apps/Office_Hours#October_2023|details and how to join]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W39"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:51, 26 September 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25655264 --> == Tech News: 2023-40 == <section begin="technews-2023-W40"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/40|Translations]] are available. '''Recent changes''' * There is a new [[Special:Preferences#mw-prefsection-rendering-advancedrendering|user preference]] for "{{int:tog-forcesafemode}}". This setting will make pages load without including any on-wiki JavaScript or on-wiki stylesheet pages. It can be useful for debugging broken JavaScript gadgets. [https://phabricator.wikimedia.org/T342347] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Gadget definitions now have a [[mw:Special:MyLanguage/Extension:Gadgets#Options|new "<var>contentModels</var>" option]]. The option takes a list of page content models, like <code><bdi lang="zxx" dir="ltr">wikitext</bdi></code> or <code><bdi lang="zxx" dir="ltr">css</bdi></code>. Gadgets that use this option will only load on pages with the given content models. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.29|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-03|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-04|en}}. It will be on all wikis from {{#time:j xg|2023-10-05|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Vector 2022 skin will no longer use the custom styles and scripts of Vector legacy (2010). The change will be made later this year or in early 2024. See [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|how to adjust the CSS and JS pages on your wiki]]. [https://phabricator.wikimedia.org/T331679] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W40"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:26, 3 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25686930 --> == Tech News: 2023-41 == <section begin="technews-2023-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/41|Translations]] are available. '''Recent changes''' * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q33291|Fon]] ([[w:fon:|<code>w:fon:</code>]]) [https://phabricator.wikimedia.org/T347935] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.41/wmf.30|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-10|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-11|en}}. It will be on all wikis from {{#time:j xg|2023-10-12|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-swwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-warwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-wowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xalwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xhwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-xmfwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-yowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zeawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zh_min_nanwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-zuwiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308139] * At some wikis, newcomers are suggested images from Commons to add to articles without any images. Starting on Tuesday, newcomers at these wikis will be able to add images to unillustrated article sections. The specific wikis are listed under "Images recommendations" [[mw:Special:MyLanguage/Growth/Deployment table|at the Growth team deployment table]]. You can [[mw:Special:MyLanguage/Help:Growth/Tools/Add an image|learn more about this feature.]] [https://phabricator.wikimedia.org/T345940] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In the mobile web skin (Minerva) the CSS ID <bdi lang="zxx" dir="ltr"><code><nowiki>#page-actions</nowiki></code></bdi> will be replaced with <bdi lang="zxx" dir="ltr"><code><nowiki>#p-views</nowiki></code></bdi>. This change is to make it consistent with other skins and to improve support for gadgets and extensions in the mobile skin. A few gadgets may need to be updated; there are [https://phabricator.wikimedia.org/T348267 details and search-links in the task]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W41"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 14:39, 9 October 2023 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25712895 --> == Tech News: 2023-42 == <section begin="technews-2023-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/42|Translations]] are available. '''Recent changes''' * The [[m:Special:MyLanguage/Help:Unified login|Unified login]] system's edge login should now be fixed for some browsers (Chrome, Edge, Opera). This means that if you visit a new sister project wiki, you should be logged in automatically without the need to click "Log in" or reload the page. Feedback on whether it's working for you is welcome. [https://phabricator.wikimedia.org/T347889] * [[mw:Special:MyLanguage/Manual:Interface/Edit_notice|Edit notices]] are now available within the MobileFrontend/Minerva skin. This feature was inspired by [[w:en:Wikipedia:EditNoticesOnMobile|the gadget on English Wikipedia]]. See more details in [[phab:T316178|T316178]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-17|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-18|en}}. It will be on all wikis from {{#time:j xg|2023-10-19|en}} ([[mw:MediaWiki 1.41/Roadmap|calendar]]). '''Future changes''' * In 3 weeks, in the Vector 2022 skin, code related to <bdi lang="zxx" dir="ltr"><code><nowiki>addPortletLink</nowiki></code></bdi> and <bdi lang="zxx" dir="ltr"><code><nowiki>#p-namespaces</nowiki></code></bdi> that was deprecated one year ago will be removed. If you notice tools that should appear next to the "Discussion" tab are then missing, please tell the gadget's maintainers to see [[phab:T347907|instructions in the Phabricator task]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W42"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:47, 16 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25745824 --> == Tech News: 2023-43 == <section begin="technews-2023-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/43|Translations]] are available. '''Recent changes''' * There is a new [[mw:Special:MyLanguage/Wikimedia Language engineering/Newsletter/2023/October|Language and internationalization newsletter]], written quarterly. It contains updates on new feature development, improvements in various language-related technical projects, and related support work. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Source map support has been enabled on all wikis. When you open the debugger in your browser's developer tools, you should be able to see the unminified JavaScript source code. [https://phabricator.wikimedia.org/T47514] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-24|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-10-25|en}}. It will be on all wikis from {{#time:j xg|2023-10-26|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W43"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:16, 23 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25782286 --> == Tech News: 2023-44 == <section begin="technews-2023-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/44|Translations]] are available. '''Recent changes''' * The Structured Content team, as part of its project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]], made some UX improvements to the upload step of choosing own vs not own work ([[phab:T347590|T347590]]), as well as to the licensing step for own work ([[phab:T347756|T347756]]). * The Design Systems team has released version 1.0.0 of [[wmdoc:codex/latest/|Codex]], the new design system for Wikimedia. See the [[mw:Special:MyLanguage/Design_Systems_Team/Announcing_Codex_1.0|full announcement about the release of Codex 1.0.0]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-10-31|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-01|en}}. It will be on all wikis from {{#time:j xg|2023-11-02|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). * Listings on category pages are sorted on each wiki for that language using a [[:w:en:International Components for Unicode|library]]. For a brief period on 2 November, changes to categories will not be sorted correctly for many languages. This is because the developers are upgrading to a new version of the library. They will then use a script to fix the existing categories. This will take a few hours or a few days depending on how big the wiki is. You can [[mw:Special:MyLanguage/Wikimedia Technical Operations/ICU announcement|read more]]. [https://phabricator.wikimedia.org/T345561][https://phabricator.wikimedia.org/T267145] * Starting November 1, the impact module (Special:Impact) will be upgraded by the Growth team. The new impact module shows newcomers more data regarding their impact on the wiki. It was tested by a few wikis during the last few months. [https://phabricator.wikimedia.org/T336203] '''Future changes''' * There is [[mw:Special:MyLanguage/Extension:Graph/Plans#Roadmap|a proposed plan]] for re-enabling the Graph Extension. You can help by reviewing this proposal and [[mw:Extension_talk:Graph/Plans#c-PPelberg_(WMF)-20231020221600-Update:_20_October|sharing what you think about it]]. * The WMF is working on making it possible for administrators to [[mw:Special:MyLanguage/Community_configuration_2.0|edit MediaWiki configuration directly]]. This is similar to previous work on Special:EditGrowthConfig. [[phab:T349757|A technical RfC is running until November 08, where you can provide feedback.]] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W44"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:21, 30 October 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25801989 --> == Tech News: 2023-45 == <section begin="technews-2023-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/45|Translations]] are available. '''Recent changes''' * In the Vector 2022 skin, the default font-size of a number of navigational elements (tagline, tools menu, navigational links, and more) has been increased slightly to match the font size used in page content. [https://phabricator.wikimedia.org/T346062] '''Problems''' * Last week, there was a problem displaying some recent edits on [https://noc.wikimedia.org/conf/highlight.php?file=dblists/s5.dblist a few wikis], for 1-6 hours. The edits were saved but not immediately shown. This was due to a database problem. [https://phabricator.wikimedia.org/T350443] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-08|en}}. It will be on all wikis from {{#time:j xg|2023-11-09|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). * The Growth team will reassign newcomers from former mentors to [[mw:Special:MyLanguage/Growth/Structured mentor list|the currently active mentors]]. They have also changed the notification language to be more user-friendly. [https://phabricator.wikimedia.org/T330071][https://phabricator.wikimedia.org/T327493] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W45"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:05, 6 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25838105 --> == Tech News: 2023-46 == <section begin="technews-2023-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/46|Translations]] are available. '''Recent changes''' * Four new wikis have been created: ** a Wikipedia in [[d:Q7598268|Moroccan Amazigh]] ([[w:zgh:|<code>w:zgh:</code>]]) [https://phabricator.wikimedia.org/T350216] ** a Wikipedia in [[d:Q35159|Dagaare]] ([[w:dga:|<code>w:dga:</code>]]) [https://phabricator.wikimedia.org/T350218] ** a Wikipedia in [[d:Q33017|Toba Batak]] ([[w:bbc:|<code>w:bbc:</code>]]) [https://phabricator.wikimedia.org/T350320] ** a Wikiquote in [[d:Q33151|Banjar]] ([[q:bjn:|<code>q:bjn:</code>]]) [https://phabricator.wikimedia.org/T350217] '''Problems''' * Last week, users who previously visited Meta-Wiki or Wikimedia Commons and then became logged out on those wikis could not log in again. The problem is now resolved. [https://phabricator.wikimedia.org/T350695] * Last week, some pop-up dialogs and menus were shown with the wrong font size. The problem is now resolved. [https://phabricator.wikimedia.org/T350544] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-15|en}}. It will be on all wikis from {{#time:j xg|2023-11-16|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). '''Future changes''' * Reference Previews are coming to many wikis as a default feature. They are popups for references, similar to the [[mw:Special:MyLanguage/Page Previews|PagePreviews feature]]. [[m:WMDE Technical Wishes/ReferencePreviews#Opt-out feature|You can opt out]] of seeing them. If you are [[Special:Preferences#mw-prefsection-gadgets|using the gadgets]] Reference Tooltips or Navigation Popups, you won’t see Reference Previews. [[phab:T282999|Deployment]] is planned for November 22, 2023. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Canary (also known as heartbeat) events will be produced into [https://stream.wikimedia.org/?doc#/streams Wikimedia event streams] from December 11. Streams users are advised to filter out these events, by discarding all events where <bdi lang="zxx" dir="ltr"><code><nowiki>meta.domain == "canary"</nowiki></code></bdi>. Updates to [[mw:Special:MyLanguage/Manual:Pywikibot|Pywikibot]] or [https://github.com/ChlodAlejandro/wikimedia-streams wikimedia-streams] will discard these events by default. [https://phabricator.wikimedia.org/T266798] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W46"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:52, 13 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25859263 --> == Tech News: 2023-47 == <section begin="technews-2023-W47"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/47|Translations]] are available. '''Changes later this week''' * There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting on Wednesday, a new set of Wikipedias will get "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]" ({{int:project-localized-name-quwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rmywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_rupwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-roa_tarawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ruewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rwwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sahwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-satwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-scowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sdwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-shwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-siwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-skwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-slwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-smwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-srnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-sswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-stqwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-suwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-szlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tcywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tetwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tgwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tkwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-towiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tpiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ttwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-twwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tywiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-tyvwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-udmwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ugwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-uzwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vecwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vepwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vlswiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-vowiki/en}}). This is part of the [[phab:T304110|progressive deployment of this tool to more Wikipedias]]. The communities can [[mw:Special:MyLanguage/Growth/Community configuration|configure how this feature works locally]]. [https://phabricator.wikimedia.org/T308141][https://phabricator.wikimedia.org/T308142][https://phabricator.wikimedia.org/T308143] * The Vector 2022 skin will have some minor visual changes to drop-down menus, column widths, and more. These changes were added to four Wikipedias last week. If no issues are found, these changes will proceed to all wikis this week. These changes will make it possible to add new menus for readability and dark mode. [[mw:Special:MyLanguage/Reading/Web/Desktop_Improvements/Updates#November_2023:_Visual_changes,_more_deployments,_and_shifting_focus|Learn more]]. [https://phabricator.wikimedia.org/T347711] '''Future changes''' * There is [[mw:Extension talk:Graph/Plans#Update: 15 November|an update on re-enabling the Graph Extension]]. To speed up the process, Vega 2 will not be supported and only [https://phabricator.wikimedia.org/T335325 some protocols] will be available at launch. You can help by sharing what you think about the plan. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/47|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W47"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:55, 21 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25884616 --> == Tech News: 2023-48 == <section begin="technews-2023-W48"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/48|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-11-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-11-29|en}}. It will be on all wikis from {{#time:j xg|2023-11-30|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] MediaWiki's JavaScript system will now allow <bdi lang="zxx" dir="ltr"><code>async</code>/<code>await</code></bdi> syntax in gadgets and user scripts. Gadget authors should remember that users' browsers may not support it, so it should be used appropriately. [https://phabricator.wikimedia.org/T343499] * The deployment of "[[mw:Special:MyLanguage/Help:Growth/Tools/Add_a_link|Add a link]]" announced [[m:Special:MyLanguage/Tech/News/2023/47|last week]] was postponed. It will resume this week. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/48|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W48"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:08, 27 November 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25906379 --> == Tech News: 2023-49 == <section begin="technews-2023-W49"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/49|Translations]] are available. '''Recent changes''' * The spacing between paragraphs on Vector 2022 has been changed from 7px to 14px to match the size of the text. This will make it easier to distinguish paragraphs from sentences. [https://phabricator.wikimedia.org/T351754] * The "{{int:Visualeditor-dialog-meta-categories-defaultsort-label}}" feature in VisualEditor is working again. You no longer need to switch to source editing to edit <bdi lang="zxx" dir="ltr"><code><nowiki>{{DEFAULTSORT:...}}</nowiki></code></bdi> keywords. [https://phabricator.wikimedia.org/T337398] '''Changes later this week''' * There is no new MediaWiki version this week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * On 6 December, people who have the enabled the preference for "{{int:Discussiontools-preference-visualenhancements}}" will notice the [[mw:Special:MyLanguage/Talk pages project/Usability|talk page usability improvements]] appear on pages that include the <bdi lang="zxx" dir="ltr"><code><nowiki>__NEWSECTIONLINK__</nowiki></code></bdi> magic word. If you notice any issues, please [[phab:T352232|share them with the team on Phabricator]]. '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge [[wikitech:News/Toolforge Grid Engine deprecation|Grid Engine shutdown process]] will start on December 14. Maintainers of [[toolforge:grid-deprecation|tools that still use this old system]] should plan to migrate to Kubernetes, or tell the team your plans on Phabricator in the task about your tool, before that date. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/VIWWQKMSQO2ED3TVUR7KPPWRTOBYBVOA/] * Communities using [[mw:Special:MyLanguage/Structured_Discussions|Structured Discussions]] are being contacted regarding [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|the upcoming deprecation of Structured Discussions]]. You can read more about this project, and share your comments, [[mw:Special:MyLanguage/Structured_Discussions/Deprecation|on the project's page]]. '''Events''' * Registration & Scholarship applications are now open for the [[mw:Special:MyLanguage/Wikimedia Hackathon 2024|Wikimedia Hackathon 2024]] that will take place from 3–5 May in Tallinn, Estonia. Scholarship applications are open until 5 January 2024. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/49|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W49"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:50, 4 December 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25914435 --> == Tech News: 2023-50 == <section begin="technews-2023-W50"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/50|Translations]] are available. '''Recent changes''' * On Wikimedia Commons, there are some minor user-interface improvements for the "choosing own vs not own work" step in the UploadWizard. This is part of the Structured Content team's project of [[:commons:Commons:WMF support for Commons/Upload Wizard Improvements|improving UploadWizard on Commons]]. [https://phabricator.wikimedia.org/T352707][https://phabricator.wikimedia.org/T352709] '''Problems''' * There was a problem showing the [[mw:Special:MyLanguage/Growth/Personalized first day/Newcomer homepage|Newcomer homepage]] feature with the "impact module" and their page-view graphs, for a few days in early December. This has now been fixed. [https://phabricator.wikimedia.org/T352352][https://phabricator.wikimedia.org/T352349] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-13|en}}. It will be on all wikis from {{#time:j xg|2023-12-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * [[File:Octicons-tools.svg|15px|link=]] The [https://wikimediafoundation.limesurvey.net/796964 2023 Developer Satisfaction Survey] is seeking the opinions of the Wikimedia developer community. Please take the survey if you have any role in developing software for the Wikimedia ecosystem. The survey is open until 5 January 2024, and has an associated [[foundation:Legal:December_2023_Developer_Satisfaction_Survey|privacy statement]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/50|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W50"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 02:12, 12 December 2023 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25945501 --> == Tech News: 2023-51 == <section begin="technews-2023-W51"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2023/51|Translations]] are available. '''Tech News''' * The next issue of Tech News will be sent out on 8 January 2024 because of [[w:en:Christmas and holiday season|the holidays]]. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2023-12-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2023-12-20|en}}. It will be on all wikis from {{#time:j xg|2023-12-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). There is no new MediaWiki version next week. [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting December 18, it won't be possible to activate Structured Discussions on a user's own talk page using the Beta feature. The Beta feature option remains available for users who want to deactivate Structured Discussions. This is part of [[mw:Structured Discussions/Deprecation|Structured Discussions' deprecation work]]. [https://phabricator.wikimedia.org/T248309] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] There will be full support for redirects in the Module namespace. The "Move Page" feature will leave an appropriate redirect behind, and such redirects will be appropriately recognized by the software (e.g. hidden from [[{{#special:UnconnectedPages}}]]). There will also be support for [[mw:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Renaming or moving modules|manual redirects]]. [https://phabricator.wikimedia.org/T120794] '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The MediaWiki JavaScript documentation is moving to a new format. During the move, you can read the old docs using [https://doc.wikimedia.org/mediawiki-core/REL1_41/js/ version 1.41]. Feedback about [https://doc.wikimedia.org/mediawiki-core/master/js/ the new site] is welcome on the [[mw:Talk:JSDoc_WMF_theme|project talk page]]. * The Wishathon is a new initiative that encourages collaboration across the Wikimedia community to develop solutions for wishes collected through the [[m:Special:MyLanguage/Community Wishlist Survey|Community Wishlist Survey]]. The first community Wishathon will take place from 15–17 March. If you are interested in a project proposal as a user, developer, designer, or product lead, you can [[m:Special:MyLanguage/Event:WishathonMarch2024|register for the event and read more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2023/51|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2023-W51"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:17, 18 December 2023 (UTC) <!-- Message sent by User:Johan (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=25959059 --> == Tech News: 2024-02 == <section begin="technews-2024-W02"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/02|Translations]] are available. '''Recent changes''' * [https://mediawiki2latex.wmflabs.org/ mediawiki2latex] is a tool that converts wiki content into the formats of LaTeX, PDF, ODT, and EPUB. The code now runs many times faster due to recent improvements. There is also an optional Docker container you can [[b:de:Benutzer:Dirk_Hünniger/wb2pdf/install#Using_Docker|install]] on your local machine. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The way that Random pages are selected has been updated. This will slowly reduce the problem of some pages having a lower chance of appearing. [https://phabricator.wikimedia.org/T309477] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.13|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-10|en}}. It will be on all wikis from {{#time:j xg|2024-01-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/02|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W02"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:19, 9 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26026251 --> == Tech News: 2024-03 == <section begin="technews-2024-W03"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/03|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Pages that use the JSON [[mw:Special:MyLanguage/Manual:ContentHandler|contentmodel]] will now use tabs instead of spaces for auto-indentation. This will significantly reduce the page size. [https://phabricator.wikimedia.org/T326065] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] and personal user scripts may now use JavaScript syntax introduced in ES6 (also known as "ES2015") and ES7 ("ES2016"). MediaWiki validates the source code to protect other site functionality from syntax errors, and to ensure scripts are valid in all [[mw:Special:MyLanguage/Compatibility#Browsers|supported browsers]]. Previously, Gadgets could use the <bdi lang="zxx" dir="ltr"><code><nowiki>requiresES6</nowiki></code></bdi> option. This option is no longer needed and will be removed in the future. [https://phabricator.wikimedia.org/T75714] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Manual:Bot passwords|Bot passwords]] and [[mw:Special:MyLanguage/OAuth/Owner-only consumers|owner-only OAuth consumers]] can now be restricted to allow editing only specific pages. [https://phabricator.wikimedia.org/T349957] * You can now [[mw:Special:MyLanguage/Extension:Thanks|thank]] edits made by bots. [https://phabricator.wikimedia.org/T341388] * An update on the status of the Community Wishlist Survey for 2024 [[m:Special:MyLanguage/Community Wishlist Survey/Future Of The Wishlist/January 4, 2024 Update|has been published]]. Please read and give your feedback. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.14|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-17|en}}. It will be on all wikis from {{#time:j xg|2024-01-18|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting on January 17, it will not be possible to login to Wikimedia wikis from some specific old versions of the Chrome browser (versions 51–66, released between 2016 and 2018). Additionally, users of iOS 12, or Safari on Mac OS 10.14, may need to login to each wiki separately. [https://phabricator.wikimedia.org/T344791] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The <bdi lang="zxx" dir="ltr"><code>jquery.cookie</code></bdi> module was deprecated and replaced with the <bdi lang="zxx" dir="ltr"><code>mediawiki.cookie</code></bdi> module last year. A script has now been run to replace any remaining uses, and this week the temporary alias will be removed. [https://phabricator.wikimedia.org/T354966] '''Future changes''' * Wikimedia Deutschland is working to [[m:WMDE Technical Wishes/Reusing references|make reusing references easier]]. They are looking for people who are interested in participating in [https://wikimedia.sslsurvey.de/User-research-into-Reusing-References-Sign-up-Form-2024/en/ individual video calls for user research in January and February]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/03|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W03"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:13, 16 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26074460 --> == Tech News: 2024-04 == <section begin="technews-2024-W04"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/04|Translations]] are available. '''Problems''' * A bug in UploadWizard prevented linking to the userpage of the uploader when uploading. It has now been fixed. [https://phabricator.wikimedia.org/T354529] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.15|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-24|en}}. It will be on all wikis from {{#time:j xg|2024-01-25|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/04|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W04"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:03, 23 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26096197 --> == Tech News: 2024-05 == <section begin="technews-2024-W05"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/05|Translations]] are available. '''Recent changes''' * Starting Monday January 29, all talk pages messages' timestamps will become a link. This link is a permanent link to the comment. It allows users to find the comment they are looking for, even if this comment was moved elsewhere. This will affect all wikis except for the English Wikipedia. You can read more about this change [https://diff.wikimedia.org/2024/01/29/talk-page-permalinks-dont-lose-your-threads/ on Diff] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk_pages_permalinking|on Mediawiki.org]].<!-- The Diff post will be published on Monday morning UTC--> [https://phabricator.wikimedia.org/T302011] * There are some improvements to the CAPTCHA to make it harder for spam bots and scripts to bypass it. If you have feedback on this change, please comment on [[phab:T141490|the task]]. Staff are monitoring metrics related to the CAPTCHA, as well as secondary metrics such as account creations and edit counts. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.16|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-01-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-01-31|en}}. It will be on all wikis from {{#time:j xg|2024-02-01|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] On February 1, a link will be added to the "Tools" menu to download a [[w:en:QR code|QR code]] that links to the page you are viewing. There will also be a new [[{{#special:QrCode}}]] page to create QR codes for any Wikimedia URL. This addresses the [[m:Community Wishlist Survey 2023/Mobile and apps/Add ability to share QR code for a page in any Wikimedia project|#19 most-voted wish]] from the [[m:Community Wishlist Survey 2023/Results|2023 Community Wishlist Survey]]. [https://phabricator.wikimedia.org/T329973] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] which only work in some skins have sometimes used the <bdi lang="zxx" dir="ltr"><code>targets</code></bdi> option to limit where you can use them. This will stop working this week. You should use the <bdi lang="zxx" dir="ltr"><code>skins</code></bdi> option instead. [https://phabricator.wikimedia.org/T328497] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/05|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W05"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:31, 29 January 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26137870 --> == Tech News: 2024-06 == <section begin="technews-2024-W06"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/06|Translations]] are available. '''Recent changes''' *The mobile site history pages now use the same HTML as the desktop history pages. If you hear of any problems relating to mobile history usage please point them to [[phab:T353388|the phabricator task]]. *On most wikis, admins can now block users from making specific actions. These actions are: uploading files, creating new pages, moving (renaming) pages, and sending thanks. The goal of this feature is to allow admins to apply blocks that are adequate to the blocked users' activity. [[m:Special:MyLanguage/Community health initiative/Partial blocks#action-blocks|Learn more about "action blocks"]]. [https://phabricator.wikimedia.org/T242541][https://phabricator.wikimedia.org/T280531] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.17|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-06|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-07|en}}. It will be on all wikis from {{#time:j xg|2024-02-08|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Talk pages permalinks that included diacritics and non-Latin script were malfunctioning. This issue is fixed. [https://phabricator.wikimedia.org/T356199] '''Future changes''' * [[m:WMDE Technical Wishes/ReferencePreviews#24WPs|24 Wikipedias]] with [[mw:Special:MyLanguage/Reference_Tooltips|Reference Tooltips]] as a default gadget are encouraged to remove that default flag. This would make [[mw:Special:MyLanguage/Help:Reference_Previews|Reference Previews]] the new default for reference popups, leading to a more consistent experience across wikis. For [[m:WMDE Technical Wishes/ReferencePreviews#46WPs|46 Wikipedias]] with less than 4 interface admins, the change is already scheduled for mid-February, [[m:Talk:WMDE Technical Wishes/ReferencePreviews#Reference Previews to become the default for previewing references on more wikis.|unless there are concerns]]. The older Reference Tooltips gadget will still remain usable and will override this feature, if it is available on your wiki and you have enabled it in your settings. [https://meta.wikimedia.org/wiki/WMDE_Technical_Wishes/ReferencePreviews#Reference_Previews_to_become_the_default_for_previewing_references_on_more_wikis][https://phabricator.wikimedia.org/T355312] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/06|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W06"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:22, 5 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26180971 --> == Tech News: 2024-07 == <section begin="technews-2024-W07"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/07|Translations]] are available. '''Recent changes''' * The [[d:Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split experiment]] is working and loaded onto 3 test servers. The team in charge is testing the split's impact and requires feedback from WDQS users through the UI or programmatically in different channels. [https://www.wikidata.org/wiki/Wikidata_talk:SPARQL_query_service/WDQS_graph_split][https://phabricator.wikimedia.org/T356773][https://www.wikidata.org/wiki/User:Sannita_(WMF)] Users' feedback will validate the impact of various use cases and workflows around the Wikidata Query service. [https://www.wikidata.org/wiki/Wikidata:SPARQL_query_service/WDQS_backend_update/October_2023_scaling_update][https://www.mediawiki.org/wiki/Wikidata_Query_Service/User_Manual#Federation] '''Problems''' *There was a bug that affected the appearance of visited links when using mobile device to access wiki sites. It made the links appear black; [[phab:T356928|this issue]] is fixed. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.18|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-13|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-14|en}}. It will be on all wikis from {{#time:j xg|2024-02-15|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] As work continues on the grid engine deprecation,[https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation] tools on the grid engine will be stopped starting on February 14th, 2024. If you have tools actively migrating you can ask for an extension so they are not stopped. [https://wikitech.wikimedia.org/wiki/Portal:Toolforge/About_Toolforge#Communication_and_support] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/07|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W07"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 05:48, 13 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26223994 --> == Tech News: 2024-08 == <section begin="technews-2024-W08"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/08|Translations]] are available. '''Recent changes''' * If you have the "{{int:Tog-enotifwatchlistpages}}" option enabled, edits by bot accounts no longer trigger notification emails. Previously, only minor edits would not trigger the notification emails. [https://phabricator.wikimedia.org/T356984] * There are changes to how user and site scripts load for [[mw:Special:MyLanguage/Skin:Vector/2022| Vector 2022]] on specific wikis. The changes impacted the following Wikis: all projects with [[mw:Special:MyLanguage/Skin:Vector|Vector legacy]] as the default skin, Wikivoyage, and Wikibooks. Other wikis will be affected over the course of the next three months. Gadgets are not impacted. If you have been affected or want to minimize the impact on your project, see [[Phab:T357580| this ticket]]. Please coordinate and take action proactively. *Newly auto-created accounts (the accounts you get when you visit a new wiki) now have the same local notification preferences as users who freshly register on that wiki. It is effected in four notification types listed in the [[phab:T353225|task's description]]. *The maximum file size when using [[c:Special:MyLanguage/Commons:Upload_Wizard|Upload Wizard]] is now 5 GiB. [https://phabricator.wikimedia.org/T191804] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.19|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-20|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-21|en}}. It will be on all wikis from {{#time:j xg|2024-02-22|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Selected tools on the grid engine have been [[wikitech:News/Toolforge_Grid_Engine_deprecation|stopped]] as we prepare to shut down the grid on March 14th, 2024. The tool's code and data have not been deleted. If you are a maintainer and you want your tool re-enabled reach out to the [[wikitech:Portal:Toolforge/About_Toolforge#Communication_and_support|team]]. Only tools that have asked for extension are still running on the grid. * The CSS <bdi lang="zxx" dir="ltr"><code>[https://developer.mozilla.org/en-US/docs/Web/CSS/filter filter]</code></bdi> property can now be used in HTML <bdi lang="zxx" dir="ltr"><code>style</code></bdi> attributes in wikitext. [https://phabricator.wikimedia.org/T308160] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/08|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W08"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 15:36, 19 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26254282 --> == Tech News: 2024-09 == <section begin="technews-2024-W09"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/09|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/VisualEditor_on_mobile|mobile visual editor]] is now the default editor for users who never edited before, at a small group of wikis. [[mw:Special:MyLanguage/VisualEditor_on_mobile/VE_mobile_default#A/B_test_results| Research ]] shows that users using this editor are slightly more successful publishing the edits they started, and slightly less successful publishing non-reverted edits. Users who defined the wikitext editor as their default on desktop will get the wikitext editor on mobile for their first edit on mobile as well. [https://phabricator.wikimedia.org/T352127] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[mw:Special:MyLanguage/ResourceLoader/Core modules#mw.config|mw.config]] value <code>wgGlobalGroups</code> now only contains groups that are active in the wiki. Scripts no longer have to check whether the group is active on the wiki via an API request. A code example of the above is: <bdi lang="zxx" dir="ltr"><code>if (/globalgroupname/.test(mw.config.get("wgGlobalGroups")))</code></bdi>. [https://phabricator.wikimedia.org/T356008] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.20|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-02-27|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-02-28|en}}. It will be on all wikis from {{#time:j xg|2024-02-29|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * The right to change [[mw:Special:MyLanguage/Manual:Tags|edit tags]] (<bdi lang="zxx" dir="ltr"><code>changetags</code></bdi>) will be removed from users in Wikimedia sites, keeping it by default for admins and bots only. Your community can ask to retain the old configuration on your wiki before this change happens. Please indicate in [[phab:T355639|this ticket]] to keep it for your community before the end of March 2024. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/09|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W09"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:23, 26 February 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26294125 --> == Tech News: 2024-10 == <section begin="technews-2024-W10"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/10|Translations]] are available. '''Recent changes''' * The <bdi lang="zxx" dir="ltr"><code>Special:Book</code></bdi> page (as well as the associated "Create a book" functionality) provided by the old [[mw:Special:MyLanguage/Extension:Collection|Collection extension]] has been removed from all Wikisource wikis, as it was broken. This does not affect the ability to download normal books, which is provided by the [[mw:Special:MyLanguage/Extension:Wikisource|Wikisource extension]]. [https://phabricator.wikimedia.org/T358437] * [[m:Wikitech|Wikitech]] now uses the next-generation [[mw:Special:MyLanguage/Parsoid|Parsoid]] wikitext parser by default to generate all pages in the Talk namespace. Report any problems on the [[mw:Talk:Parsoid/Parser_Unification/Known_Issues|Known Issues discussion page]]. You can use the [[mw:Special:MyLanguage/Extension:ParserMigration|ParserMigration]] extension to control the use of Parsoid; see the [[mw:Special:MyLanguage/Help:Extension:ParserMigration|ParserMigration help documentation]] for more details. * Maintenance on [https://etherpad.wikimedia.org etherpad] is completed. If you encounter any issues, please indicate in [[phab:T316421|this ticket]]. * [[File:Octicons-tools.svg|12px|link=|alt=| Advanced item]] [[mw:Special:MyLanguage/Extension:Gadgets|Gadgets]] allow interface admins to create custom features with CSS and JavaScript. The <bdi lang="zxx" dir="ltr"><code>Gadget</code></bdi> and <bdi lang="zxx" dir="ltr"><code>Gadget_definition</code></bdi> namespaces and <bdi lang="zxx" dir="ltr"><code>gadgets-definition-edit</code></bdi> user right were reserved for an experiment in 2015, but were never used. These were visible on Special:Search and Special:ListGroupRights. The unused namespaces and user rights are now removed. No pages are moved, and no changes need to be made. [https://phabricator.wikimedia.org/T31272] * A usability improvement to the "Add a citation" in Wikipedia workflow has been made, the insert button was moved to the popup header. [https://phabricator.wikimedia.org/T354847] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.21|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-05|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-06|en}}. It will be on all wikis from {{#time:j xg|2024-03-07|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233] * The HTML markup of headings and section edit links will be changed later this year to improve accessibility. See [[mw:Special:MyLanguage/Heading_HTML_changes|Heading HTML changes]] for details. The new markup will be the same as in the new Parsoid wikitext parser. You can test your gadget or stylesheet with the new markup if you add <bdi lang="zxx" dir="ltr"><code>?useparsoid=1</code></bdi> to your URL ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Selecting_a_parser_using_a_URL_query_string|more info]]) or turn on Parsoid read views in your user options ([[mw:Special:MyLanguage/Help:Extension:ParserMigration#Enabling_via_user_preference|more info]]). * '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/10|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W10"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 19:47, 4 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26329807 --> == Tech News: 2024-11 == <section begin="technews-2024-W11"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/11|Translations]] are available. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.22|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-12|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-13|en}}. It will be on all wikis from {{#time:j xg|2024-03-14|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * After consulting with various communities, the line height of the text on the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] will be increased to its previous value of 1.65. Different options for typography can also be set using the options in the menu, as needed. [https://phabricator.wikimedia.org/T358498] *The active link color in [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva]] will be changed to provide more consistency with our other platforms and best practices. [https://phabricator.wikimedia.org/T358516] * [[c:Special:MyLanguage/Commons:Structured data|Structured data on Commons]] will no longer ask whether you want to leave the page without saving. This will prevent the “information you’ve entered may not be saved” popups from appearing when no information have been entered. It will also make file pages on Commons load faster in certain cases. However, the popups will be hidden even if information has indeed been entered. If you accidentally close the page before saving the structured data you entered, that data will be lost. [https://phabricator.wikimedia.org/T312315] '''Future changes''' * All wikis will be read-only for a few minutes on March 20. This is planned at 14:00 UTC. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/11|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W11"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:04, 11 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26374013 --> == Tech News: 2024-12 == <section begin="technews-2024-W12"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/12|Translations]] are available. '''Recent changes''' * The notice "Language links are at the top of the page" that appears in the [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]] main menu has been removed now that users have learned the new location of the Language switcher. [https://phabricator.wikimedia.org/T353619] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/IP_Editing:_Privacy_Enhancement_and_Abuse_Mitigation/IP_Info_feature|IP info feature]] displays data from Spur, an IP addresses database. Previously, the only data source for this feature was MaxMind. Now, IP info is more useful for patrollers. [https://phabricator.wikimedia.org/T341395] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The Toolforge Grid Engine services have been shut down after the final migration process from Grid Engine to Kubernetes. [https://wikitech.wikimedia.org/wiki/Obsolete:Toolforge/Grid][https://wikitech.wikimedia.org/wiki/News/Toolforge_Grid_Engine_deprecation][https://techblog.wikimedia.org/2022/03/14/toolforge-and-grid-engine/] * Communities can now customize the default reasons for undeleting a page by creating [[MediaWiki:Undelete-comment-dropdown]]. [https://phabricator.wikimedia.org/T326746] '''Problems''' * [[m:Special:MyLanguage/WMDE_Technical_Wishes/RevisionSlider|RevisionSlider]] is an interface to interactively browse a page's history. Users in [[mw:Special:MyLanguage/Extension:RevisionSlider/Developing_a_RTL-accessible_feature_in_MediaWiki_-_what_we%27ve_learned_while_creating_the_RevisionSlider|right-to-left]] languages reported RevisionSlider reacting wrong to mouse clicks. This should be fixed now. [https://phabricator.wikimedia.org/T352169] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.23|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-19|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-20|en}}. It will be on all wikis from {{#time:j xg|2024-03-21|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * All wikis will be read-only for a few minutes on March 20. This is planned at [https://zonestamp.toolforge.org/1710943200 14:00 UTC]. [https://phabricator.wikimedia.org/T358233][https://meta.wikimedia.org/wiki/Special:MyLanguage/Tech/Server_switch] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/12|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W12"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 17:39, 18 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26410165 --> == Tech News: 2024-13 == <section begin="technews-2024-W13"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/13|Translations]] are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] An update was made on March 18th 2024 to how various projects load site, user JavaScript and CSS in [[mw:Special:MyLanguage/Skin:Vector/2022|Vector 2022 skin]]. A [[phab:T360384|checklist]] is provided for site admins to follow. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.24|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-03-26|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-03-27|en}}. It will be on all wikis from {{#time:j xg|2024-03-28|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/13|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W13"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 18:56, 25 March 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26446209 --> == Tech News: 2024-14 == <section begin="technews-2024-W14"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/14|Translations]] are available. '''Recent changes''' * Users of the [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading|reading accessibility]] beta feature will notice that the default line height for the standard and large text options has changed. [https://phabricator.wikimedia.org/T359030] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.25|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-02|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-03|en}}. It will be on all wikis from {{#time:j xg|2024-04-04|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * The Wikimedia Foundation has an annual plan. The annual plan decides what the Wikimedia Foundation will work on. You can now read [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product & Technology OKRs#Draft Key Results|the draft key results]] for the Product and Technology department. They are suggestions for what results the Foundation wants from big technical changes from July 2024 to June 2025. You can [[m:Talk:Wikimedia Foundation Annual Plan/2024-2025/Product & Technology OKRs|comment on the talk page]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/14|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W14"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 03:36, 2 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26462933 --> == Tech News: 2024-15 == <section begin="technews-2024-W15"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/15|Translations]] are available. '''Recent changes''' * Web browsers can use tools called [[:w:en:Browser extension|extensions]]. There is now a Chrome extension called [[m:Future Audiences/Experiment:Citation Needed|Citation Needed]] which you can use to see if an online statement is supported by a Wikipedia article. This is a small experiment to see if Wikipedia can be used this way. Because it is a small experiment, it can only be used in Chrome in English. * [[File:Octicons-gift.svg|12px|link=|alt=|Wishlist item]] A new [[mw:Special:MyLanguage/Help:Edit Recovery|Edit Recovery]] feature has been added to all wikis, available as a [[Special:Preferences#mw-prefsection-editing|user preference]]. Once you enable it, your in-progress edits will be stored in your web browser, and if you accidentally close an editing window or your browser or computer crashes, you will be prompted to recover the unpublished text. Please leave any feedback on the [[m:Special:MyLanguage/Talk:Community Wishlist Survey 2023/Edit-recovery feature|project talk page]]. This was the #8 wish in the 2023 Community Wishlist Survey. * Initial results of [[mw:Special:MyLanguage/Edit check|Edit check]] experiments [[mw:Special:MyLanguage/Edit_check#4_April_2024|have been published]]. Edit Check is now deployed as a default feature at [[phab:T342930#9538364|the wikis that tested it]]. [[mw:Talk:Edit check|Let us know]] if you want your wiki to be part of the next deployment of Edit check. [https://phabricator.wikimedia.org/T342930][https://phabricator.wikimedia.org/T361727] * Readers using the [[mw:Special:MyLanguage/Skin:Minerva Neue|Minerva skin]] on mobile will notice there has been an improvement in the line height across all typography settings. [https://phabricator.wikimedia.org/T359029] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.42/wmf.26|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-09|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-10|en}}. It will be on all wikis from {{#time:j xg|2024-04-11|en}} ([[mw:MediaWiki 1.42/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * New accounts and logged-out users will get the [[mw:Special:MyLanguage/VisualEditor|visual editor]] as their default editor on mobile. This deployment is made at all wikis except for the English Wikipedia. [https://phabricator.wikimedia.org/T361134] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/15|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W15"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:37, 8 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26564838 --> == Tech News: 2024-16 == <section begin="technews-2024-W16"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/16|Translations]] are available. '''Problems''' * Between 2 April and 8 April, on wikis using [[mw:Special:MyLanguage/Extension:FlaggedRevs|Flagged Revisions]], the "{{Int:tag-mw-reverted}}" tag was not applied to undone edits. In addition, page moves, protections and imports were not autoreviewed. This problem is now fixed. [https://phabricator.wikimedia.org/T361918][https://phabricator.wikimedia.org/T361940] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.1|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-16|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-17|en}}. It will be on all wikis from {{#time:j xg|2024-04-18|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[mw:Special:MyLanguage/Help:Magic words#DEFAULTSORT|Default category sort keys]] will now affect categories added by templates placed in [[mw:Special:MyLanguage/Help:Cite|footnotes]]. Previously footnotes used the page title as the default sort key even if a different default sort key was specified (category-specific sort keys already worked). [https://phabricator.wikimedia.org/T40435] * A new variable <bdi lang="zxx" dir="ltr"><code>page_last_edit_age</code></bdi> will be added to [[Special:AbuseFilter|abuse filters]]. It tells how many seconds ago the last edit to a page was made. [https://phabricator.wikimedia.org/T269769] '''Future changes''' * Volunteer developers are kindly asked to update the code of their tools and features to handle [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]]. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Four database fields will be removed from database replicas (including [[quarry:|Quarry]]). This affects only the <bdi lang="zxx" dir="ltr"><code>abuse_filter</code></bdi> and <bdi lang="zxx" dir="ltr"><code>abuse_filter_history</code></bdi> tables. Some queries might need to be updated. [https://phabricator.wikimedia.org/T361996] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/16|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W16"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:29, 15 April 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26564838 --> == Tech News: 2024-17 == <section begin="technews-2024-W17"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/17|Translations]] are available. '''Recent changes''' * Starting this week, newcomers editing Wikipedia [[mw:Special:MyLanguage/Growth/Positive reinforcement#Leveling up 3|will be encouraged]] to try structured tasks. [[mw:Special:MyLanguage/Growth/Feature summary#Newcomer tasks|Structured tasks]] have been shown to [[mw:Special:MyLanguage/Growth/Personalized first day/Structured tasks/Add a link/Experiment analysis, December 2021|improve newcomer activation and retention]]. [https://phabricator.wikimedia.org/T348086] * You can [[m:Special:MyLanguage/Coolest Tool Award|nominate your favorite tools]] for the fifth edition of the Coolest Tool Award. Nominations will be open until May 10. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.2|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-23|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-04-24|en}}. It will be on all wikis from {{#time:j xg|2024-04-25|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * This is the last warning that by the end of May 2024 the Vector 2022 skin will no longer share site and user scripts/styles with old Vector. For user-scripts that you want to keep using on Vector 2022, copy the contents of [[{{#special:MyPage}}/vector.js]] to [[{{#special:MyPage}}/vector-2022.js]]. There are [[mw:Special:MyLanguage/Reading/Web/Desktop Improvements/Features/Loading Vector 2010 scripts|more technical details]] available. Interface administrators who foresee this leading to lots of technical support questions may wish to send a mass message to your community, as was done on French Wikipedia. [https://phabricator.wikimedia.org/T362701] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/17|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W17"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:28, 22 April 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26647188 --> == Tech News: 2024-18 == <section begin="technews-2024-W18"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/18|Translations]] are available. '''Recent changes''' [[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]] * The appearance of talk pages changed for the following wikis: {{int:project-localized-name-azwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-bnwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-dewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-fawiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hewiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-hiwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-idwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-kowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-nlwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ptwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-rowiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-thwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-trwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-ukwiki/en}}{{int:comma-separator/en}}{{int:project-localized-name-viwiki/en}}. These wikis participated to a test, where 50% of users got the new design, for one year. As this test [[Mw:Special:MyLanguage/Talk pages project/Usability/Analysis|gave positive results]], the new design is deployed on these wikis as the default design. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] ("{{int:discussiontools-preference-visualenhancements}}"). The deployment will happen at all wikis in the coming weeks. [https://phabricator.wikimedia.org/T341491] * Seven new wikis have been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q33014|Betawi]] ([[w:bew:|<code>w:bew:</code>]]) [https://phabricator.wikimedia.org/T357866] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35708|Kusaal]] ([[w:kus:|<code>w:kus:</code>]]) [https://phabricator.wikimedia.org/T359757] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q35513|Igala]] ([[w:igl:|<code>w:igl:</code>]]) [https://phabricator.wikimedia.org/T361644] ** a {{int:project-localized-name-group-wiktionary}} in [[d:Q33541|Karakalpak]] ([[wikt:kaa:|<code>wikt:kaa:</code>]]) [https://phabricator.wikimedia.org/T362135] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q9228|Burmese]] ([[s:my:|<code>s:my:</code>]]) [https://phabricator.wikimedia.org/T361085] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q9237|Malay]] ([[s:ms:|<code>s:ms:</code>]]) [https://phabricator.wikimedia.org/T363039] ** a {{int:project-localized-name-group-wikisource}} in [[d:Q8108|Georgian]] ([[s:ka:|<code>s:ka:</code>]]) [https://phabricator.wikimedia.org/T363085] * You can now [https://translatewiki.net/wiki/Support#Early_access:_Watch_Message_Groups_on_Translatewiki.net watch message groups/projects] on [[m:Special:MyLanguage/translatewiki.net|Translatewiki.net]]. Initially, this feature will notify you of added or deleted messages in these groups. [https://phabricator.wikimedia.org/T348501] * Dark mode is now available on all wikis, on mobile web for logged-in users who opt into the [[Special:MobileOptions|advanced mode]]. This is the early release of the feature. Technical editors are invited to [https://night-mode-checker.wmcloud.org/ check for accessibility issues on wikis]. See [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-04|more detailed guidelines]]. '''Problems''' * [[mw:Special:MyLanguage/Help:Extension:Kartographer|Kartographer]] maps can use an alternative visual style without labels, by using <bdi lang="zxx" dir="ltr"><code><nowiki>mapstyle="osm"</nowiki></code></bdi>. This wasn't working in previews, creating the wrong impression that it wasn't supported. This has now been fixed. [https://phabricator.wikimedia.org/T362531] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.3|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-04-30|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-01|en}}. It will be on all wikis from {{#time:j xg|2024-05-02|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/18|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W18"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 03:33, 30 April 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26689057 --> == Tech News: 2024-19 == <section begin="technews-2024-W19"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/19|Translations]] are available. '''Recent changes''' [[File:Talk_pages_default_look_(April_2023).jpg|thumb|alt=Screenshot of the visual improvements made on talk pages|Example of a talk page with the new design, in French.]] * The appearance of talk pages changed for all wikis, except for Commons, Wikidata and most Wikipedias ([[m:Special:MyLanguage/Tech/News/2024/18|a few]] have already received this design change). You can read the detail of the changes [[diffblog:2024/05/02/making-talk-pages-better-for-everyone/|on ''Diff'']]. It is possible to opt-out these changes [[Special:Preferences#mw-prefsection-editing|in user preferences]] ("{{int:discussiontools-preference-visualenhancements}}"). The deployment will happen at remaining wikis in the coming weeks. [https://phabricator.wikimedia.org/T352087][https://phabricator.wikimedia.org/T319146] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Interface admins now have greater control over the styling of article components on mobile with the introduction of the <code>SiteAdminHelper</code>. More information on how styles can be disabled can be found [[mw:Special:MyLanguage/Extension:WikimediaMessages#Site_admin_helper|at the extension's page]]. [https://phabricator.wikimedia.org/T363932] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]] has added article body sections in JSON format and a curated short description field to the existing parsed Infobox. This expansion to the API is also available via Wikimedia Cloud Services. [https://enterprise.wikimedia.com/blog/article-sections-and-description/] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.4|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-07|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-08|en}}. It will be on all wikis from {{#time:j xg|2024-05-09|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * When you look at the Special:Log page, the first view is labelled "All public logs", but it only shows some logs. This label will now say "Main public logs". [https://phabricator.wikimedia.org/T237729] '''Future changes''' * A new service will be built to replace [[mw:Special:MyLanguage/Extension:Graph|Extension:Graph]]. Details can be found in [[mw:Special:MyLanguage/Extension:Graph/Plans|the latest update]] regarding this extension. * Starting May 21, English Wikipedia and German Wikipedia will get the possibility to activate "[[mw:Special:MyLanguage/Help:Growth/Tools/Add a link|Add a link]]". This is part of the [[phab:T304110|progressive deployment of this tool to all Wikipedias]]. These communities can [[mw:Special:MyLanguage/Growth/Community configuration|activate and configure the feature locally]]. [https://phabricator.wikimedia.org/T308144] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/19|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W19"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 16:44, 6 May 2024 (UTC) <!-- Message sent by User:Trizek (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26729363 --> == Tech News: 2024-20 == <section begin="technews-2024-W20"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/20|Translations]] are available. '''Recent changes''' * On Wikisource there is a special page listing pages of works without corresponding scan images. Now you can use the new magic word <bdi lang="zxx" dir="ltr"><code>__EXPECTWITHOUTSCANS__</code></bdi> to exclude certain pages (list of editions or translations of works) from that list. [https://phabricator.wikimedia.org/T344214] * If you use the [[Special:Preferences#mw-prefsection-editing|user-preference]] "{{int:tog-uselivepreview}}", then the template-page feature "{{int:Templatesandbox-editform-legend}}" will now also work without reloading the page. [https://phabricator.wikimedia.org/T136907] * [[mw:Special:Mylanguage/Extension:Kartographer|Kartographer]] maps can now specify an alternative text via the <bdi lang="zxx" dir="ltr"><code><nowiki>alt=</nowiki></code></bdi> attribute. This is identical in usage to the <bdi lang="zxx" dir="ltr"><code><nowiki>alt=</nowiki></code></bdi> attribute in the [[mw:Special:MyLanguage/Help:Images#Syntax|image and gallery syntax]]. An exception for this feature is wikis like Wikivoyage where the miniature maps are interactive. [https://phabricator.wikimedia.org/T328137] * The old [[mw:Special:MyLanguage/Extension:GuidedTour|Guided Tour]] for the "[[mw:Special:MyLanguage/Edit Review Improvements/New filters for edit review|New Filters for Edit Review]]" feature has been removed. It was created in 2017 to show people with older accounts how the interface had changed, and has now been seen by most of the intended people. [https://phabricator.wikimedia.org/T217451] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.5|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-14|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-15|en}}. It will be on all wikis from {{#time:j xg|2024-05-16|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The [[{{#special:search}}]] results page will now use CSS flex attributes, for better accessibility, instead of a table. If you have a gadget or script that adjusts search results, you should update your script to the new HTML structure. [https://phabricator.wikimedia.org/T320295] '''Future changes''' * In the Vector 2022 skin, main pages will be displayed at full width (like special pages). The goal is to keep the number of characters per line large enough. This is related to the coming changes to typography in Vector 2022. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates|Learn more]]. [https://phabricator.wikimedia.org/T357706] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Two columns of the <bdi lang="zxx" dir="ltr"><code>[[mw:Special:MyLanguage/Manual:pagelinks table|pagelinks]]</code></bdi> database table (<bdi lang="zxx" dir="ltr"><code>pl_namespace</code></bdi> and <bdi lang="zxx" dir="ltr"><code>pl_title</code></bdi>) are being dropped soon. Users must use two columns of the new <bdi lang="zxx" dir="ltr"><code>[[mw:special:MyLanguage/Manual:linktarget table|linktarget]]</code></bdi> table instead (<bdi lang="zxx" dir="ltr"><code>lt_namespace</code></bdi> and <bdi lang="zxx" dir="ltr"><code>lt_title</code></bdi>). In your existing SQL queries: *# Replace <bdi lang="zxx" dir="ltr"><code>JOIN pagelinks</code></bdi> with <bdi lang="zxx" dir="ltr"><code>JOIN linktarget</code></bdi> and <bdi lang="zxx" dir="ltr"><code>pl_</code></bdi> with <bdi lang="zxx" dir="ltr"><code>lt_</code></bdi> in the <bdi lang="zxx" dir="ltr"><code>ON</code></bdi> statement *# Below that add <bdi lang="zxx" dir="ltr"><code>JOIN pagelinks ON lt_id = pl_target_id</code></bdi> ** See <bdi lang="en" dir="ltr">[[phab:T222224]]</bdi> for technical reasoning. [https://phabricator.wikimedia.org/T222224][https://phabricator.wikimedia.org/T299947] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/20|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W20"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:58, 13 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26762074 --> == Tech News: 2024-21 == <section begin="technews-2024-W21"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/21|Translations]] are available. '''Recent changes''' * The [[mw:Special:MyLanguage/Extension:Nuke|Nuke]] feature, which enables administrators to mass delete pages, will now correctly delete pages which were moved to another title. [https://phabricator.wikimedia.org/T43351] * New changes have been made to the UploadWizard in Wikimedia Commons: the overall layout has been improved, by following new styling and spacing for the form and its fields; the headers and helper text for each of the fields was changed; the Caption field is now a required field, and there is an option for users to copy their caption into the media description. [https://commons.wikimedia.org/wiki/Commons:WMF_support_for_Commons/Upload_Wizard_Improvements#Changes_to_%22Describe%22_workflow][https://phabricator.wikimedia.org/T361049] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.6|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-21|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-22|en}}. It will be on all wikis from {{#time:j xg|2024-05-23|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML used to render all headings [[mw:Heading_HTML_changes|is being changed to improve accessibility]]. It will change on 22 May in some skins (Timeless, Modern, CologneBlue, Nostalgia, and Monobook). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in all other skins. The developers are also considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/21|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W21"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:04, 20 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26786311 --> == Tech News: 2024-22 == <section begin="technews-2024-W22"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/22|Translations]] are available. '''Recent changes''' * Several bugs related to the latest updates to the UploadWizard on Wikimedia Commons have been fixed. For more information, see [[:phab:T365107|T365107]] and [[:phab:T365119|T365119]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] In March 2024 a new [[mw:ResourceLoader/Core_modules#addPortlet|addPortlet]] API was added to allow gadgets to create new portlets (menus) in the skin. In certain skins this can be used to create dropdowns. Gadget developers are invited to try it and [[phab:T361661|give feedback]]. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Some CSS in the Minerva skin has been removed to enable easier community configuration. Interface editors should check the rendering on mobile devices for aspects related to the classes: <bdi lang="zxx" dir="ltr"><code>.collapsible</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.multicol</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.reflist</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.coordinates</code></bdi>{{int:comma-separator/en}}<bdi lang="zxx" dir="ltr"><code>.topicon</code></bdi>. [[phab:T361659|Further details are available on replacement CSS]] if it is needed. '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.7|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-05-28|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-05-29|en}}. It will be on all wikis from {{#time:j xg|2024-05-30|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * When you visit a wiki where you don't yet have a local account, local rules such as edit filters can sometimes prevent your account from being created. Starting this week, MediaWiki takes your global rights into account when evaluating whether you can override such local rules. [https://phabricator.wikimedia.org/T316303] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/22|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W22"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:15, 28 May 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26832205 --> == Tech News: 2024-23 == <section begin="technews-2024-W23"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/23|Translations]] are available. '''Recent changes''' * It is now possible for local administrators to add new links to the bottom of the site Tools menu without JavaScript. [[mw:Manual:Interface/Sidebar#Add or remove toolbox sections|Documentation is available]]. [https://phabricator.wikimedia.org/T6086] * The message name for the definition of the tracking category of WikiHiero has changed from "<bdi lang="zxx" dir="ltr"><code>MediaWiki:Wikhiero-usage-tracking-category</code></bdi>" to "<bdi lang="zxx" dir="ltr"><code>MediaWiki:Wikihiero-usage-tracking-category</code></bdi>". [https://gerrit.wikimedia.org/r/c/mediawiki/extensions/wikihiero/+/1035855] * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q5317225|Kadazandusun]] ([[w:dtp:|<code>w:dtp:</code>]]) [https://phabricator.wikimedia.org/T365220] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.8|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-04|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-05|en}}. It will be on all wikis from {{#time:j xg|2024-06-06|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] '''Future changes''' * Next week, on wikis with the Vector 2022 skin as the default, logged-out desktop users will be able to choose between different font sizes. The default font size will also be increased for them. This is to make Wikimedia projects easier to read. [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-06 deployments|Learn more]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/23|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W23"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:35, 3 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26844397 --> == Tech News: 2024-24 == <section begin="technews-2024-W24"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/24|Translations]] are available. '''Recent changes''' * The software used to render SVG files has been updated to a new version, fixing many longstanding bugs in SVG rendering. [https://phabricator.wikimedia.org/T265549] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML used to render all headings [[mw:Heading HTML changes|is being changed to improve accessibility]]. It was changed last week in some skins (Vector legacy and Minerva). Please test gadgets on your wiki on these skins and [[phab:T13555|report any related problems]] so that they can be resolved before this change is made in Vector-2022. The developers are still considering the introduction of a [[phab:T337286|Gadget API for adding buttons to section titles]] if that would be helpful to tool creators, and would appreciate any input you have on that. * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The HTML markup used for citations by [[mw:Special:MyLanguage/Parsoid|Parsoid]] changed last week. In places where Parsoid previously added the <bdi lang="zxx" dir="ltr"><code>mw-reference-text</code></bdi> class, Parsoid now also adds the <bdi lang="zxx" dir="ltr"><code>reference-text</code></bdi> class for better compatibility with the legacy parser. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1036705] '''Problems''' * There was a bug with the Content Translation interface that caused the tools menus to appear in the wrong location. This has now been fixed. [https://phabricator.wikimedia.org/T366374] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.9|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-11|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-12|en}}. It will be on all wikis from {{#time:j xg|2024-06-13|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] The new version of MediaWiki includes another change to the HTML markup used for citations: [[mw:Special:MyLanguage/Parsoid|Parsoid]] will now generate a <bdi lang="zxx" dir="ltr"><code><nowiki><span class="mw-cite-backlink"></nowiki></code></bdi> wrapper for both named and unnamed references for better compatibility with the legacy parser. Interface administrators should verify that gadgets that interact with citations are compatible with the new markup. [[mw:Specs/HTML/2.8.0/Extensions/Cite/Announcement|More details are available]]. [https://gerrit.wikimedia.org/r/1035809] * On multilingual wikis that use the <bdi lang="zxx" dir="ltr"><code><nowiki><translate></nowiki></code></bdi> system, there is a feature that shows potentially-outdated translations with a pink background until they are updated or confirmed. From this week, confirming translations will be logged, and there is a new user-right that can be required for confirming translations if the community [[m:Special:MyLanguage/Requesting wiki configuration changes|requests it]]. [https://phabricator.wikimedia.org/T49177] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/24|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W24"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:20, 10 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26893898 --> == Tech News: 2024-25 == <section begin="technews-2024-W25"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/25|Translations]] are available. '''Recent changes''' * People who attempt to add an external link in the visual editor will now receive immediate feedback if they attempt to link to a domain that a project has decided to block. Please see [[mw:Special:MyLanguage/Edit_check#11_June_2024|Edit check]] for more details. [https://phabricator.wikimedia.org/T366751] * The new [[mw:Special:MyLanguage/Extension:CommunityConfiguration|Community Configuration extension]] is available [[testwiki:Special:CommunityConfiguration|on Test Wikipedia]]. This extension allows communities to customize specific features to meet their local needs. Currently only Growth features are configurable, but the extension will support other [[mw:Special:MyLanguage/Community_configuration#Use_cases|Community Configuration use cases]] in the future. [https://phabricator.wikimedia.org/T323811][https://phabricator.wikimedia.org/T360954] * The dark mode [[Special:Preferences#mw-prefsection-betafeatures|beta feature]] is now available on category and help pages, as well as more special pages. There may be contrast issues. Please report bugs on the [[mw:Talk:Reading/Web/Accessibility_for_reading|project talk page]]. [https://phabricator.wikimedia.org/T366370] '''Problems''' * [[File:Octicons-tools.svg|12px|link=|alt=|Advanced item]] Cloud Services tools were not available for 25 minutes last week. This was caused by a faulty hardware cable in the data center. [https://wikitech.wikimedia.org/wiki/Incidents/2024-06-11_WMCS_Ceph] * Last week, styling updates were made to the Vector 2022 skin. This caused unforeseen issues with templates, hatnotes, and images. Changes to templates and hatnotes were reverted. Most issues with images were fixed. If you still see any, [[phab:T367463|report them here]]. [https://phabricator.wikimedia.org/T367480] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.10|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-18|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-19|en}}. It will be on all wikis from {{#time:j xg|2024-06-20|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting June 18, the [[mw:Special:MyLanguage/Help:Edit check#ref|Reference Edit Check]] will be deployed to [[phab:T361843|a new set of Wikipedias]]. This feature is intended to help newcomers and to assist edit-patrollers by inviting people who are adding new content to a Wikipedia article to add a citation when they do not do so themselves. During [[mw:Special:MyLanguage/Edit_check#Reference_Check_A/B_Test|a test at 11 wikis]], the number of citations added [https://diff.wikimedia.org/?p=127553 more than doubled] when Reference Check was shown to people. Reference Check is [[mw:Special:MyLanguage/Edit check/Configuration|community configurable]]. [https://phabricator.wikimedia.org/T361843]<!-- NOTE: THE DIFF BLOG WILL BE PUBLISHED ON MONDAY --> * [[m:Special:MyLanguage/Mailing_lists|Mailing lists]] will be unavailable for roughly two hours on Tuesday 10:00–12:00 UTC. This is to enable migration to a new server and upgrade its software. [https://phabricator.wikimedia.org/T367521] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/25|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W25"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:48, 17 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26911987 --> == Tech News: 2024-26 == <section begin="technews-2024-W26"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/26|Translations]] are available. '''Recent changes''' * Editors will notice that there have been some changes to the background color of text in the diff view, and the color of the byte-change numbers, last week. These changes are intended to make text more readable in both light mode and dark mode, and are part of a larger effort to increase accessibility. You can share your comments or questions [[mw:Talk:Reading/Web/Accessibility for reading|on the project talkpage]]. [https://phabricator.wikimedia.org/T361717] * The text colors that are used for visited-links, hovered-links, and active-links, were also slightly changed last week to improve their accessibility in both light mode and dark mode. [https://phabricator.wikimedia.org/T366515] '''Problems''' * You can [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|copy permanent links to talk page comments]] by clicking on a comment's timestamp. [[mw:Talk pages project/Permalinks|This feature]] did not always work when the topic title was very long and the link was used as a wikitext link. This has been fixed. Thanks to Lofhi for submitting the bug. [https://phabricator.wikimedia.org/T356196] '''Changes later this week''' * [[File:Octicons-sync.svg|12px|link=|alt=|Recurrent item]] The [[mw:MediaWiki 1.43/wmf.11|new version]] of MediaWiki will be on test wikis and MediaWiki.org from {{#time:j xg|2024-06-25|en}}. It will be on non-Wikipedia wikis and some Wikipedias from {{#time:j xg|2024-06-26|en}}. It will be on all wikis from {{#time:j xg|2024-06-27|en}} ([[mw:MediaWiki 1.43/Roadmap|calendar]]). [https://wikitech.wikimedia.org/wiki/Deployments/Train][https://wikitech.wikimedia.org/wiki/Deployments/Yearly_calendar] * Starting 26 June, all talk pages messages' timestamps will become a link at English Wikipedia, making this feature available for you to use at all wikis. This link is a permanent link to the comment. It allows users to find the comment they were linked to, even if this comment has since been moved elsewhere. You can read more about this feature [[DiffBlog:/2024/01/29/talk-page-permalinks-dont-lose-your-threads/|on Diff]] or [[mw:Special:MyLanguage/Help:DiscussionTools#Talk pages permalinking|on Mediawiki.org]]. [https://phabricator.wikimedia.org/T365974] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/26|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W26"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:32, 24 June 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=26989424 --> == Tech News: 2024-27 == <section begin="technews-2024-W27"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/27|Translations]] are available. '''Recent changes''' * Over the next three weeks, dark mode will become available for all users, both logged-in and logged-out, starting with the mobile web version. This fulfils one of the [[m:Special:MyLanguage/Community_Wishlist_Survey_2023/Reading/Dark_mode|top-requested community wishes]], and improves low-contrast reading and usage in low-light settings. As part of these changes, dark mode will also work on User-pages and Portals. There is more information in [[mw:Special:MyLanguage/Reading/Web/Accessibility_for_reading/Updates#June_2024:_Typography_and_dark_mode_deployments,_new_global_preferences|the latest Web team update]]. [https://phabricator.wikimedia.org/T366364] * Logged-in users can now set [[m:Special:GlobalPreferences#mw-prefsection-rendering-skin-skin-prefs|global preferences for the text-size and dark-mode]], thanks to a combined effort across Foundation teams. This allows Wikimedians using multiple wikis to set up a consistent reading experience easily, for example by switching between light and dark mode only once for all wikis. [https://phabricator.wikimedia.org/T341278] * If you use a very old web browser some features might not work on the Wikimedia wikis. This affects Internet Explorer 11 and versions of Chrome, Firefox and Safari older than 2016. This change makes it possible to use new [[d:Q46441|CSS]] features and to send less code to all readers. [https://phabricator.wikimedia.org/T288287][https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:How_to_make_a_MediaWiki_skin#Using_CSS_variables_for_supporting_different_themes_e.g._dark_mode] * Wikipedia Admins can customize local wiki configuration options easily using [[mw:Special:MyLanguage/Community Configuration|Community Configuration]]. Community Configuration was created to allow communities to customize how some features work, because each language wiki has unique needs. At the moment, admins can configure [[mw:Special:MyLanguage/Growth/Feature_summary|Growth features]] on their home wikis, in order to better recruit and retain new editors. More options will be provided in the coming months. [https://phabricator.wikimedia.org/T366458] * Editors interested in language issues that are related to [[w:en:Unicode|Unicode standards]], can now discuss those topics at [[mw:Talk:WMF membership with Unicode Consortium|a new conversation space in MediaWiki.org]]. The Wikimedia Foundation is now a [[mw:Special:MyLanguage/WMF membership with Unicode Consortium|member of the Unicode Consortium]], and the coordination group can collaboratively review the issues discussed and, where appropriate, bring them to the attention of the Unicode Consortium. * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2891049|Mandailing]] ([[w:btm:|<code>w:btm:</code>]]) [https://phabricator.wikimedia.org/T368038] '''Problems''' * Editors can once again click on links within the visual editor's citation-preview, thanks to a bug fix by the Editing Team. [https://phabricator.wikimedia.org/T368119] '''Future changes''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 2 weeks. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/27|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W27"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:59, 1 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27038456 --> == Tech News: 2024-28 == <section begin="technews-2024-W28"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/28|Translations]] are available. '''Recent changes''' * At the Wikimedia Foundation a new task force was formed to replace the disabled Graph with [[mw:Special:MyLanguage/Extension:Chart/Project|more secure, easy to use, and extensible Chart]]. You can [[mw:Special:MyLanguage/Newsletter:Chart Project|subscribe to the newsletter]] to get notified about new project updates and other news about Chart. * The [[m:Special:MyLanguage/CampaignEvents|CampaignEvents]] extension is now available on Meta-wiki, Igbo Wikipedia, and Swahili Wikipedia, and can be requested on your wiki. This extension helps in managing and making events more visible, giving Event organizers the ability to use tools like the Event registration tool. To learn more about the deployment status and how to request this extension for your wiki, visit the [[m:Special:MyLanguage/CampaignEvents/Deployment_status|CampaignEvents page on Meta-wiki]]. * Editors using the iOS Wikipedia app who have more than 50 edits can now use the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits#Add an image|Add an Image]] feature. This feature presents opportunities for small but useful contributions to Wikipedia. * Thank you to [[mw:MediaWiki Product Insights/Contributor retention and growth/Celebration|all of the authors]] who have contributed to MediaWiki Core. As a result of these contributions, the [[mw:MediaWiki Product Insights/Contributor retention and growth|percentage of authors contributing more than 5 patches has increased by 25% since last year]], which helps ensure the sustainability of the platform for the Wikimedia projects. '''Problems''' * A problem with the color of the talkpage tabs always showing as blue, even for non-existent pages which should have been red, affecting the Vector 2022 skin, [[phab:T367982|has been fixed]]. '''Future changes''' * The Trust and Safety Product team wants to introduce [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] with as little disruption to tools and workflows as possible. Volunteer developers, including gadget and user-script maintainers, are kindly asked to update the code of their tools and features to handle temporary accounts. The team has [[mw:Trust and Safety Product/Temporary Accounts/For developers|created documentation]] explaining how to do the update. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers/2024-04 CTA|Learn more]]. '''Tech News survey''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 1 more week. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/28|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W28"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:31, 8 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27080357 --> == Tech News: 2024-29 == <section begin="technews-2024-W29"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/29|Translations]] are available. '''Tech News survey''' * Please [https://wikimediafoundation.limesurvey.net/758713?lang=en help us to improve Tech News by taking this short survey]. The goal is to better meet the needs of the various types of people who read Tech News. The survey will be open for 3 more days. The survey is covered by [https://foundation.wikimedia.org/wiki/Legal:Tech_News_Survey_2024_Privacy_Statement this privacy statement]. Some translations are available. '''Recent changes''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Wikimedia developers can now officially continue to use both [[mw:Special:MyLanguage/Gerrit|Gerrit]] and [[mw:Special:MyLanguage/GitLab|GitLab]], due to a June 24 decision by the Wikimedia Foundation to support software development on both platforms. Gerrit and GitLab are both code repositories used by developers to write, review, and deploy the software code that supports the MediaWiki software that the wiki projects are built on, as well as the tools used by editors to create and improve content. This decision will safeguard the productivity of our developers and prevent problems in code review from affecting our users. More details are available in the [[mw:GitLab/Migration status|Migration status]] page. * The Wikimedia Foundation seeks applicants for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product and Technology Advisory Council]] (PTAC). This group will bring technical contributors and Wikimedia Foundation together to co-define a more resilient, future-proof technological platform. Council members will evaluate and consult on the movement's product and technical activities, so that we develop multi-generational projects. We are looking for a range of technical contributors across the globe, from a variety of Wikimedia projects. [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal#Joining the PTAC as a technical volunteer|Please apply here by August 10]]. * Editors with rollback user-rights who use the Wikipedia App for Android can use the new [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android/Anti Vandalism|Edit Patrol]] features. These features include a new feed of Recent Changes, related links such as Undo and Rollback, and the ability to create and save a personal library of user talk messages to use while patrolling. If your wiki wants to make these features available to users who do not have rollback rights but have reached a certain edit threshold, [[mw:Special:MyLanguage/Wikimedia Apps/Team/Android#Contact us|you can contact the team]]. You can [[diffblog:2024/07/10/ِaddressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/|read more about this project on Diff blog]]. * Editors who have access to [[m:Special:MyLanguage/The_Wikipedia_Library|The Wikipedia Library]] can once again use non-open access content in SpringerLinks, after the Foundation [[phab:T368865|contacted]] them to restore access. You can read more about [[m:Tech/News/Recently_resolved_community_tasks|this and 21 other community-submitted tasks that were completed last week]]. '''Changes later this week''' * This week, [[mw:Special:MyLanguage/Reading/Web/Accessibility for reading/Updates/2024-07 deployments|dark mode will be available on a number of Wikipedias]], both desktop and mobile, for logged-in and logged-out users. Interface admins and user script maintainers are encouraged to check gadgets and user scripts in the dark mode, to find any hard-coded colors and fix them. There are some [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations for dark mode compatibility]] to help. '''Future changes''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Next week, functionaries, volunteers maintaining tools, and software development teams are invited to test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on testwiki. Temporary accounts is a feature that will help improve privacy on the wikis. No further temporary account deployments are scheduled yet. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]]. [https://phabricator.wikimedia.org/T348895] * Editors who upload files cross-wiki, or teach other people how to do so, may wish to join a Wikimedia Commons discussion. The Commons community is discussing limiting who can upload files through the cross-wiki upload/Upload dialog feature to users auto-confirmed on Wikimedia Commons. This is due to the large amount of copyright violations uploaded this way. There is a short summary at [[c:Special:MyLanguage/Commons:Cross-wiki upload|Commons:Cross-wiki upload]] and [[c:Commons:Village pump/Proposals#Deactivate cross-wiki uploads for new users|discussion at Commons:Village Pump]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/29|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]]. </div><section end="technews-2024-W29"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:31, 16 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27124561 --> == Tech News: 2024-30 == <section begin="technews-2024-W30"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/30|Translations]] are available. '''Feature News''' * Stewards can now [[:m:Special:MyLanguage/Global_blocks|globally block]] accounts. Before [[phab:T17294|the change]] only IP addresses and IP ranges could be blocked globally. Global account blocks are useful when the blocked user should not be logged out. [[:m:Special:MyLanguage/Global_locks|Global locks]] (a similar tool logging the user out of their account) are unaffected by this change. The new global account block feature is related to the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project, which is a new type of user account that replaces IP addresses of unregistered editors that are no longer made public. * Later this week, Wikimedia site users will notice that the Interface of [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as "Pending Changes") is improved and consistent with the rest of the MediaWiki interface and [[mw:Special:MyLanguage/Codex|Wikimedia's design system]]. The FlaggedRevs interface experience on mobile and [[mw:Special:MyLanguage/Skin:MinervaNeue|Minerva skin]] was inconsistent before it was fixed and ported to [[mw:Special:MyLanguage/Codex|Codex]] by the WMF Growth team and some volunteers. [https://phabricator.wikimedia.org/T191156] * Wikimedia site users can now submit account vanishing requests via [[m:Special:GlobalVanishRequest|GlobalVanishRequest]]. This feature is used when a contributor wishes to stop editing forever. It helps you hide your past association and edit to protect your privacy. Once processed, the account will be locked and renamed. [https://phabricator.wikimedia.org/T367329] * Have you tried monitoring and addressing vandalism in Wikipedia using your phone? [https://diff.wikimedia.org/2024/07/10/%d9%90addressing-vandalism-with-a-tap-the-journey-of-introducing-the-patrolling-feature-in-the-mobile-app/ A Diff blog post on Patrolling features in the Mobile App] highlights some of the new capabilities of the feature, including swiping through a feed of recent changes and a personal library of user talk messages for use when patrolling from your phone. * Wikimedia contributors and GLAM (galleries, libraries, archives, and museums) organisations can now learn and measure the impact Wikimedia Commons is having towards creating quality encyclopedic content using the [https://doc.wikimedia.org/generated-data-platform/aqs/analytics-api/reference/commons.html Commons Impact Metrics] analytics dashboard. The dashboard offers organizations analytics on things like monthly edits in a category, the most viewed files, and which Wikimedia articles are using Commons images. As a result of these new data dumps, GLAM organisation can more reliably measure their return on investment for programs bringing content into the digital Commons. [https://diff.wikimedia.org/2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/] '''Project Updates''' * Come share your ideas for improving the wikis on the newly reopened [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]]. The Community Wishlist is Wikimedia’s forum for volunteers to share ideas (called wishes) to improve how the wikis work. The new version of the wishlist is always open, works with both wikitext and Visual Editor, and allows wishes in any language. '''Learn more''' * Have you ever wondered how Wikimedia software works across over 300 languages? This is 253 languages more than the Google Chrome interface, and it's no accident. The Language and Product Localization Team at the Wikimedia Foundation supports your work by adapting all the tools and interfaces in the MediaWiki software so that contributors in our movement who translate pages and strings can translate them and have the sites in all languages. Read more about the team and their upcoming work on [https://diff.wikimedia.org/2024/07/17/building-towards-a-robust-multilingual-knowledge-ecosystem-for-the-wikimedia-movement/ Diff]. * How can Wikimedia build innovative and experimental products while maintaining such heavily used websites? A recent [https://diff.wikimedia.org/2024/07/09/on-the-value-of-experimentation/ blog post] by WMF staff Johan Jönsson highlights the work of the [[m:Future Audiences#Objectives and Key Results|WMF Future Audience initiative]], where the goal is not to build polished products but test out new ideas, such as a [[m:Future_Audiences/Experiments: conversational/generative AI|ChatGPT plugin]] and [[m:Future_Audiences/Experiment:Add a Fact|Add a Fact]], to help take Wikimedia into the future. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/30|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' You can also get other news from the [[m:Special:MyLanguage/Wikimedia Foundation Bulletin|Wikimedia Foundation Bulletin]]. </div><section end="technews-2024-W30"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:04, 23 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27142915 --> == Tech News: 2024-31 == <section begin="technews-2024-W31"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/31|Translations]] are available. '''Feature news''' * Editors using the Visual Editor in languages that use non-Latin characters for numbers, such as Hindi, Manipuri and Eastern Arabic, may notice some changes in the formatting of reference numbers. This is a side effect of preparing a new sub-referencing feature, and will also allow fixing some general numbering issues in Visual Editor. If you notice any related problems on your wiki, please share details at the [[m:Talk:WMDE Technical Wishes/Sub-referencing|project talkpage]]. '''Bugs status''' * Some logged-in editors were briefly unable to edit or load pages last week. [[phab:T370304|These errors]] were mainly due to the addition of new [[mw:Special:MyLanguage/Help:Extension:Linter|linter]] rules which led to caching problems. Fixes have been applied and investigations are continuing. * Editors can use the [[mw:Special:MyLanguage/Trust and Safety Product/IP Info|IP Information tool]] to get information about IP addresses. This tool is available as a Beta Feature in your preferences. The tool was not available for a few days last week, but is now working again. Thank you to Shizhao for filing the bug report. You can read about that, and [[m:Tech/News/Recently resolved community tasks#2024-07-25|28 other community-submitted tasks]] that were resolved last week. '''Project updates''' * There are new features and improvements to Phabricator from the Release Engineering and Collaboration Services teams, and some volunteers, including: the search systems, the new task creation system, the login systems, the translation setup which has resulted in support for more languages (thanks to Pppery), and fixes for many edge-case errors. You can [[phab:phame/post/view/316/iterative_improvements/|read details about these and other improvements in this summary]]. * There is an [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|update on the Charts project]]. The team has decided which visualization library to use, which chart types to start focusing on, and where to store chart definitions. * One new wiki has been created: a {{int:project-localized-name-group-wikivoyage}} in [[d:Q9056|Czech]] ([[voy:cs:|<code>voy:cs:</code>]]) [https://phabricator.wikimedia.org/T370905] '''Learn more''' * There is a [[diffblog:2024/07/26/the-journey-to-open-our-first-data-center-in-south-america/|new Wikimedia Foundation data center]] in São Paulo, Brazil which helps to reduce load times. * There is new [[diffblog:2024/07/22/the-perplexing-process-of-uploading-images-to-wikipedia/|user research]] on problems with the process of uploading images. * Commons Impact Metrics are [[diffblog:2024/07/19/commons-impact-metrics-now-available-via-data-dumps-and-api/|now available]] via data dumps and API. * The latest quarterly [[mw:Technical Community Newsletter/2024/July|Technical Community Newsletter]] is now available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/31|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W31"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:10, 29 July 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27164109 --> == Tech News: 2024-32 == <section begin="technews-2024-W32"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/32|Translations]] are available. '''Feature news''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Two new parser functions will be available this week: <code><nowiki>{{</nowiki>[[mw:Special:MyLanguage/Help:Magic_words#dir|#dir]]<nowiki>}}</nowiki></code> and <code><nowiki>{{</nowiki>[[mw:Special:MyLanguage/Help:Magic_words#bcp47|#bcp47]]<nowiki>}}</nowiki></code>. These will reduce the need for <code>Template:Dir</code> and <code>Template:BCP47</code> on Commons and allow us to [[phab:T343131|drop 100 million rows]] from the "what links here" database. Editors at any wiki that use these templates, can help by replacing the templates with these new functions. The templates at Commons will be updated during the Hackathon at Wikimania. [https://phabricator.wikimedia.org/T359761][https://phabricator.wikimedia.org/T366623] * Communities can request the activation of the visual editor on entire namespaces where discussions sometimes happen (for instance ''Wikipedia:'' or ''Wikisource:'' namespaces) if they understand the [[mw:Special:MyLanguage/Help:VisualEditor/FAQ#WPNS|known limitations]]. For discussions, users can already use [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]] in these namespaces. * The tracking category "Pages using Timeline" has been renamed to "Pages using the EasyTimeline extension" [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3ATimeline-tracking-category&namespace=8 in TranslateWiki]. Wikis that have created the category locally should rename their local creation to match. '''Project updates''' * Editors who help to organize WikiProjects and similar on-wiki collaborations, are invited to share ideas and examples of successful collaborations with the Campaigns and Programs teams. You can fill out [[m:Special:MyLanguage/Campaigns/WikiProjects|a brief survey]] or share your thoughts [[m:Talk:Campaigns/WikiProjects|on the talkpage]]. The teams are particularly looking for details about successful collaborations on non-English wikis. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The new parser is being rolled out on {{int:project-localized-name-group-wikivoyage}} wikis over the next few months. The {{int:project-localized-name-enwikivoyage}} and {{int:project-localized-name-hewikivoyage}} were [[phab:T365367|switched]] to Parsoid last week. For more information, see [[mw:Parsoid/Parser_Unification|Parsoid/Parser Unification]]. '''Learn more''' * There will be more than 200 sessions at Wikimania this week. Here is a summary of some of the [[diffblog:2024/08/05/interested-in-product-and-tech-here-are-some-wikimania-sessions-you-dont-want-to-miss/|key sessions related to the product and technology area]]. * The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/07-02|Wikimedia Foundation Bulletin]] is available. * The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/July|Language and Internationalization newsletter]] is available. It includes: New design previews for Translatable pages; Updates about MinT for Wiki Readers; the release of Translation dumps; and more. * The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/31|Growth newsletter]] is available. * The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/July 2024|MediaWiki Product Insights newsletter]] is available. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/32|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W32"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:43, 5 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27233905 --> == Tech News: 2024-33 == <section begin="technews-2024-W33"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/33|Translations]] are available. '''Feature news''' * [[mw:Special:MyLanguage/Extension:AbuseFilter|AbuseFilter]] editors and maintainers can now [[mw:Special:MyLanguage/Extension:AbuseFilter/Actions#Show a CAPTCHA|make a CAPTCHA show if a filter matches an edit]]. This allows communities to quickly respond to spamming by automated bots. [https://phabricator.wikimedia.org/T20110] * [[m:Special:MyLanguage/Stewards|Stewards]] can now specify if global blocks should prevent account creation. Before [[phab:T17273|this change]] by the [[mw:Special:MyLanguage/Trust and Safety Product|Trust and Safety Product]] Team, all global blocks would prevent account creation. This will allow stewards to reduce the unintended side-effects of global blocks on IP addresses. '''Project updates''' * [[wikitech:Help talk:Toolforge/Toolforge standards committee#August_2024_committee_nominations|Nominations are open on Wikitech]] for new members to refresh the [[wikitech:Help:Toolforge/Toolforge standards committee|Toolforge standards committee]]. The committee oversees the Toolforge [[wikitech:Help:Toolforge/Right to fork policy|Right to fork policy]] and [[wikitech:Help:Toolforge/Abandoned tool policy|Abandoned tool policy]] among other duties. Nominations will remain open until at least 2024-08-26. * One new wiki has been created: a {{int:project-localized-name-group-wikipedia}} in [[d:Q2880037|West Coast Bajau]] ([[w:bdr:|<code>w:bdr:</code>]]) [https://phabricator.wikimedia.org/T371757] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/33|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W33"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:21, 12 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27253654 --> == Tech News: 2024-34 == <section begin="technews-2024-W34"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/34|Translations]] are available. '''Feature news''' * Editors who want to re-use references but with different details such as page numbers, will be able to do so by the end of 2024, using a new [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Sub-referencing in a nutshell|sub-referencing]] feature. You can read more [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing|about the project]] and [[m:Special:MyLanguage/WMDE Technical Wishes/Sub-referencing#Test|how to test the prototype]]. * Editors using tracking categories to identify which pages use specific extensions may notice that six of the categories have been renamed to make them more easily understood and consistent. These categories are automatically added to pages that use specialized MediaWiki extensions. The affected names are for: [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aintersection-category&namespace=8 DynamicPageList], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Akartographer-tracking-category&namespace=8 Kartographer], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Aphonos-tracking-category&namespace=8 Phonos], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Arss-tracking-category&namespace=8 RSS], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Ascore-use-category&namespace=8 Score], [https://translatewiki.net/wiki/Special:Translations?message=MediaWiki%3Awikihiero-usage-tracking-category&namespace=8 WikiHiero]. Wikis that have created the category locally should rename their local creation to match. Thanks to Pppery for these improvements. [https://phabricator.wikimedia.org/T347324] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Technical volunteers who edit modules and want to get a list of the categories used on a page, can now do so using the <code><bdi lang="zxx" dir="ltr">categories</bdi></code> property of <code><bdi lang="zxx" dir="ltr">[[mediawikiwiki:Special:MyLanguage/Extension:Scribunto/Lua reference manual#Title objects|mw.title objects]]</bdi></code>. This enables wikis to configure workflows such as category-specific edit notices. Thanks to SD001 for these improvements. [https://phabricator.wikimedia.org/T50175][https://phabricator.wikimedia.org/T85372] '''Bugs status''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Your help is needed to check if any pages need to be moved or deleted. A maintenance script was run to clean up unreachable pages (due to Unicode issues or introduction of new namespaces/namespace aliases). The script tried to find appropriate names for the pages (e.g. by following the Unicode changes or by moving pages whose titles on Wikipedia start with <code>Talk:WP:</code> so that their titles start with <code>Wikipedia talk:</code>), but it may have failed for some pages, and moved them to <bdi lang="zxx" dir="ltr">[[Special:PrefixIndex/T195546/]]</bdi> instead. Your community should check if any pages are listed there, and move them to the correct titles, or delete them if they are no longer needed. A full log (including pages for which appropriate names could be found) is available in [[phab:P67388]]. * Editors who volunteer as [[mw:Special:MyLanguage/Help:Growth/Mentorship|mentors]] to newcomers on their wiki are once again able to access lists of potential mentees who they can connect with to offer help and guidance. This functionality was restored thanks to [[phab:T372164|a bug fix]]. Thank you to Mbch331 for filing the bug report. You can read about that, and 18 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Project updates''' * The application deadline for the [[m:Special:MyLanguage/Product and Technology Advisory Council/Proposal|Product & Technology Advisory Council]] (PTAC) has been extended to September 16. Members will help by providing advice to Foundation Product and Technology leadership on short and long term plans, on complex strategic problems, and help to get feedback from more contributors and technical communities. Selected members should expect to spend roughly 5 hours per month for the Council, during the one year pilot. Please consider applying, and spread the word to volunteers you think would make a positive contribution to the committee. '''Learn more''' * The [[m:Special:MyLanguage/Coolest Tool Award#2024 Winners|2024 Coolest Tool Awards]] were awarded at Wikimania, in seven categories. For example, one award went to the ISA Tool, used for adding structured data to files on Commons, which was recently improved during the [[m:Event:Wiki Mentor Africa ISA Hackathon 2024|Wiki Mentor Africa Hackathon]]. You can see video demonstrations of each tool at the awards page. Congratulations to this year's recipients, and thank you to all tool creators and maintainers. * The latest [[m:Special:MyLanguage/Wikimedia Foundation Bulletin/2024/08-01|Wikimedia Foundation Bulletin]] is available, and includes some highlights from Wikimania, an upcoming Language community meeting, and other news from the movement. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/34|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W34"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:54, 20 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27307284 --> == Tech News: 2024-35 == <section begin="technews-2024-W35"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/35|Translations]] are available. '''Feature news''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Administrators can now test the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] feature on test2wiki. This was done to allow cross-wiki testing of temporary accounts, for when temporary accounts switch between projects. The feature was enabled on testwiki a few weeks ago. No further temporary account deployments are scheduled yet. Temporary Accounts is a project to create a new type of user account that replaces IP addresses of unregistered editors which are no longer made public. Please [[mw:Talk:Trust and Safety Product/Temporary Accounts|share your opinions and questions on the project talk page]]. * Later this week, editors at wikis that use [[mw:Special:MyLanguage/Extension:FlaggedRevs|FlaggedRevs]] (also known as "Pending Changes") may notice that the indicators at the top of articles have changed. This change makes the system more consistent with the rest of the MediaWiki interface. [https://phabricator.wikimedia.org/T191156] '''Bugs status''' * Editors who use the 2010 wikitext editor, and use the Character Insert buttons, will [[phab:T361465|no longer]] experience problems with the buttons adding content into the edit-summary instead of the edit-window. You can read more about that, and 26 other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Project updates''' * [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Please review and vote on [[m:Special:MyLanguage/Community Wishlist/Focus areas|Focus Areas]], which are groups of wishes that share a problem. Focus Areas were created for the newly reopened Community Wishlist, which is now open year-round for submissions. The first batch of focus areas are specific to moderator workflows, around welcoming newcomers, minimizing repetitive tasks, and prioritizing tasks. Once volunteers have reviewed and voted on focus areas, the Foundation will then review and select focus areas for prioritization. * Do you have a project and are willing to provide a three (3) month mentorship for an intern? [[mw:Special:MyLanguage/Outreachy|Outreachy]] is a twice a year program for people to participate in a paid internship that will start in December 2024 and end in early March 2025, and they need mentors and projects to work on. Projects can be focused on coding or non-coding (design, documentation, translation, research). See the Outreachy page for more details, and a list of past projects since 2013. '''Learn more''' * If you're curious about the product and technology improvements made by the Wikimedia Foundation last year, read [[diffblog:2024/08/21/wikimedia-foundation-product-technology-improving-the-user-experience/|this recent highlights summary on Diff]]. * To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Community Configuration - Shaping On-Wiki Functionality Together.webm|Community Configuration - Shaping On-Wiki Functionality Together]] (55 mins) - about the [[mw:Special:MyLanguage/Community Configuration|Community Configuration]] project. ** [[c:File:Wikimania 2024 - Belgrade - Day 1 - Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views.webm|Future of MediaWiki. A sustainable platform to support a collaborative user base and billions of page views]] (30 mins) - an overview for both technical and non technical audiences, covering some of the challenges and open questions, related to the [[mw:MediaWiki Product Insights|platform evolution, stewardship and developer experiences]] research. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/35|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W35"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:33, 26 August 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27341211 --> == Tech News: 2024-36 == <section begin="technews-2024-W36"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/36|Translations]] are available. '''Weekly highlight''' * Editors and volunteer developers interested in data visualisation can now test the new software for charts. Its early version is available on beta Commons and beta Wikipedia. This is an important milestone before making charts available on regular wikis. You can [[mw:Special:MyLanguage/Extension:Chart/Project/Updates|read more about this project update]] and help to test the charts. '''Feature news''' * Editors who use the [[{{#special:Unusedtemplates}}]] page can now filter out pages which are expected to be there permanently, such as sandboxes, test-cases, and templates that are always substituted. Editors can add the new magic word [[mw:Special:MyLanguage/Help:Magic words#EXPECTUNUSEDTEMPLATE|<code dir="ltr"><nowiki>__EXPECTUNUSEDTEMPLATE__</nowiki></code>]] to a template page to hide it from the listing. Thanks to Sophivorus and DannyS712 for these improvements. [https://phabricator.wikimedia.org/T184633] * Editors who use the New Topic tool on discussion pages, will [[phab:T334163|now be reminded]] to add a section header, which should help reduce the quantity of newcomers who add sections without a header. You can read more about that, and {{formatnum:28}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. * Last week, some Toolforge tools had occasional connection problems. The cause is still being investigated, but the problems have been resolved for now. [https://phabricator.wikimedia.org/T373243] * Translation administrators at multilingual wikis, when editing multiple translation units, can now easily mark which changes require updates to the translation. This is possible with the [[phab:T298852#10087288|new dropdown menu]]. '''Project updates''' * A new draft text of a policy discussing the use of Wikimedia's APIs [[m:Special:MyLanguage/API Policy Update 2024|has been published on Meta-Wiki]]. The draft text does not reflect a change in policy around the APIs; instead, it is an attempt to codify existing API rules. Comments, questions, and suggestions are welcome on [[m:Talk:API Policy Update 2024|the proposed update’s talk page]] until September 13 or until those discussions have concluded. '''Learn more''' * To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Ohrid - Day 2 - Charts, the successor of Graphs - A secure and extensible tool for data visualization.webm|Charts, the successor of Graphs - A secure and extensible tool for data visualization]] (25 mins) – about the above-mentioned Charts project. ** [[c:File:Wikimania 2024 - Ohrid - Day 3 - State of Language Technology and Onboarding at Wikimedia.webm|State of Language Technology and Onboarding at Wikimedia]] (90 mins) – about some of the language tools that support Wikimedia sites, such as [[mw:Special:MyLanguage/Content translation|Content]]/[[mw:Special:MyLanguage/Content translation/Section translation|Section Translation]], [[mw:Special:MyLanguage/MinT|MinT]], and LanguageConverter; also the current state and future of languages onboarding. [https://phabricator.wikimedia.org/T368772] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/36|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W36"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 01:07, 3 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27390268 --> == Tech News: 2024-37 == <section begin="technews-2024-W37"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/37|Translations]] are available. '''Feature news''' * Starting this week, the standard [[mw:Special:MyLanguage/Extension:CodeMirror|syntax highlighter]] will receive new colors that make them compatible in dark mode. This is the first of many changes to come as part of a major upgrade to syntax highlighting. You can learn more about what's to come on the [[mw:Special:MyLanguage/Help:Extension:CodeMirror|help page]]. [https://phabricator.wikimedia.org/T365311][https://phabricator.wikimedia.org/T259059] * Editors of wikis using Wikidata will now be notified of only relevant Wikidata changes in their watchlist. This is because the Lua functions <bdi lang="zxx" dir="ltr"><code>entity:getSitelink()</code></bdi> and <bdi lang="zxx" dir="ltr"><code>mw.wikibase.getSitelink(qid)</code></bdi> will have their logic unified for tracking different aspects of sitelinks to reduce junk notifications from [[m:Wikidata For Wikimedia Projects/Projects/Watchlist Wikidata Sitelinks Tracking|inconsistent sitelinks tracking]]. [https://phabricator.wikimedia.org/T295356] '''Project updates''' * Users of all Wikis will have access to Wikimedia sites as read-only for a few minutes on September 25, starting at 15:00 UTC. This is a planned datacenter switchover for maintenance purposes. More information will be published in Tech News and will also be posted on individual wikis in the coming weeks. [https://phabricator.wikimedia.org/T370962] * Contributors of [[phab:T363538#10123348|11 Wikipedias]], including English will have a new <bdi lang="zxx" dir="ltr"><code>MOS</code></bdi> namespace added to their Wikipedias. This improvement ensures that links beginning with <bdi lang="zxx" dir="ltr"><code>MOS:</code></bdi> (usually shortcuts to the [[w:en:Wikipedia:Manual of Style|Manual of Style]]) are not broken by [[w:en:Mooré|Mooré]] Wikipedia (language code <bdi lang="zxx" dir="ltr"><code>mos</code></bdi>). [https://phabricator.wikimedia.org/T363538] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/37|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W37"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 18:52, 9 September 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27424457 --> == Tech News: 2024-38 == <section begin="technews-2024-W38"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/38|Translations]] are available. '''Improvements and Maintenance''' * [[File:Octicons-gift.svg|12px|link=|class=skin-invert|Wishlist item]] Editors interested in templates can help by reading the latest Wishlist focus area, [[m:Special:MyLanguage/Community Wishlist/Focus areas/Template recall and discovery|Template recall and discovery]], and share your feedback on the talkpage. This input helps the Community Tech team to decide the right technical approach to build. Everyone is also encouraged to continue adding [[m:Special:MyLanguage/Community Wishlist|new wishes]]. * The new automated [[{{#special:NamespaceInfo}}]] page helps editors understand which [[mw:Special:MyLanguage/Help:Namespaces|namespaces]] exist on each wiki, and some details about how they are configured. Thanks to DannyS712 for these improvements. [https://phabricator.wikimedia.org/T263513] * [[mw:Special:MyLanguage/Help:Edit check#Reference check|References Check]] is a feature that encourages editors to add a citation when they add a new paragraph to a Wikipedia article. For a short time, the corresponding tag "Edit Check (references) activated" was erroneously being applied to some edits outside of the main namespace. This has been fixed. [https://phabricator.wikimedia.org/T373692] * It is now possible for a wiki community to change the order in which a page’s categories are displayed on their wiki. By default, categories are displayed in the order they appear in the wikitext. Now, wikis with a consensus to do so can [[m:Special:MyLanguage/Requesting wiki configuration changes|request]] a configuration change to display them in alphabetical order. [https://phabricator.wikimedia.org/T373480] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Tool authors can now access ToolsDB's [[wikitech:Portal:Data Services#ToolsDB|public databases]] from both [[m:Special:MyLanguage/Research:Quarry|Quarry]] and [[wikitech:Superset|Superset]]. Those databases have always been accessible to every [[wikitech:Portal:Toolforge|Toolforge]] user, but they are now more broadly accessible, as Quarry can be accessed by anyone with a Wikimedia account. In addition, Quarry's internal database can now be [[m:Special:MyLanguage/Research:Quarry#Querying Quarry's own database|queried from Quarry itself]]. This database contains information about all queries that are being run and starred by users in Quarry. This information was already public through the web interface, but you can now query it using SQL. You can read more about that, and {{formatnum:20}} other community-submitted tasks that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. * Any pages or tools that still use the very old CSS classes <bdi lang="zxx" dir="ltr"><code>mw-message-box</code></bdi> need to be updated. These old classes will be removed next week or soon afterwards. Editors can use a [https://global-search.toolforge.org/?q=mw-message-box&regex=1&namespaces=&title= global-search] to determine what needs to be changed. It is possible to use the newer <bdi lang="zxx" dir="ltr"><code>cdx-message</code></bdi> group of classes as a replacement (see [https://doc.wikimedia.org/codex/latest/components/demos/message.html#css-only-version the relevant Codex documentation], and [https://meta.wikimedia.org/w/index.php?title=Tech/Header&diff=prev&oldid=27449042 an example update]), but using locally defined onwiki classes would be best. [https://phabricator.wikimedia.org/T374499] '''Technical project updates''' * Next week, all Wikimedia wikis will be read-only for a few minutes. This will start on September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. This is a planned datacenter switchover for maintenance purposes. [[m:Special:MyLanguage/Tech/Server switch|This maintenance process also targets other services.]] The previous switchover took 3 minutes, and the Site Reliability Engineering teams use many tools to make sure that this essential maintenance work happens as quickly as possible. [https://phabricator.wikimedia.org/T370962] '''Tech in depth''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/August 2024|MediaWiki Product Insights newsletter]] is available. This edition includes details about: research about [[mw:Special:MyLanguage/Manual:Hooks|hook]] handlers to help simplify development, research about performance improvements, work to improve the REST API for end-users, and more. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] To learn more about the technology behind the Wikimedia projects, you can now watch sessions from the technology track at Wikimania 2024 on Commons. This week, check out: ** [[c:File:Wikimania 2024 - Auditorium Kyiv - Day 4 - Hackathon Showcase.webm|Hackathon Showcase]] (45 mins) - 19 short presentations by some of the Hackathon participants, describing some of the projects they worked on, such as automated testing of maintenance scripts, a video-cutting command line tool, and interface improvements for various tools. There are [[phab:T369234|more details and links available]] in the Phabricator task. ** [[c:File:Co-Creating a Sustainable Future for the Toolforge Ecosystem.webm|Co-Creating a Sustainable Future for the Toolforge Ecosystem]] (40 mins) - a roundtable discussion for tool-maintainers, users, and supporters of Toolforge about how to make the platform sustainable and how to evaluate the tools available there. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/38|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W38"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:02, 17 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27460876 --> == Tech News: 2024-39 == <section begin="technews-2024-W39"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/39|Translations]] are available. '''Weekly highlight''' * All wikis will be [[m:Special:MyLanguage/Tech/Server switch|read-only]] for a few minutes on Wednesday September 25 at [https://zonestamp.toolforge.org/1727276400 15:00 UTC]. Reading the wikis will not be interrupted, but editing will be paused. These twice-yearly processes allow WMF's site reliability engineering teams to remain prepared to keep the wikis functioning even in the event of a major interruption to one of our data centers. '''Updates for editors''' [[File:Add alt text from a halfsheet, with the article behind.png|thumb|A screenshot of the interface for the Alt Text suggested-edit feature]] * Editors who use the iOS Wikipedia app in Spanish, Portuguese, French, or Chinese, may see the [[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|Alt Text suggested-edit experiment]] after editing an article, or completing a suggested edit using "[[mw:Special:MyLanguage/Wikimedia Apps/iOS Suggested edits project#Hypothesis 2 Add an Image Suggested Edit|Add an image]]". Alt-text helps people with visual impairments to read Wikipedia articles. The team aims to learn if adding alt-text to images is a task that editors can be successful with. Please share any feedback on [[mw:Talk:Wikimedia Apps/iOS Suggested edits project/Alt Text Experiment|the discussion page]]. * The Codex color palette has been updated with new and revised colors for the MediaWiki user interfaces. The [[mw:Special:MyLanguage/Design System Team/Color/Design documentation#Updates|most noticeable changes]] for editors include updates for: dark mode colors for Links and for quiet Buttons (progressive and destructive), visited Link colors for both light and dark modes, and background colors for system-messages in both light and dark modes. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] It is now possible to include clickable wikilinks and external links inside code blocks. This includes links that are used within <code><nowiki><syntaxhighlight></nowiki></code> tags and on code pages (JavaScript, CSS, Scribunto and Sanitized CSS). Uses of template syntax <code><nowiki>{{…}}</nowiki></code> are also linked to the template page. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T368166] * Two bugs were fixed in the [[m:Special:MyLanguage/Account vanishing|GlobalVanishRequest]] system by improving the logging and by removing an incorrect placeholder message. [https://phabricator.wikimedia.org/T370595][https://phabricator.wikimedia.org/T372223] * View all {{formatnum:25}} community-submitted {{PLURAL:25|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] From [[m:Special:MyLanguage/Wikimedia Enterprise|Wikimedia Enterprise]]: ** The API now enables 5,000 on-demand API requests per month and twice-monthly HTML snapshots freely (gratis and libre). More information on the updates and also improvements to the software development kits (SDK) are explained on [https://enterprise.wikimedia.com/blog/enhanced-free-api/ the project's blog post]. While Wikimedia Enterprise APIs are designed for high-volume commercial reusers, this change enables many more community use-cases to be built on the service too. ** The Snapshot API (html dumps) have added beta Structured Contents endpoints ([https://enterprise.wikimedia.com/blog/structured-contents-snapshot-api/ blog post on that]) as well as released two beta datasets (English and French Wikipedia) from that endpoint to Hugging Face for public use and feedback ([https://enterprise.wikimedia.com/blog/hugging-face-dataset/ blog post on that]). These pre-parsed data sets enable new options for researchers, developers, and data scientists to use and study the content. '''In depth''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] The Wikidata Query Service (WDQS) is used to get answers to questions using the Wikidata data set. As Wikidata grows, we had to make a major architectural change so that WDQS could remain performant. As part of the [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS graph split|WDQS Graph Split project]], we have new SPARQL endpoints available for serving the "[https://query-scholarly.wikidata.org scholarly]" and "[https://query-main.wikidata.org main]" subgraphs of Wikidata. The [http://query.wikidata.org query.wikidata.org endpoint] will continue to serve the full Wikidata graph until March 2025. After this date, it will only serve the main graph. For more information, please see [[d:Special:MyLanguage/Wikidata:SPARQL query service/WDQS backend update/September 2024 scaling update|the announcement on Wikidata]]. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/39|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W39"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:36, 23 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27493779 --> == Tech News: 2024-40 == <section begin="technews-2024-W40"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/40|Translations]] are available. '''Updates for editors''' * Readers of [[phab:T375401|42 more wikis]] can now use Dark Mode. If the option is not yet available for logged-out users of your wiki, this is likely because many templates do not yet display well in Dark Mode. Please use the [https://night-mode-checker.wmcloud.org/ night-mode-checker tool] if you are interested in helping to reduce the number of issues. The [[mw:Special:MyLanguage/Recommendations for night mode compatibility on Wikimedia wikis|recommendations page]] provides guidance on this. Dark Mode is enabled on additional wikis once per month. * Editors using the 2010 wikitext editor as their default can access features from the 2017 wikitext editor by adding <code dir=ltr>?veaction=editsource</code> to the URL. If you would like to enable the 2017 wikitext editor as your default, it can be set in [[Special:Preferences#mw-input-wpvisualeditor-newwikitext|your preferences]]. [https://phabricator.wikimedia.org/T239796] * For logged-out readers using the Vector 2022 skin, the "donate" link has been moved from a collapsible menu next to the content area into a more prominent top menu, next to "Create an account". This restores the link to the level of prominence it had in the Vector 2010 skin. [[mw:Readers/2024 Reader and Donor Experiences#Donor Experiences (Key Result WE 3.2 and the related hypotheses)|Learn more]] about the changes related to donor experiences. [https://phabricator.wikimedia.org/T373585] * The CampaignEvents extension provides tools for organizers to more easily manage events, communicate with participants, and promote their events on the wikis. The extension has been [[m:Special:MyLanguage/CampaignEvents/Deployment status|enabled]] on Arabic Wikipedia, Igbo Wikipedia, Swahili Wikipedia, and Meta-Wiki. [[w:zh:Wikipedia:互助客栈/其他#引進CampaignEvents擴充功能|Chinese Wikipedia has decided]] to enable the extension, and discussions on the extension are in progress [[w:es:Wikipedia:Votaciones/2024/Sobre la política de Organizadores de Eventos|on Spanish Wikipedia]] and [[d:Wikidata:Project chat#Enabling the CampaignEvents Extention on Wikidata|on Wikidata]]. To learn how to enable the extension on your wiki, you can visit [[m:Special:MyLanguage/CampaignEvents|the CampaignEvents page on Meta-Wiki]]. * View all {{formatnum:22}} community-submitted {{PLURAL:22|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * Developers with an account on Wikitech-wiki should [[wikitech:Wikitech/SUL-migration|check if any action is required]] for their accounts. The wiki is being changed to use the single-user-login (SUL) system, and other configuration changes. This change will help reduce the overall complexity for the weekly software updates across all our wikis. '''In depth''' * The [[m:Special:MyLanguage/Tech/Server switch|server switch]] was completed successfully last week with a read-only time of [[wikitech:Switch Datacenter#Past Switches|only 2 minutes 46 seconds]]. This periodic process makes sure that engineers can switch data centers and keep all of the wikis available for readers, even if there are major technical issues. It also gives engineers a chance to do maintenance and upgrades on systems that normally run 24 hours a day, and often helps to reveal weaknesses in the infrastructure. The process involves dozens of software services and hundreds of hardware servers, and requires multiple teams working together. Work over the past few years has reduced the time from 17 minutes down to 2–3 minutes. [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/66ZW7B2MG63AESQVTXDIFQBDBS766JGW/] '''Meetings and events''' * October 4–6: [[m:Special:MyLanguage/WikiIndaba conference 2024|WikiIndaba Conference's Hackathon]] in Johannesburg, South Africa * November 4–6: [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] in Vienna, Austria '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/40|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W40"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 22:20, 30 September 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27530062 --> == Tech News: 2024-41 == <section begin="technews-2024-W41"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/41|Translations]] are available. '''Weekly highlight''' * Communities can now request installation of [[mw:Special:MyLanguage/Moderator Tools/Automoderator|Automoderator]] on their wiki. Automoderator is an automated anti-vandalism tool that reverts bad edits based on scores from the new "Revert Risk" machine learning model. You can [[mw:Special:MyLanguage/Extension:AutoModerator/Deploying|read details about the necessary steps]] for installation and configuration. [https://phabricator.wikimedia.org/T336934] '''Updates for editors''' * Translators in wikis where [[mw:Special:MyLanguage/Content translation/Section translation#Try the tool|the mobile experience of Content Translation is available]], can now customize their articles suggestion list from 41 filtering options when using the tool. This topic-based article suggestion feature makes it easy for translators to self-discover relevant articles based on their area of interest and translate them. You can [https://test.wikipedia.org/w/index.php?title=Special:ContentTranslation&active-list=suggestions try it with your mobile device]. [https://phabricator.wikimedia.org/T368422] * View all {{formatnum:12}} community-submitted {{PLURAL:12|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. '''Updates for technical contributors''' * It is now possible for <bdi lang="zxx" dir="ltr"><code><nowiki><syntaxhighlight></nowiki></code></bdi> code blocks to offer readers a "Copy" button if the <bdi lang="zxx" dir="ltr"><code><nowiki>copy=1</nowiki></code></bdi> attribute is [[mw:Special:MyLanguage/Extension:SyntaxHighlight#copy|set on the tag]]. Thanks to SD0001 for these improvements. [https://phabricator.wikimedia.org/T40932] * Customized copyright footer messages on all wikis will be updated. The new versions will use wikitext markup instead of requiring editing raw HTML. [https://phabricator.wikimedia.org/T375789] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Later this month, [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] will be rolled out on several pilot wikis. The final list of the wikis will be published in the second half of the month. If you maintain any tools, bots, or gadgets on [[phab:T376499|these 11 wikis]], and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]]. * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Rate limiting has been enabled for the code review tools [[Wikitech:Gerrit|Gerrit]] and [[Wikitech:GitLab|GitLab]] to address ongoing issues caused by malicious traffic and scraping. Clients that open too many concurrent connections will be restricted for a few minutes. This rate limiting is managed through [[Wikitech:nftables|nftables]] firewall rules. For more details, see Wikitech's pages on [[Wikitech:Firewall#Throttling with nftables|Firewall]], [[Wikitech:GitLab/Abuse and rate limiting|GitLab limits]] and [[Wikitech:Gerrit/Operations#Throttling IPs|Gerrit operations]]. * Five new wikis have been created: ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q49224|Komering]] ([[w:kge:|<code>w:kge:</code>]]) [https://phabricator.wikimedia.org/T374813] ** a {{int:project-localized-name-group-wikipedia}} in [[d:Q36096|Mooré]] ([[m:mos:|<code>m:mos:</code>]]) [https://phabricator.wikimedia.org/T374641] ** a {{int:project-localized-name-group-wiktionary}} in [[d:Q36213|Madurese]] ([[wikt:mad:|<code>wikt:mad:</code>]]) [https://phabricator.wikimedia.org/T374968] ** a {{int:project-localized-name-group-wikiquote}} in [[d:Q2501174|Gorontalo]] ([[q:gor:|<code>q:gor:</code>]]) [https://phabricator.wikimedia.org/T375088] ** a {{int:project-localized-name-group-wikinews}} in [[d:Q56482|Shan]] ([[n:shn:|<code>n:shn:</code>]]) [https://phabricator.wikimedia.org/T375430] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/41|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W41"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 23:42, 7 October 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27557422 --> == Tech News: 2024-42 == <section begin="technews-2024-W42"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/42|Translations]] are available. '''Updates for editors''' * The Structured Discussion extension (also known as Flow) is starting to be removed. This extension is unmaintained and causes issues. It will be replaced by [[mw:Special:MyLanguage/Help:DiscussionTools|DiscussionTools]], which is used on any regular talk page. [[mw:Special:MyLanguage/Structured Discussions/Deprecation#Deprecation timeline|A first set of wikis]] are being contacted. These wikis are invited to stop using Flow, and to move all Flow boards to sub-pages, as archives. At these wikis, a script will move all Flow pages that aren't a sub-page to a sub-page automatically, starting on 22 October 2024. On 28 October 2024, all Flow boards at these wikis will be set in read-only mode. [https://www.mediawiki.org/wiki/Structured_Discussions/Deprecation][https://phabricator.wikimedia.org/T370722] * WMF's Search Platform team is working on making it easier for readers to perform text searches in their language. A [[phab:T332342|change last week]] on over 30 languages makes it easier to find words with accents and other diacritics. This applies to both full-text search and to types of advanced search such as the <bdi lang="en" dir="ltr">''hastemplate''</bdi> and <bdi lang="en" dir="ltr">''incategory''</bdi> keywords. More technical details (including a few other minor search upgrades) are available. [https://www.mediawiki.org/wiki/User:TJones_%28WMF%29/Notes/Language_Analyzer_Harmonization_Notes#ASCII-folding/ICU-folding_%28T332342%29] * View all {{formatnum:20}} community-submitted {{PLURAL:20|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[mw:Special:MyLanguage/Help:Edit check|EditCheck]] was installed at Russian Wikipedia, and fixes were made for some missing user interface styles. '''Updates for technical contributors''' * Editors who use the Toolforge tool [[toolforge:copyvios|Earwig's Copyright Violation Detector]] will now be required to log in with their Wikimedia account before running checks using the "search engine" option. This change is needed to help prevent external bots from misusing the system. Thanks to Chlod for these improvements. [https://en.wikipedia.org/wiki/Wikipedia_talk:New_pages_patrol/Reviewers#Authentication_is_now_required_for_search_engine_checks_on_Earwig's_Copyvio_Tool] * [[m:Special:MyLanguage/Phabricator|Phabricator]] users can create tickets and add comments on existing tickets via Email again. [[mw:Special:MyLanguage/Phabricator/Help#Using email|Sending email to Phabricator]] has been fixed. [https://phabricator.wikimedia.org/T356077] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Some HTML elements in the interface are now wrapped with a <code><nowiki><bdi></nowiki></code> element, to make our HTML output more aligned with Web standards. More changes like this will be coming in future weeks. This change might break some tools that rely on the previous HTML structure of the interface. Note that relying on the HTML structure of the interface is [[mw:Special:MyLanguage/Stable interface policy/Frontend#What is not stable?|not recommended]] and might break at any time. [https://phabricator.wikimedia.org/T375975] '''In depth''' * The latest monthly [[mw:Special:MyLanguage/MediaWiki Product Insights/Reports/September 2024|MediaWiki Product Insights newsletter]] is available. This edition includes: updates on Wikimedia's authentication system, research to simplify feature development in the MediaWiki platform, updates on Parser Unification and MathML rollout, and more. * The latest quarterly [[mw:Technical Community Newsletter/2024/October|Technical Community Newsletter]] is now available. This edition include: research about improving topic suggestions related to countries, improvements to PHPUnit tests, and more. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/42|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W42"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 21:21, 14 October 2024 (UTC) <!-- Message sent by User:Quiddity (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27597254 --> == Tech News: 2024-43 == <section begin="technews-2024-W43"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/43|Translations]] are available. '''Weekly highlight''' * The Mobile Apps team has released an [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh#Phase 1: Creating a user Profile Menu (T373714)|update]] to the iOS app's navigation, and it is now available in the latest App store version. The team added a new Profile menu that allows for easy access to editor features like Notifications and Watchlist from the Article view, and brings the "Donate" button into a more accessible place for users who are reading an article. This is the first phase of a larger planned [[mw:Special:MyLanguage/Wikimedia Apps/Team/iOS/Navigation Refresh|navigation refresh]] to help the iOS app transition from a primarily reader-focused app, to an app that fully supports reading and editing. The Wikimedia Foundation has added more editing features and support for on-wiki communication based on volunteer requests in recent years. [[File:IOS App Navigation refresh first phase 05.png|thumb|iOS Wikipedia App's profile menu and contents]] '''Updates for editors''' * Wikipedia readers can now download a browser extension to experiment with some early ideas on potential features that recommend articles for further reading, automatically summarize articles, and improve search functionality. For more details and to stay updated, check out the Web team's [[mw:Special:MyLanguage/Reading/Web/Content Discovery Experiments|Content Discovery Experiments page]] and [[mw:Special:MyLanguage/Newsletter:Web team's projects|subscribe to their newsletter]]. * Later this month, logged-out editors of [[phab:T376499|these 12 wikis]] will start to have [[mw:Special:Mylanguage/Trust and Safety Product/Temporary Accounts|temporary accounts]] created. The list may slightly change - some wikis may be removed but none will be added. Temporary account is a new [[mw:Special:MyLanguage/User account types|type of user account]]. It enhances the logged-out editors' privacy and makes it easier for community members to communicate with them. If you maintain any tools, bots, or gadgets on these 12 wikis, and your software is using data about IP addresses or is available for logged-out users, please check if it needs to be updated to work with temporary accounts. [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/For developers|Guidance on how to update the code is available]]. Read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|deployment plan across all wikis]]. * View all {{formatnum:33}} community-submitted {{PLURAL:33|task|tasks}} that were [[m:Tech/News/Recently resolved community tasks|resolved last week]]. For example, the [[w:nr:Main Page|South Ndebele]], [[w:rsk:Главни бок|Pannonian Rusyn]], [[w:ann:Uwu|Obolo]], [[w:iba:Lambar Keterubah|Iban]] and [[w:tdd:ᥞᥨᥝᥴ ᥘᥣᥲ ᥖᥥᥰ|Tai Nüa]] Wikipedia languages were created last week. [https://www.wikidata.org/wiki/Q36785][https://www.wikidata.org/wiki/Q35660][https://www.wikidata.org/wiki/Q36614][https://www.wikidata.org/wiki/Q33424][https://www.wikidata.org/wiki/Q36556] * It is now possible to create functions on Wikifunctions using Wikidata lexemes, through the new [[f:Z6005|Wikidata lexeme type]] launched last week. When you go to one of these functions, the user interface provides a lexeme selector that helps you pick a lexeme from Wikidata that matches the word you type. After hitting run, your selected lexeme is retrieved from Wikidata, transformed into a Wikidata lexeme type, and passed into the selected function. Read more about this in [[f:Special:MyLanguage/Wikifunctions:Status updates/2024-10-17#Function of the Week: select representation from lexeme|the latest Wikifunctions newsletter]]. '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Users of the Wikimedia sites can now format dates more easily in different languages with the new <code dir="ltr">{{[[mw:Special:MyLanguage/Help:Extension:ParserFunctions##timef|#timef]]:…}}</code> parser function. For example, <code dir="ltr"><nowiki>{{#timef:now|date|en}}</nowiki></code> will show as "<bdi lang="en" dir="ltr">{{#timef:now|date|en}}</bdi>". Previously, <code dir="ltr"><nowiki>{{#time:…}}</nowiki></code> could be used to format dates, but this required knowledge of the order of the time and date components and their intervening punctuation. <code dir="ltr">#timef</code> (or <code dir="ltr">#timefl</code> for local time) provides access to the standard date formats that MediaWiki uses in its user interface. This may help to simplify some templates on multi-lingual wikis like Commons and Meta. [https://phabricator.wikimedia.org/T223772][https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Extension:ParserFunctions##timef] * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] Commons and Meta users can now efficiently [[mw:Special:MyLanguage/Help:Magic words#Localization|retrieve the user's language]] using <code dir="ltr"><nowiki>{{USERLANGUAGE}}</nowiki></code> instead of using <code dir="ltr"><nowiki>{{int:lang}}</nowiki></code>. [https://phabricator.wikimedia.org/T4085] * The [[m:Special:MyLanguage/Product and Technology Advisory Council|Product and Tech Advisory Council]] (PTAC) now has its pilot members with representation across Africa, Asia, Europe, North America and South America. They will work to address the [[Special:MyLanguage/Movement Strategy/Initiatives/Technology Council|Movement Strategy's Technology Council]] initiative of having a co-defined and more resilient technological platform. [https://meta.wikimedia.org/wiki/Movement_Strategy/Initiatives/Technology_Council] '''In depth''' * The latest quarterly [[mw:Special:MyLanguage/Growth/Newsletters/32|Growth newsletter]] is available. It includes: an upcoming Newcomer Homepage Community Updates module, new Community Configuration options, and details on new projects. * The Wikimedia Foundation is [[mw:Special:MyLanguage/Wikimedia Security Team#CNA Partnership|now an official partner of the CVE program]], which is an international effort to catalog publicly disclosed cybersecurity vulnerabilities. This partnership will allow the Security Team to instantly publish [[w:en:Common Vulnerabilities and Exposures|common vulnerabilities and exposures]] (CVE) records that are affecting MediaWiki core, extensions, and skins, along with any other code the Foundation is a steward of. * The [[m:Special:MyLanguage/Community Wishlist|Community Wishlist]] is now [[m:Community Wishlist/Updates#October 16, 2024: Conversations Made Easier: Machine-Translated Wishes Are Here!|testing machine translations]] for Wishlist content. Volunteers can now read machine-translated versions of wishes and dive into discussions even before translators arrive to translate content. '''Meetings and events''' * 24 October - Wiki Education Speaker Series Webinar - [https://lists.wikimedia.org/hyperkitty/list/wikitech-l@lists.wikimedia.org/thread/N4XTB4G55BUY3M3PNGUAKQWJ7A4UOPAK/ Open Source Tech: Building the Wiki Education Dashboard], featuring Wikimedia interns and a Web developer in the panel. * 20–22 December 2024 - [[m:Special:MyLanguage/Indic Wikimedia Hackathon Bhubaneswar 2024|Indic Wikimedia Hackathon Bhubaneswar 2024]] in Odisha, India. A hackathon for community members, including developers, designers and content editors, to build technical solutions that improve contributors' experiences. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/43|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W43"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:52, 21 October 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27634672 --> == Tech News: 2024-44 == <section begin="technews-2024-W44"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/44|Translations]] are available. '''Updates for editors''' * Later in November, the Charts extension will be deployed to the test wikis in order to help identify and fix any issue. A security review is underway to then enable deployment to pilot wikis for broader testing. You can read [[mw:Special:MyLanguage/Extension:Chart/Project/Updates#October 2024: Working towards production deployment|the October project update]] and see the [https://en.wikipedia.beta.wmflabs.org/wiki/Charts latest documentation and examples on Beta Wikipedia]. * View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, [[w:en:PediaPress|Pediapress.com]], an external service that creates books from Wikipedia, can now use [[mw:Special:MyLanguage/Wikimedia Maps|Wikimedia Maps]] to include existing pre-rendered infobox map images in their printed books on Wikipedia. [https://phabricator.wikimedia.org/T375761] '''Updates for technical contributors''' * Wikis can use [[:mw:Special:MyLanguage/Extension:GuidedTour|the Guided Tour extension]] to help newcomers understand how to edit. The Guided Tours extension now works with [[mw:Special:MyLanguage/Manual:Dark mode|dark mode]]. Guided Tour maintainers can check their tours to see that nothing looks odd. They can also set <code>emitTransitionOnStep</code> to <code>true</code> to fix an old bug. They can use the new flag <code>allowAutomaticBack</code> to avoid back-buttons they don't want. [https://phabricator.wikimedia.org/T73927#10241528] * Administrators in the Wikimedia projects who use the [[mw:Special:MyLanguage/Help:Extension:Nuke|Nuke Extension]] will notice that mass deletions done with this tool have the "Nuke" tag. This change will make reviewing and analyzing deletions performed with the tool easier. [https://phabricator.wikimedia.org/T366068] '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/44|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W44"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:56, 28 October 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27668811 --> == Tech News: 2024-45 == <section begin="technews-2024-W45"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/45|Translations]] are available. '''Updates for editors''' * Stewards can now make [[m:Special:MyLanguage/Global blocks|global account blocks]] cause global [[mw:Special:MyLanguage/Autoblock|autoblocks]]. This will assist stewards in preventing abuse from users who have been globally blocked. This includes preventing globally blocked temporary accounts from exiting their session or switching browsers to make subsequent edits for 24 hours. Previously, temporary accounts could exit their current session or switch browsers to continue editing. This is an anti-abuse tool improvement for the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|Temporary Accounts]] project. You can read more about the [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts/Updates|progress on key features for temporary accounts]]. [https://phabricator.wikimedia.org/T368949] * Wikis that have the [[m:Special:MyLanguage/CampaignEvents/Deployment status|CampaignEvents extension enabled]] can now use the [[m:Special:MyLanguage/Campaigns/Foundation Product Team/Event list#October 29, 2024: Collaboration List launched|Collaboration List]] feature. This list provides a new, easy way for contributors to learn about WikiProjects on their wikis. Thanks to the Campaign team for this work that is part of [[m:Special:MyLanguage/Wikimedia Foundation Annual Plan/2024-2025/Product %26 Technology OKRs#WE KRs|the 2024/25 annual plan]]. If you are interested in bringing the CampaignEvents extension to your wiki, you can [[m:Special:MyLanguage/CampaignEvents/Deployment status#How to Request the CampaignEvents Extension for your wiki|follow these steps]] or you can reach out to User:Udehb-WMF for help. * The text color for red links will be slightly changed later this week to improve their contrast in light mode. [https://phabricator.wikimedia.org/T370446] * View all {{formatnum:32}} community-submitted {{PLURAL:32|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, on multilingual wikis, users [[phab:T216368|can now]] hide translations from the WhatLinksHere special page. '''Updates for technical contributors''' * XML [[m:Special:MyLanguage/Data dumps|data dumps]] have been temporarily paused whilst a bug is investigated. [https://lists.wikimedia.org/hyperkitty/list/xmldatadumps-l@lists.wikimedia.org/message/BXWJDPO5QI2QMBCY7HO36ELDCRO6HRM4/] '''In depth''' * Temporary Accounts have been deployed to six wikis; thanks to the Trust and Safety Product team for [[mw:Special:MyLanguage/Trust and Safety Product/Temporary Accounts|this work]], you can read about [[phab:T340001|the deployment plans]]. Beginning next week, Temporary Accounts will also be enabled on [[phab:T378336|seven other projects]]. If you are active on these wikis and need help migrating your tools, please reach out to [[m:User:Udehb-WMF|User:Udehb-WMF]] for assistance. * The latest quarterly [[mw:Special:MyLanguage/Wikimedia Language and Product Localization/Newsletter/2024/October|Language and Internationalization newsletter]] is available. It includes: New languages supported in translatewiki or in MediaWiki; New keyboard input methods for some languages; details about recent and upcoming meetings, and more. '''Meetings and events''' * [[mw:Special:MyLanguage/MediaWiki Users and Developers Conference Fall 2024|MediaWiki Users and Developers Conference Fall 2024]] is happening in Vienna, Austria and online from 4 to 6 November 2024. The conference will feature discussions around the usage of MediaWiki software by and within companies in different industries and will inspire and onboard new users. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/45|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W45"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 20:50, 4 November 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27693917 --> == Tech News: 2024-46 == <section begin="technews-2024-W46"/><div class="plainlinks"> Latest '''[[m:Special:MyLanguage/Tech/News|tech news]]''' from the Wikimedia technical community. Please tell other users about these changes. Not all changes will affect you. [[m:Special:MyLanguage/Tech/News/2024/46|Translations]] are available. '''Updates for editors''' * On wikis with the [[mw:Special:MyLanguage/Help:Extension:Translate|Translate extension]] enabled, users will notice that the FuzzyBot will now automatically create translated versions of categories used on translated pages. [https://phabricator.wikimedia.org/T285463] * View all {{formatnum:29}} community-submitted {{PLURAL:29|task|tasks}} that were [[m:Special:MyLanguage/Tech/News/Recently resolved community tasks|resolved last week]]. For example, the submitted task to use the [[mw:Special:MyLanguage/Extension:SecurePoll|SecurePoll extension]] for English Wikipedia's special [[w:en:Wikipedia:Administrator elections|administrator election]] was resolved on time. [https://phabricator.wikimedia.org/T371454] '''Updates for technical contributors''' * [[File:Octicons-tools.svg|12px|link=|class=skin-invert|Advanced item]] In <code dir="ltr">[[mw:MediaWiki_1.44/wmf.2|1.44.0-wmf-2]]</code>, the logic of Wikibase function <code>getAllStatements</code> changed to behave like <code>getBestStatements</code>. Invoking the function now returns a copy of values which are immutable. [https://phabricator.wikimedia.org/T270851] * [https://en.wikipedia.org/api/rest_v1/ Wikimedia REST API] users, such as bot operators and tool maintainers, may be affected by ongoing upgrades. The API will be rerouting some page content endpoints from RESTbase to the newer [[mw:Special:MyLanguage/API:REST API|MediaWiki REST API]] endpoints. The [[phab:T374683|impacted endpoints]] include getting page/revision metadata and rendered HTML content. These changes will be available on testwiki later this week, with other projects to follow. This change should not affect existing functionality, but active users of the impacted endpoints should verify behavior on testwiki, and raise any concerns on the related [[phab:T374683|Phabricator ticket]]. '''In depth''' * Admins and users of the Wikimedia projects [[mw:Special:MyLanguage/Moderator_Tools/Automoderator#Usage|where Automoderator is enabled]] can now monitor and evaluate important metrics related to Automoderator's actions. [https://superset.wmcloud.org/superset/dashboard/unified-automoderator-activity-dashboard/ This Superset dashboard] calculates and aggregates metrics about Automoderator's behaviour on the projects in which it is deployed. Thanks to the Moderator Tools team for this Dashboard; you can visit [[mw:Special:MyLanguage/Moderator Tools/Automoderator/Unified Activity Dashboard|the documentation page]] for more information about this work. [https://phabricator.wikimedia.org/T369488] '''Meetings and events''' * 21 November 2024 ([[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 8:00 UTC|8:00 UTC]] & [[m:Special:MyLanguage/Event:Commons community discussion - 21 November 2024 16:00 UTC|16:00 UTC]]) - [[c:Commons:WMF support for Commons/Commons community calls|Community call]] with Wikimedia Commons volunteers and stakeholders to help prioritize support efforts for 2025-2026 Fiscal Year. The theme of this call is how content should be organised on Wikimedia Commons. '''''[[m:Special:MyLanguage/Tech/News|Tech news]]''' prepared by [[m:Special:MyLanguage/Tech/News/Writers|Tech News writers]] and posted by [[m:Special:MyLanguage/User:MediaWiki message delivery|bot]]&nbsp;• [[m:Special:MyLanguage/Tech/News#contribute|Contribute]]&nbsp;• [[m:Special:MyLanguage/Tech/News/2024/46|Translate]]&nbsp;• [[m:Tech|Get help]]&nbsp;• [[m:Talk:Tech/News|Give feedback]]&nbsp;• [[m:Global message delivery/Targets/Tech ambassadors|Subscribe or unsubscribe]].'' </div><section end="technews-2024-W46"/> <bdi lang="en" dir="ltr">[[User:MediaWiki message delivery|MediaWiki message delivery]]</bdi> 00:07, 12 November 2024 (UTC) <!-- Message sent by User:UOzurumba (WMF)@metawiki using the list at https://meta.wikimedia.org/w/index.php?title=Global_message_delivery/Targets/Tech_ambassadors&oldid=27732268 --> i74wz5qb0mz8b0yrnvxd0hetty42sam User:VeronicaJeanAnderson 2 257428 2684034 2682332 2024-11-11T23:43:36Z PurpleProjectsPDX97123 2965707 2684034 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | 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style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== 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style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; 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style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} f6tteqpcgbfmk8jqr99w0cnzveqb6x7 2684037 2684034 2024-11-11T23:44:28Z PurpleProjectsPDX97123 2965707 2684037 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ #◯ #⓪ #① #② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; color: #000;" | ◯ | style="background:#000; color: #fff;" | ⬤ | style="background:silver; color: gold;" | 0 | style="background:#808080; color: gold;" | o | style="background:indigo; color: gold;" | O | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ |- | | style="background:#808080; color: hsl(60, 100%, 50%);" | ① | style="background:#808080; color: hsl(60, 100%, 50%);" | 1 | style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⑩ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⑪ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⑫ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⑬ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⑭ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} rq2uc8qdcm6j8oeaexv4tp1a2b4xuyb 2684038 2684037 2024-11-11T23:45:01Z PurpleProjectsPDX97123 2965707 2684038 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ *◯ *⓪ #① #② #③ #④ #⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span 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style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; color: red; } .center { text-align: center; color: red; } p.center { text-align: center; color: red; } table { width: 100%; } body { background-color: #321; background-image: url("d:/VeronicaJinTheNazarene/art/000.svg"), url("d:/VeronicaJinTheNazarene/art/drawing.svg"); background-size: cover; font-family: "Poppins", sans-serif; font-weight: 300; font-style: normal; color: hsl(60, 033%, 080%, 100%); text-align: center; } /* unvisited link */ a:link { color: black; } /* visited link */ a:visited { color: #808080; } /* mouse over link */ a:hover { color: pink; } /* selected link */ a:active { color: hotpink; } h6{ font-family: "Cairo Play", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-variation-settings: "slnt" 0; } h5 { font-family: "Playwrite US Trad", cursive; font-optical-sizing: auto; font-weight: 100; font-style: normal; color: hsl(276, 50%, 070%, 100%); font-size: 10px; } h4 { font-family: "Zen Kurenaido", sans-serif; font-weight: 400; font-style: normal; } h3 { font-family: "Playwrite CO", cursive; font-optical-sizing: auto; font-weight: 200; font-style: normal; color: hsl(30, 050%, 070%, 100%); } h2 { font-family: "Quicksand", sans-serif; font-optical-sizing: auto; font-weight: 300; font-style: normal; } h1 { font-family: "Sacramento", cursive; font-weight: 400; font-style: normal; } def { font-family: "Poppins", sans-serif; font-weight: 100; font-style: normal; font-size: 8px; color: #fff; } code { font-family: "Dosis", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-size: 12px; color: #808080; } mark { background-color: hsl(0, 050%, 080%, 100%); color: teal; } /* .zen-kurenaido-regular { font-family: "Zen Kurenaido", sans-serif; font-weight: 400; font-style: normal; } // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 200 to 1000 .cairo-play-<uniquifier> { font-family: "Cairo Play", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-variation-settings: "slnt" 0; } */ /* // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 300 to 700 .quicksand-<uniquifier> { font-family: "Quicksand", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 100 to 400 .playwrite-us-trad-<uniquifier> { font-family: "Playwrite US Trad", cursive; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* .sacramento-regular { font-family: "Sacramento", cursive; font-weight: 400; font-style: normal; } */ /* Dosis // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 200 to 800 .dosis-<uniquifier> { font-family: "Dosis", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* Playwrite // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 100 to 400 .playwrite-co-<uniquifier> { font-family: "Playwrite CO", cursive; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* .poppins-thin { font-family: "Poppins", sans-serif; font-weight: 100; font-style: normal; } .poppins-extralight { font-family: "Poppins", sans-serif; font-weight: 200; font-style: normal; } .poppins-light { font-family: "Poppins", sans-serif; font-weight: 300; font-style: normal; } .poppins-regular { font-family: "Poppins", sans-serif; font-weight: 400; font-style: normal; } .poppins-medium { font-family: "Poppins", sans-serif; font-weight: 500; font-style: normal; } .poppins-semibold { font-family: "Poppins", sans-serif; font-weight: 600; font-style: normal; } .poppins-bold { font-family: "Poppins", sans-serif; font-weight: 700; font-style: normal; } .poppins-extrabold { font-family: "Poppins", sans-serif; font-weight: 800; font-style: normal; } .poppins-black { font-family: "Poppins", sans-serif; font-weight: 900; font-style: normal; } .poppins-thin-italic { font-family: "Poppins", sans-serif; font-weight: 100; font-style: italic; } .poppins-extralight-italic { font-family: "Poppins", sans-serif; font-weight: 200; font-style: italic; } .poppins-light-italic { font-family: "Poppins", sans-serif; font-weight: 300; font-style: italic; } .poppins-regular-italic { font-family: "Poppins", sans-serif; font-weight: 400; font-style: italic; } .poppins-medium-italic { font-family: "Poppins", sans-serif; font-weight: 500; font-style: italic; } .poppins-semibold-italic { font-family: "Poppins", sans-serif; font-weight: 600; font-style: italic; } .poppins-bold-italic { font-family: "Poppins", sans-serif; font-weight: 700; font-style: italic; } .poppins-extrabold-italic { font-family: "Poppins", sans-serif; font-weight: 800; font-style: italic; } .poppins-black-italic { font-family: "Poppins", sans-serif; font-weight: 900; font-style: italic; } */ .zer0 { color: #fff; } .vjtn-00 { color: #000; } .vjtn-01 { color: hsl(60, 050%, 050%, 100%); } .vjtn-02 { color: hsl(48, 050%, 050%, 100%); } .vjtn-03 { color: hsl(36, 050%, 050%, 100%); } .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== 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style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} 0qj9dozuu75n01w3fhszklpj8lpcubo 2684039 2684038 2024-11-11T23:46:19Z PurpleProjectsPDX97123 2965707 2684039 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ *◯ *⓪ #① #② #③ #④ #⑤ #⑥ #⑦ #⑧ #⑨ #⑩ #⑪ #⑫ #⑬ #⑭ #⑮ #⑯ #⑰ #⑱ #⑲ #⑳ #㉑ #㉒ #㉓ #㉔ #㉕ #㉖ #㉗ #㉘ #㉙ #㉚ #㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span 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style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ 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style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span 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hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; color: #000;" | ◯ | style="background:#000; color: #fff;" | ⬤ | style="background:silver; color: gold;" | 0 | style="background:#808080; color: gold;" | o | style="background:indigo; color: gold;" | O | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ |- | | style="background:#808080; color: hsl(60, 100%, 50%);" | ① | style="background:#808080; color: hsl(60, 100%, 50%);" | 1 | style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⑩ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⑪ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⑫ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⑬ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⑭ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} 3tc6rby4gi4is3u216ea90fi0oalha8 2684041 2684039 2024-11-11T23:48:19Z PurpleProjectsPDX97123 2965707 2684041 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ *◯ D:/`OBS output/124-10-08 *⓪ #① D:Wasteland #② #③ #④ #⑤ #⑥ #⑦ #⑧ #⑨ #⑩ #⑪ #⑫ #⑬ #⑭ #⑮ #⑯ #⑰ #⑱ #⑲ #⑳ #㉑ #㉒ #㉓ #㉔ #㉕ #㉖ #㉗ #㉘ #㉙ #㉚ #㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; color: #000;" | ◯ | style="background:#000; color: #fff;" | ⬤ | style="background:silver; color: gold;" | 0 | style="background:#808080; color: gold;" | o | style="background:indigo; color: gold;" | O | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ |- | | style="background:#808080; color: hsl(60, 100%, 50%);" | ① | style="background:#808080; color: hsl(60, 100%, 50%);" | 1 | style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⑩ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⑪ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⑫ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⑬ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⑭ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} rt3jm6vua7mj2fggq7gx5jq8pfts3w9 2684043 2684041 2024-11-11T23:51:11Z PurpleProjectsPDX97123 2965707 2684043 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ *◯ D:/`OBS output/124-10-08 *⓪ D:Wasteland #① ../`START HERE/`START_HERE.html #② ../`START HERE/index.html #③ #④ #⑤ #⑥ #⑦ #⑧ #⑨ #⑩ #⑪ #⑫ #⑬ #⑭ #⑮ #⑯ #⑰ #⑱ #⑲ #⑳ #㉑ #㉒ #㉓ #㉔ #㉕ #㉖ #㉗ #㉘ #㉙ #㉚ #㉛ {| class=wikitable 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style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span 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50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; color: red; } .center { text-align: center; color: red; } p.center { text-align: center; color: red; } table { width: 100%; } body { background-color: #321; background-image: url("d:/VeronicaJinTheNazarene/art/000.svg"), url("d:/VeronicaJinTheNazarene/art/drawing.svg"); background-size: cover; font-family: "Poppins", sans-serif; font-weight: 300; font-style: normal; color: hsl(60, 033%, 080%, 100%); text-align: center; } /* unvisited link */ a:link { color: black; } /* visited link */ a:visited { color: #808080; } /* mouse over link */ a:hover { color: pink; } /* selected link */ a:active { color: hotpink; } h6{ font-family: "Cairo Play", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-variation-settings: "slnt" 0; } h5 { font-family: "Playwrite US Trad", cursive; font-optical-sizing: auto; font-weight: 100; font-style: normal; color: hsl(276, 50%, 070%, 100%); font-size: 10px; } h4 { font-family: "Zen Kurenaido", sans-serif; font-weight: 400; font-style: normal; } h3 { font-family: "Playwrite CO", cursive; font-optical-sizing: auto; font-weight: 200; font-style: normal; color: hsl(30, 050%, 070%, 100%); } h2 { font-family: "Quicksand", sans-serif; font-optical-sizing: auto; font-weight: 300; font-style: normal; } h1 { font-family: "Sacramento", cursive; font-weight: 400; font-style: normal; } def { font-family: "Poppins", sans-serif; font-weight: 100; font-style: normal; font-size: 8px; color: #fff; } code { font-family: "Dosis", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-size: 12px; color: #808080; } mark { background-color: hsl(0, 050%, 080%, 100%); color: teal; } /* .zen-kurenaido-regular { font-family: "Zen Kurenaido", sans-serif; font-weight: 400; font-style: normal; } // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 200 to 1000 .cairo-play-<uniquifier> { font-family: "Cairo Play", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; font-variation-settings: "slnt" 0; } */ /* // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 300 to 700 .quicksand-<uniquifier> { font-family: "Quicksand", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 100 to 400 .playwrite-us-trad-<uniquifier> { font-family: "Playwrite US Trad", cursive; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* .sacramento-regular { font-family: "Sacramento", cursive; font-weight: 400; font-style: normal; } */ /* Dosis // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 200 to 800 .dosis-<uniquifier> { font-family: "Dosis", sans-serif; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* Playwrite // <uniquifier>: Use a unique and descriptive class name // <weight>: Use a value from 100 to 400 .playwrite-co-<uniquifier> { font-family: "Playwrite CO", cursive; font-optical-sizing: auto; font-weight: <weight>; font-style: normal; } */ /* .poppins-thin { font-family: "Poppins", sans-serif; font-weight: 100; font-style: normal; } .poppins-extralight { font-family: "Poppins", sans-serif; font-weight: 200; font-style: normal; } .poppins-light { font-family: "Poppins", sans-serif; font-weight: 300; font-style: normal; } .poppins-regular { font-family: "Poppins", sans-serif; font-weight: 400; font-style: normal; } .poppins-medium { font-family: "Poppins", sans-serif; font-weight: 500; font-style: normal; } .poppins-semibold { font-family: "Poppins", sans-serif; font-weight: 600; font-style: normal; } .poppins-bold { font-family: "Poppins", sans-serif; font-weight: 700; font-style: normal; } .poppins-extrabold { font-family: "Poppins", sans-serif; font-weight: 800; font-style: normal; } .poppins-black { font-family: "Poppins", sans-serif; font-weight: 900; font-style: normal; } .poppins-thin-italic { font-family: "Poppins", sans-serif; font-weight: 100; font-style: italic; } .poppins-extralight-italic { font-family: "Poppins", sans-serif; font-weight: 200; font-style: italic; } .poppins-light-italic { font-family: "Poppins", sans-serif; font-weight: 300; font-style: italic; } .poppins-regular-italic { font-family: "Poppins", sans-serif; font-weight: 400; font-style: italic; } .poppins-medium-italic { font-family: "Poppins", sans-serif; font-weight: 500; font-style: italic; } .poppins-semibold-italic { font-family: "Poppins", sans-serif; font-weight: 600; font-style: italic; } .poppins-bold-italic { font-family: "Poppins", sans-serif; font-weight: 700; font-style: italic; } .poppins-extrabold-italic { font-family: "Poppins", sans-serif; font-weight: 800; font-style: italic; } .poppins-black-italic { font-family: "Poppins", sans-serif; font-weight: 900; font-style: italic; } */ .zer0 { color: #fff; } .vjtn-00 { color: #000; } .vjtn-01 { color: hsl(60, 050%, 050%, 100%); } .vjtn-02 { color: hsl(48, 050%, 050%, 100%); } .vjtn-03 { color: hsl(36, 050%, 050%, 100%); } .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; color: #000;" | ◯ | style="background:#000; color: #fff;" | ⬤ | style="background:silver; color: gold;" | 0 | style="background:#808080; color: gold;" | o | style="background:indigo; color: gold;" | O | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ |- | | style="background:#808080; color: hsl(60, 100%, 50%);" | ① | style="background:#808080; color: hsl(60, 100%, 50%);" | 1 | style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⑩ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⑪ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⑫ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⑬ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⑭ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} 5yss6199z2su0xdshos9i9fs20hynqr 2684044 2684043 2024-11-11T23:53:07Z PurpleProjectsPDX97123 2965707 2684044 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ %60 = ~ %20 = space *◯ D:/`OBS output/124-10-08 *⓪ D:Wasteland #① ../`START HERE/`START_HERE.html #② ../`START HERE/index.html #③ #④ #⑤ #⑥ #⑦ #⑧ #⑨ #⑩ #⑪ #⑫ #⑬ #⑭ #⑮ #⑯ #⑰ #⑱ #⑲ #⑳ #㉑ #㉒ #㉓ #㉔ #㉕ #㉖ #㉗ #㉘ #㉙ #㉚ #㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | 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style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-04 { color: hsl(24, 050%, 050%, 100%); } .vjtn-05 { color: hsl(12, 050%, 050%, 100%); } .vjtn-06 { color: hsl(360, 050%, 050%, 100%); } .vjtn-07 { color: hsl(348, 050%, 050%, 100%); } .vjtn-08 { color: hsl(336, 050%, 050%, 100%); } .vjtn-09 { color: hsl(324, 050%, 050%, 100%); } .vjtn-10 { color: hsl(312, 050%, 050%, 100%); } .vjtn-11 { color: hsl(300, 050%, 050%, 100%); } .vjtn-12 { color: hsl(288, 050%, 050%, 100%); } .vjtn-13 { color: hsl(276, 050%, 050%, 100%); } .vjtn-14 { color: hsl(264, 050%, 050%, 100%); } .vjtn-15 { color: hsl(252, 050%, 050%, 100%); } .vjtn-16 { color: hsl(240, 050%, 050%, 100%); } .vjtn-17 { color: hsl(228, 050%, 050%, 100%); } .vjtn-18 { color: hsl(216, 050%, 050%, 100%); } .vjtn-19 { color: hsl(204, 050%, 050%, 100%); } .vjtn-20 { color: hsl(192, 050%, 050%, 100%); } .vjtn-21 { color: hsl(180, 050%, 050%, 100%); } .vjtn-22 { color: hsl(168, 050%, 050%, 100%); } .vjtn-23 { color: hsl(156, 050%, 050%, 100%); } .vjtn-24 { color: hsl(144, 050%, 050%, 100%); } .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; color: #000;" | ◯ | style="background:#000; color: #fff;" | ⬤ | style="background:silver; color: gold;" | 0 | style="background:#808080; color: gold;" | o | style="background:indigo; color: gold;" | O | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ |- | | style="background:#808080; color: hsl(60, 100%, 50%);" | ① | style="background:#808080; color: hsl(60, 100%, 50%);" | 1 | style="background:#808080; color: hsl(60, 100%, 50%);" | appl | style="background:#808080; color: hsl(60, 100%, 50%);" | i | style="background:#808080; color: hsl(60, 100%, 50%);" | cation | style="background:#808080; color: hsl(60, 100%, 50%);" | vero | style="background:#808080; color: hsl(60, 100%, 50%);" | nica | style="background:#808080; color: hsl(60, 100%, 50%);" | jin | style="background:#808080; color: hsl(60, 100%, 50%);" | The | style="background:#808080; color: hsl(60, 100%, 50%);" | Naza | style="background:#808080; color: hsl(60, 100%, 50%);" | rene | style="background:#808080; color: hsl(60, 100%, 50%);" | VUE | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | vue | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ |} {|{{align|center}} |- || 0 | 🧿 || ∈ | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: hsl(54, 100%, 50%);" | ① | style="background:#808080; color: hsl(48, 100%, 50%);" | ② | style="background:#808080; color: hsl(42, 100%, 50%);" | ③ | style="background:#808080; color: hsl(36, 100%, 50%);" | ④ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⑤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⑥ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⑦ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⑧ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⑨ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⑩ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⑪ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⑫ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⑬ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⑭ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⑮ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⑯ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⑰ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⑱ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⑲ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⑳ | style="background:#808080; color: hsl(294, 100%, 50%);" | ㉑ | style="background:#808080; color: hsl(288, 100%, 50%);" | ㉒ | style="background:#808080; color: hsl(282, 100%, 50%);" | ㉓ | style="background:#808080; color: hsl(276, 100%, 50%);" | ㉔ | style="background:#808080; color: hsl(270, 100%, 50%);" | ㉕ | style="background:#808080; color: hsl(264, 100%, 50%);" | ㉖ | style="background:#808080; color: hsl(258, 100%, 50%);" | ㉗ | style="background:#808080; color: hsl(252, 100%, 50%);" | ㉘ | style="background:#808080; color: hsl(246, 100%, 50%);" | ㉙ | style="background:#808080; color: hsl(240, 100%, 50%);" | ㉚ | style="background:#808080; color: hsl(234, 100%, 50%);" | ㉛ | style="background:#808080; color: hsl(228, 100%, 50%);" | ㉜ | style="background:#808080; color: hsl(222, 100%, 50%);" | ㉝ | style="background:#808080; color: hsl(216, 100%, 50%);" | ㉞ | style="background:#808080; color: hsl(210, 100%, 50%);" | ㉟ | style="background:#808080; color: hsl(204, 100%, 50%);" | ㊱ | style="background:#808080; color: hsl(198, 100%, 50%);" | ㊲ | style="background:#808080; color: hsl(192, 100%, 50%);" | ㊳ | style="background:#808080; color: hsl(186, 100%, 50%);" | ㊴ | style="background:#808080; color: hsl(180, 100%, 50%);" | ㊵ | style="background:#808080; color: hsl(174, 100%, 50%);" | ㊶ | style="background:#808080; color: hsl(168, 100%, 50%);" | ㊷ | style="background:#808080; color: hsl(160, 100%, 50%);" | ㊸ | style="background:#808080; color: hsl(154, 100%, 50%);" | ㊹ | style="background:#808080; color: hsl(148, 100%, 50%);" | ㊺ | style="background:#808080; color: hsl(142, 100%, 50%);" | ㊻ | style="background:#808080; color: hsl(136, 100%, 50%);" | ㊼ | style="background:#808080; color: hsl(130, 100%, 50%);" | ㊽ | style="background:#808080; color: hsl(124, 100%, 50%);" | ㊾ | style="background:#808080; color: hsl(118, 100%, 50%);" | ㊿ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||1 ||∈ | style="background:#808080; color: lime;" |⋅ | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ ||① ||② ||③ ||④ ||⑤ ||⑥ ||⑦ ||⑧ ||⑨ ||⑩ ||⑪ ||⑫ ||⑬ ||⑭ ||⑮ ||⑯ ||⑰ ||⑱ ||⑲ ||⑳ ||㉑ ||㉒ ||㉓ ||㉔ ||㉕ ||㉖ ||㉗ ||㉘ ||㉙ ||㉚ ||㉛ ||㉜ ||㉝ ||㉞ ||㉟ ||㊱ ||㊲ ||㊳ ||㊴ ||㊵ ||㊶ ||㊷ ||㊸ ||㊹ ||㊺ ||㊻ ||㊼ ||㊽ ||㊾ ||㊿ |- ||2 | style="background:#808080; color: lime;" | ⋅ | style="background:#808080; color: lime;" | ⬤ | style="background:#808080; color: lime;" | ◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ | style="background:#808080; color: gold;" | ⬤ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(54, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(48, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(42, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(36, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(30, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(24, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(18, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(12, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(366, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(360, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(354, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(348, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(342, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(336, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(330, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(324, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(318, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(312, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(306, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(300, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(294, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(288, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(282, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(276, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(270, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(264, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(258, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(252, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(246, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(240, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(234, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(228, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(222, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(216, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(210, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(204, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(198, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(192, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(186, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(180, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(174, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(168, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(160, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(154, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(148, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(142, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(136, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} b873es1zos8upio5uypgxwdw8stig85 2684059 2684044 2024-11-12T00:16:27Z PurpleProjectsPDX97123 2965707 2684059 wikitext text/x-wiki ◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ %60 = ~ %20 = space *◯ D:/`OBS output/124-10-08 *⓪ D:Wasteland #① ../`START HERE/`START_HERE.html #② ../`START HERE/index.html #③ vue #④ jupyter #⑤ #⑥ #⑦ #⑧ #⑨ #⑩ #⑪ #⑫ #⑬ #⑭ #⑮ #⑯ #⑰ #⑱ #⑲ #⑳ #㉑ #㉒ #㉓ #㉔ #㉕ #㉖ #㉗ #㉘ #㉙ #㉚ #㉛ {| class=wikitable style="text-align: center;" |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |- || [https://www.timeanddate.com/countdown 🏠] | style="background:#000;" | <span style="color: #fff"> 愛 </span> || [https://www.timeanddate.com/countdown 🟨] || [https://www.timeanddate.com/countdown 🟥] || [https://www.timeanddate.com/countdown 🟦] || [https://www.timeanddate.com/countdown 🟩] || [https://www.timeanddate.com/countdown 🧿] || [https://www.timeanddate.com/countdown 👣] || [https://www.timeanddate.com/countdown 🍎] |} "Without resolve, you don't have the strength to wipe away your own tears" kiru la kiru "Another example of heuristic making an algorithm faster occurs in certain search problems. Initially, the heuristic tries every possibility at each step," [https://en.wikipedia.org/wiki/Heuristic_(computer_science) ^] {|◯ ⓪ ① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ ⑰ ⑱ ⑲ ⑳ ㉑ ㉒ ㉓ ㉔ ㉕ ㉖ ㉗ ㉘ ㉙ ㉚ ㉛ |- | style="background:;" | <span style="color: #000"> ◯ </span> | style="background:#000;" | <span style="color: #fff"> ⓪ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ① </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ② </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ③ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ④ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⑤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⑥ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⑦ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⑧ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⑨ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⑩ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⑪ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⑫ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⑬ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⑭ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⑮ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⑯ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⑰ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⑱ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⑲ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⑳ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ㉑ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ㉒ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ㉓ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ㉔ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ㉕ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ㉖ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ㉗ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ㉘ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ㉙ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ㉚ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ㉛ </span> |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:#000;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} My ORCID record is https://orcid.org/0009-0001-7799-7107 {| |- | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} =VeronicaJinTheNazarene= 🈁 {{User alternative account|VeronicaJeanAnderson}} ==local Start Here== 🈁 {{User alternative account|VeronicaJeanAnderson}} 🧿 “We become what we hold onto.” -The Man Who Killed Don Quixote 🏫 https://en.wikiversity.org/wiki/User:VeronicaJeanAnderson] 愛 file:///D:/VeronicaJinTheNazarene/index.html ⬤ ◯ 👣 Coelecanth 🍎 growingGenkiness 🏠 ⌂ [{(恋)}] ⬤ ◯ 🍎 | 🏠 | ⌂ | Coelecanth | growingGenkiness | Vue3Vite wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . ⋮ mature ⋮⋮ блять ⋮ くそ ⋮ fuck ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ ⋮⋮ ⋮⋮⋮ ⋮⋮ ⋮ : . https://www.youtube.com/watch?v=bH6tKOPqcMM wiki.eng:lang⋮v⋮g⋮⋮gg⋮⋮⋮ggg⋮⋮pro⋮mature⋮⋮coos⋮⋮⋮kuso⋮⋮fu⋮hu⋮⋮YYY⋮⋮⋮yy⋮⋮y⋮wai⋮⋮ai⋮⋮⋮i⋮⋮ii⋮𝒊:A.aα∞8)}][{()}][ ]{ }( ◯ ) { × } [ | ] 愛 I I i . . . 👣 i think this is the size of f👣tprints that I want to make and I (singular) want to make them right 🈁: 👣 恋 can parse bulk it into publishable editable redactable content that both he and I can live with :: ♥恋❤️ 👂【こい】鯉 aka common carp (Cyprinus carpio) ::: 耳 👂 me!me! along with my children once they figure out Tyra Banks only published a glimpse of the emotion she internalized the real war these last decades has been a war of ♀ against other 👩 and against still other women putin's emotions are tied to women so there his coffers go also. (parenthetically, I want 3 black faced Switzerland sheep: two ewes and a ram) in more recent years, I'd not be surprised if his largest coffers go to daughters who are trying to mitigate generational sins that none of us caused directly measured in "Haley's comets" rather than days or a lunar months... none of us want to be judged by what we've done, only by what we've intended to do, but there are some costs that can't be repaid. 母 There are a lot of Russian 母 Mothers who are praying Ukrainians demonstrate self control enough to allow their sons to surrender. And there are Russian Mothers who would spit on their own son should he return alive while others didn't. And there are Russians Mothers hanging out in international waters in areas least likely to sabotaged by extreme weathers cutting up their GUCCI bags while walking on their New Zealand Trophy in stilettoes. And there are Russian Mothers who had their son stolen from them decades before and held within them a distrust of others that can never be quenched And there are Mothers like me who knew nothing of Russia, especially cannibal island until her husband outgrew his beard and found family among strangers locally Who weirdly appreciated Trump for making relations between Russia and America a bit warmer; enough to let our guard down and recognize that "us" and "them" had blurred. =🎱= ==🈁== ===🏊=== ====⛹==== =====🟨===== =====🟥===== =====🟦===== ===== 1 = R\Q / (ℝ\ℚ) = ⬤ ===== a promise kept 🎱 what's in the fanny pack? 🈁 right where you left him that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🎱 a promise kept 🏊 what have I done? I want to spend my time in "pre" and "code" - with enough 'p' for my boys and their infinite cousins to feel loved. I'm told p is kept in ⛹, but I digress. > I believe that if I yield enough narrative in pre, code, &, p &, &, mel'scomp will be able to mine my code for useful bits. that ___ http://lab.sectorfour/-/ide/project/vonGeist/ele/tree/main/-/body.tex/ 🟨 1 🟥 1 🟦 1 🟦 1 🟥 1 🟨 what's in The Guards's fanny pack? irrational numbers 1 = R\Q / (ℝ\ℚ) = ⬤ R Q ℝ ℚ - 0 + 一𝒊 ◯ 十𝒊 —1 |⬤| ᛭1 🧿 🤍 🖤 👁‍🗨 🐾 D:/index wikiversity localhost:8080 twitch BeaverBank adjust all_inclusive vignette visibility terrain [abc...oO [ 🟨 ] 0123456789] {abc...oO { 🟥 } 0123456789} (abc...oO ( 🟦 ) 0123456789) 1 = R\Q / (ℝ\ℚ) = ⬤ [https://www.latex-project.org/ 🎱 git a ⚽ clu & <3 🎮 LaTeX 🈁 👣 🏊 ] ===\beamer@sectionintoc {1}{IntroductionVeronicaJeanAnderson}{3}{0}{1}=== gv^💛🧡💗💜💙💚🤍🖤👁‍🗨🧠💦🤎G`~ ===\beamer@sectionintoc {2}{Literature Review Wikiversity}{5}{0}{2}=== 十 + ===\beamer@sectionintoc {3}{Methods Nazarene Japanese Ainu Chemawa Russian UK et tu}{9}{0}{3}=== ✜ 🕈 ✝ ✞ ✟ ===\beamer@sectionintoc {4}{Results mixed}{11}{0}{4}=== g g g g g g g g g g v v v v v v v v v v ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 💛 💛 💛 💛 💛 💛 💛 💛 💛 💛 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 🧡 💗 💗 💗 💗 💗 💗 💗 💗 💗 💗 💜 💜 💜 💜 💜 💜 💜 💜 💜 💜 💙 💙 💙 💙 💙 💙 💙 💙 💙 💙 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 ️💚 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🤍 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 🖤 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 👁‍🗨 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 🧠 💦 💦 💦 💦 💦 💦 💦 💦 💦 💦 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 🤎 G G G G G G G G G G `~ `~ `~ `~ `~ `~ `~ `~ `~ `~ ===\beamer@sectionintoc {5}{Conclusion to be determined}{16}{0}{5}=== Every Public Defense Attorney in Oregon was just fired a few days ago. I'm a bit unclear as to by whom and certainly don't know the logistics. Rumors include all of the commission for Public Defenders was fired while a few or half or whatever were immediately reinstated causing a paperwork break and new application process. I'm quite happy with my public defender and I suppose my persistent woman attitude [[ARCHIVED_START_HERE_2020]] npo papers for atlassian [[G:/%60.me/meta/meta.html file:///G:/%60.me/meta/meta.html]] https://www.twitch.tv/veronicajinthenazarene | nazareneoregonian@gmail.com | p a t r e o n .com/VeronicaJinTheNazarene | nazareneoregonian@outlook.com | (will remove) =Programmars Start at zer0= yes, I spelled that programmar rather than programmer. It makes me feel like I'm listening to the soft sciences. =0= I prefer to use fonts that differentiate between o.O ⋅ 0 My step zer0 is D:\VeronicaJinTheNazarene\index.html with VeronicaJinTheNazarene.css This same css is used in the next vue document. My index.html provides personalized references documenting code from https://www.w3schools.com/ <-- == 🗀 VeronicaJinTheNazarene == === 🗀 art === 000.svg drawing.svg VeronicaJinTheNazarene.ico VeronicaJinTheNazarene.png VeronicaJinTheNazarene.kra === 🗀 backups === === 🗀 coelecanth === Latimeria_chalumnae_replica.jpg from wikipedia Latimeria_chalumnae_replica.png without background Latimeria_chalumnae_replica.kra Krita-fied === 🗀 Stream Sudos === twitch-ToSudo.txt TheModerator.png === 🗀 vjn-vue === .eslintrc.cjs .gitignore .prettierrc.json env.d.ts index.html package.json packate-lock.json postcss.config.cjs readme.md tailwind.config.js tsconfig.app.json tsconfig.node.json tsconfig.vitest.json vite.config.ts vitest.config.ts ====🗀 .git==== ====🗀 .vscode==== ====🗀 node_modules==== ====🗀 public==== ====🗀 src==== App.vue main.tx ===== 🗀 assets ===== ====== 000.svg====== ====== base.css====== ====== coelecanth.png ====== ====== logo.svg ====== ====== main.css ====== ====== tailwind.css ====== ====== vuelogo.svg ====== ===== 🗀 components ===== ===== 🗀 router ===== ===== 🗀 stores ===== ===== 🗀 views ===== === 🗎 index.html === === 🗎 VeronicaJinTheNazarene.css === {| |- | style="background:;" | <span style="color: #000"> ⬤ </span> | style="background:;" | <span style="color: #fff"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(48, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(36, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(24, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(12, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(0, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(348, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(336, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(324, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(312, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(300, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(288, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(276, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(264, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(252, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(240, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(228, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(216, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(204, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(192, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(180, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(168, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(156, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(144, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(132, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(120, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(108, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(96, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(84, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(72, 50%, 50%)"> ⬤ </span> | style="background:;" | <span style="color: hsl(60, 50%, 50%)"> ⬤ </span> |} #para0 { text-align: center; 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} .vjtn-25 { color: hsl(132, 050%, 050%, 100%); } .vjtn-26 { color: hsl(120, 050%, 050%, 100%); } .vjtn-27 { color: hsl(108, 050%, 050%, 100%); } .vjtn-28 { color: hsl(96, 050%, 050%, 100%); } .vjtn-29 { color: hsl(84, 050%, 050%, 100%); } .vjtn-30 { color: hsl(72, 050%, 050%, 100%); } .vjtn-31 { color: hsl(60, 050%, 050%, 100%); } table { width: 100%; } =124= idiosyncrasies of mine include spelling some things in a unique manner for neuroplasticity reasons pandaemic | pandemic diabeties | diabetes color | colour Also, 2020 20/20 seemed like a good date to restart the numbering on my calendar and as a programmar, I should be able to date my 物|もの|mono however I choose. 1900 = 0 1975 = 75 1999 = 99 2020 = 120 2021 = 121 2022 = 122 2023 = 123 2024 = 124 2030 = 130 =8 Principles of Celebrate Recovery= == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D is for delta === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === =12 Steps= once begun is half done == 1 is for == === Anthrax === == 2 is for == === Blood === == 3 is for == === Coelecanth === == 4 is for == === D === == 5 is for == === Elephants === == 6 is for == === F === == 7 is for == === Genkiness === == 8 is for == === H === == 9 is for == === I === == 10 is for == === J === == 11 is for == === K === == 12 is for == === L === =Alphabet Art Therapy= once begun is half done == A is for == === Anthrax === The FBI came to my home looking for Anthrax under the Trump administration == B is for == === Blood === I have army blood in me. Not only did my father serve in the army at Fort Bragg and Okinawa, but I've also had a blood transfusion in/around 1978 at Fort Bragg. == C is for == === Coelecanth === == D is for == === D === == E is for == === Elephants === == F is for == === F === == G is for == === Genkiness === == H is for == === H === == I is for == === I === == J is for == === J === == K is for == === K === == L is for == === L === == M is for == === M === == N is for == === N === == O is for == === O === == P is for == === P === == Q is for == === Q === == R is for == === R === == S is for == === S === == T is for == === T === == U is for == === U === == V is for == === V === == W is for == === W === == X is for == === Xenophobia === == Y is for == === Yodel === == Z is for == === Zither === == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== =1= == 22 == ===333=== ====4444==== =====55555===== ======666666====== {|{{align|center}} |- | ⓪ | style="background:#fff; 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color: hsl(130, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(124, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(118, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(112, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(106, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(100, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(94, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(88, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(82, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(76, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(70, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(64, 100%, 50%);" | ⬤ | style="background:#808080; color: hsl(58, 100%, 50%);" | ⬤ |- ||3 | style="background:#808080; color: lime;"|⬤ | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||4 | style="background:#808080; color: lime;"|◯ | style="background:#808080; color: hsl(60, 100%, 50%);" | ⓪ |- ||5 |} ikvzxf6wgfm3a5c7cajhseu8394qh2n Social Victorians/People/Feversham 0 263739 2683987 2682156 2024-11-11T21:07:51Z Scogdill 1331941 2683987 wikitext text/x-wiki == Overview == [[File:Vincent E Vanity Fair 1899-04-20.jpg|thumb|alt=Old colored drawing of a man in a 19th-century black suit with grey and black striped trousers standing very erect, his hands behind his back and a full beard and moustache, looking to his left|"Eastern finance" (Sir Edgar Vincent) ''Vanity Fair'', 20 April 1899]] [[Social Victorians/People/Helmsley | Viscount Helmsley]] was the courtesy title for the eldest son and heir apparent of the Earl of Feversham (during the second half of the 19th century). The people who attended the [[Social Victorians/1897 Fancy Dress Ball |Duchess of Devonshire's fancy-dress ball]] from this family are the Earl and Countess of Feversham, their two youngest daughters and their husbands. == Acquaintances, Friends and Enemies == == Timeline == '''1851 August 7''', William Duncombe (at that time 2nd Baron Feversham of Duncombe Park) and Mabel Graham married.<ref name=":0">"Mabel Violet Graham." {{Cite web|url=https://thepeerage.com/p2288.htm#i22879|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1881 July 14, Thursday afternoon, beginning about 2 p.m.''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1881-07-14 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1881 July 22, Friday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to — and likely attended — [[Social Victorians/1881-07-22 Marlborough House Party|the party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1882 July 13, Thursday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1882-07-13 Marlborough House Garden Party|Garden Party at Marlborough House for Queen Victoria]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1884 July 03''', William, Earl of Feversham and Mabel, Countess of Feversham attended [[Social Victorians/1884-07-03 Munster Reception|Count Münster's Reception at the German Embassy]], Carlton House Terrace. '''1886 July 21, Wednesday''', the Earl and Countess of Feversham and the Ladies Duncombe were invited to — and likely attended — [[Social Victorians/1886-07-21 Ball at Marlborough House|the Ball at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1888 March 8''', Sir Richard James Graham's father died, so he succeeded as the 4th Baronet Graham of Netherby.<ref>"Sir Frederick Ulric Graham, 3rd Bt." {{Cite web|url=https://thepeerage.com/p5396.htm#i53954|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1889 June 27''', Lady Cynthia Duncombe and Sir Richard James Graham, 4th Baronet of Netherby married. '''1890 September 24''', Lady Helen Venetia Duncombe and Edgar Vincent married.<ref name=":1">"Lady Helen Venetia Duncombe." {{Cite web|url=https://thepeerage.com/p23311.htm#i233108|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1891 July 9, Thursday''', William, Earl of Feversham seems to have been invited to a [[Social Victorians/1891-07-09 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], to which about 3,000 people were invited. '''1892 May 18, Wednesday''', Mabel, Countess of Feversham attended [[Social Victorians/Timeline/1892#18 May 1892, Wednesday18 May 1892, Wednesday|the Queen's Drawing-room at Buckingham Palace]] and presented Lady Ulrica Duncombe to her Royal Highness Princess Christian of Schleswig-Holstein, who held the drawing-room on behalf of Queen Victoria. '''1894 July 19, Thursday''', William, Earl of Feversham and Lady Ulrica Duncombe attended [[Social Victorians/Timeline/1894#19 July 1894, Thursday|a ball hosted by the Duke and Duchess of Devonshire at Devonshire House that followed a dinner for the Prince and Princess of Wales]], some of their children, the Russian Ambassador, the Portuguese Minister [is this de Soveral?] and a few British dignitaries and aristocratic friends and family. '''1897 June 28, Monday''', William, Earl of Feversham and Mabel, Countess of Feversham were invited to [[Social Victorians/Diamond Jubilee Garden Party|Queen Victoria's immense Diamond Jubilee garden party at Buckingham Palace]]. '''1897 July 2, Friday''', Lady Helen and Sir Edgar Vincent attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House as did Lord and Lady Feversham, the Earl and Countess Feversham. Sir R. and Lady C. Graham were also present. '''1897 July 31, Saturday''', William, Earl of Feversham and Mabel, Countess of Feversham gave Mabel Wombwell a "silver-gilt inkstand and candlesticks"<ref>"Marriage of Mr. H. R. Hohler and Miss Wombwell." ''Morning Post'' 2 August 1897, Monday: 6 [of 8], Col. 3a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970802/067/0006 (accessed June 2019).</ref> for [[Social Victorians/Timeline/1897#31 July 1897, Saturday|her wedding to Henry R. Hohler]]. '''1899 April 20''', a caricature portrait (above right) by Leslie Ward ("Spy") of "Eastern Finance" (Sir Edgar Vincent) appeared in this issue of ''Vanity Fair'', as Number 746 in its "Men of the Day" series.<ref>{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).</ref> (Note the differences between the figure and the shadow in this caricature.) '''1926 February 20''', Edgar Vincent was created 1st Viscount D'Abernon, of Esher and Stoke D'Abernon, County Surrey.<ref name=":2">"Edgar Vincent, 1st and last Viscount D'Abernon." {{Cite web|url=https://thepeerage.com/p23310.htm#i233094|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1936 March 2''', Edgar Vincent succeeded as the 16th Baronet Vincent, of D'Abernon, County Surrey.<ref name=":2" /> [[File:Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a tiara and a black feather plume on top of her head|Helen Vincent as a Genoese Lady, after Vandyck. ©National Portrait Gallery, London.]] == Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball == === William, Earl of Feversham and Mabel, Countess of Feversham === William Ernest Duncombe, 1st Earl of Feversham and Mabel Violet Graham Duncombe, Countess Feversham were present at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]], as were their daughters Lady Helen Vincent and Lady Cynthia Graham and their husbands. Nothing is known about the costumes of the Earl and Countess of Feversham. === Lady Helen Vincent === [[File:Den Haag - Mauritshuis - Anthony van Dyck (1599-1641) - Portrait of Anna Wake (1605-before 1669), wife of Peter Stevens 1618.jpg|thumb|left|alt=Old portrait of a woman richly dressed in black and white, with jewelry, in a gold frame|Portrait of Anna Wake, wife of Peter Stevens, by Antony Van Dyke (1618)]] Lady Helen Vincent sat at Table 12 for the first seating for supper and was dressed as Contessa Valentina Gateago in the 17th-century procession.<ref name=":3">"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref><ref name=":4">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref> Lady Helen's high status among the group of people attending the ball is revealed by her presence in the first supper seating. Henry Van der Weyde's portrait (above right) of "Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck" in costume is photogravure #83 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.<ref name=":5">"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.</ref> The printing on the portrait says, "Lady Helen Vincent as a Genoese Lady, after Vandyck."<ref>"Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158441/Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.</ref> Van Dyke's 1628 portrait of Anna Wake (left) does not look like the original of Lady Helen Vincent's dress, but it shows the painter's treatment of a similar subject. ==== Commentary on Lady Vincent's Costume ==== * No newspapers described or commented on Lady Helen's dress. * Lady Vincent's dress is a hodgepodge of elements, many Victorian but with an approximately 17th-century collar and ruffled peplum. The waist is the most notable Victorian element. The ruffles (or little puffs) at the bottom of the bodice and the pearl belt emphasize and flatter her waist, as do the broad shoulders and collar. Similar ruffles (or little puffs or ruches) also appear at the neckline. * Lady Helen's sleeves are Victorian in how short and high they are. Although the slashed puff is a 17th-century element, its silhouette echoes the shape of sleeves popular in the 1890s. The treatment of the sleeve below the single puff is odd, difficult to know what on earth the designer was thinking, how it was constructed and what keeps it above the elbow. * Lady Helen has pulled her skirts to the front on both sides for the photograph, distorting the front panel of the skirt slightly. The skirt appears to have stripes made by stitching strips of the same satin fabric cut from the crosswise grain, which gives this very plain skirt more texture. The center piece of the skirt is reminiscent of an underskirt. This black-and-white photograph is too dark to permit clear analysis of the features of the skirt. * The border at the bottom of the skirt and train is stiffened — probably with horsehair — preventing the fabric from hanging straight down, resulting in an A-line. In the 1890s,<blockquote>Skirts were lined with cambric or taffeta and trained gowns were weighted and disciplined by facings of horsehair which might be as deep as eighteen inches at center back.<ref>Payne, Blanche. ''History of Costume: From the Ancient Egyptians to the Twentieth Century''. Harper & Row, 1965.</ref> (532)</blockquote> * This costume lacks the sophistication that would have been present in a dress designed by [[Social Victorians/People/Dressmakers and Costumiers#Mrs. Mason|Mrs. Mason]], for example, [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Charles Alias]] or the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]]. Aesthetically, the [[Social Victorians/Terminology#Frou-frou|frou-frou]] on the top is not balanced by the simplicity of the design on the skirt and train, although, because of the stripes the costume might have looked more interesting in motion than it does in this photograph. *The photograph appears to have been retouched on the right side of Lady Helen's waist, under her right arm, a common practice. *Lady Helen's headdress looks like a crown because of the points made by the pearls. A single black plume rises straight up from the center of the headdress. *Lady Helen's jewelry is primarily strands of pearls with two brooch ornaments, one pendant from one of the necklaces and the other at the center of the neckline of her bodice. Besides the several strands of pearls at her neck and on her headdress are pearls on her sleeves and at her waist. *Lady Vincent's jewels do not display the kind of wealth that someone like the Duchess of Devonshire or Mrs. Arthur Paget, for example, had. * The wired collar should be standing up behind her head to frame her face, but the wires cannot hold up the center back because of the cut of the lace, which should have been attached differently. [[File:Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.jpg|thumb|alt=Black-and-white photograph of a standing man richly dressed in an historical costume with a large ruff around his neck, a large hat, and a sword|Edgar Vincent as a Dutch Stadtholder, after Frans Hals. ©National Portrait Gallery, London.]] === Sir Edgar Vincent === [[File:Frans Hals 042.jpg|thumb|left|alt=Old portrait of a proud gentleman with a big white ruff, big hat, and sword|Frans Hals, ''Willem van Heythuyzen'']] According to the newspapers, Sir Edgar Vincent was dressed as II Conte Oravio<ref name=":4" /> or Orayio<ref name=":3" /> in the 17th-century procession. He is not listed as having been in the first supper seating although Lady Helen Vincent is. Henry Van der Weyde's portrait (right) of "Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals" in costume is photogravure #84 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.<ref name=":5" /> The printing on the portrait says, "Sir Edgar Vincent as a Dutch Stadtholder after Frans Hals."<ref>"Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158442/Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.</ref> Van der Weyde's photograph of Sir Edgar Vincent is similar enough to Frans Hals's 1625-1630? portrait of Willem van Heythuyzen (left) that Hals's seems to be the original. Sir Edgar Vincent is striking a very similar pose, and even the photographer's drapery and set seem to refer to the Hals painting. ==== Commentary on Sir Edgar Vincent's Costume ==== The photograph of Sir Edgar is a close copy of the portrait of Willem van Heythuyzen by Frans Hals, but the clothing worn by the Victorian has been modified, as always, for the people at this ball, to accommodate standards of beauty contemporary to their own time. The painting is very dark, affecting our sense especially of the black-on-black details. * In spite of the similarity between the two portraits, the doublet worn by Sir Edgar reflects Victorian rather than Elizabethan fashion. * Sir Edgar's collar is not stiffened. The folds are more limp, suggesting a [[Social Victorians/Terminology#Cavalier|Cavalier]] collar, unlike the stiffened folds on the Hals portrait. But more important is that the collar in the Hals portrait has a lot of fabric, which alone can account for the fullness. Sir Edgar's collar may be starched, but it lies flatter because the costumier used so much less fabric. * The ornament below the collar on Sir Edgar is large and probably made of lace, as is van Heythuyzen's. We cannot tell what it is or what it symbolizes. * The fabric used for Sir Edgar's doublet and knee breeches appears to be textured, possibly a brocade or a velvet brocade. While the cloak is black like the doublet and breeches, the fabric is a more subtle, less textured brocade. Yet another fabric was used for the lining of the cloak. The textures in the fabrics are what makes this costume so sophisticated: the color is all the same. * Sir Edgar's sleeves were made to look like they were tied to the doublet, as Elizabethan sleeves would be, but were probably sewn to it. * The bodice of Sir Edgar's doublet is not stiffened and pointed, which changes the line of the garment, making it looser and more Victorian than Elizabethan. * The level (rather than pointed) bodice changes the waistline and the [[Social Victorians/Terminology#Peplum|peplum]] as well. * The garments in both portraits have decorated belts or braid at the waist. Aglets are suspended from ribbon at the waistline on both portraits. * Sir Edgar's knee breeches and sleeves are full, so they might be padded. * Sir Edgar's white cuffs fold back from the wrists and have tiny starched pleats and lace edging (like the cuffs in Van den Weyde's portrait), but they are not as stiffly starched. The tiny tucks or pleats in van Heythuyzen's cuffs give them stiffness and texture; Sir Edgar's cuffs are looser and less controlled. * The buttons on the sides of the breeches look decorative rather than functional. * The ornament at the bottom of the knee breeches actually appears to be similar in size in both portraits, but Sir Edgar's is a simple bow that is less decorative than what looks like lacy, beaded trim on van Heythuyzen. * The shoes are dominated by the bows, which may be velvet, in the Hals portrait. Sir Edgar's bows are placed below the tongue and are smaller. * Sir Edgar's shoes have flat heels, and the tongue rises above the bow. Van Heythuyzen's shoes appear to have wooden pattens beneath the soles. * The metal tips attached to ribbons at the waists of the men in both portraits are [[Social Victorians/Terminology#Aglet, Aiglet|aglets or aiglets]]. Historically, breeches could be tied to the doublet with ribbons or cords whose ends were tipped with aglets. Sir Edgar's ribboned aglets are definitely decorative, but it is not clear whether Van Heythuyzen's are decorative or functional. * Sir Edgar and Van Heythuyzen are carrying ornate cavalier rapiers. Early cavalier rapiers were long like these are, later becoming smallswords. In the portraits, the rapiers are in scabbards. Hanging from the waist of Sir Edgar's doublet is a rapier belt to hold the rapier in its scabbard. Van Heythuyzen's scabbard is quite ornate, but Sir Edgar's is simple. Both rapiers have very ornate hand guards, which is what makes them look like cavalier weapons. * The two swords — especially the hand guards — are so like each other, did Sir Edgar find the same sword? or have this one made? Is the sword in a collection somewhere? ==== The Historical William van Heythuyzen ==== While the ''Times'' and the ''Morning Post'' say that Sir Edgar Vincent was in the 17th-century Italian procession, the description in the [[Social Victorians/1897 Fancy Dress Ball/Photographs#The Album of Photographs|commemorative album]] associates his costume with a painting rather than a person. The man in the painting is Willem van Heythuyzen, Dutch cloth merchant and , dressed in early [[Social Victorians/Terminology#Cavalier|Cavalier style]].<ref name=":10">{{Cite journal|date=2023-08-27|title=Willem van Heythuysen|url=https://en.wikipedia.org/w/index.php?title=Willem_van_Heythuysen&oldid=1172477813|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Willem_van_Heythuysen.</ref> Van Heythuyzen was the founder of Hofje van Willem Heythuijsen. (A hofje is a group of almshouses surrounding an open courtyard in which poor, elderly people, especially women, can live.<ref>{{Cite journal|date=2023-08-09|title=Hofje|url=https://en.wikipedia.org/w/index.php?title=Hofje&oldid=1169559641|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Hofje.</ref>) Hofje van Willem Heythuijsen — the hofje founded by Willem van Heythuyzen — is still in existence.<ref name=":10" /> === Lady Cynthia Graham and Sir Richard Graham === Lady Cynthia Graham of Netherby and [[Social Victorians/People/Pless|Princess Henry of Pless]] were dressed as the Queen of Sheba and led of the "Oriental" Procession.<ref name=":3" /><ref name=":4" />{{rp|p. 7, Col. 5b}} At this time, no photograph of Lady Cynthia Graham in this costume exists. (Lady Cynthia Graham is the Earl of Feversham's youngest daugther and Sir Richard Graham's second wife.) ==== Newspaper Accounts ==== Three actual accounts of Lady Cynthia's costume exist, two reprinted elsewhere. * Lady Cynthia Graham "was in white satin and gauze, embroidered in gold and silver and bright rose."<ref>"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." London ''Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and https://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|p. 5, Col. 7c}} * "Lady Cynthia Graham appeared as Queen of Sheba, in a robe of white Bengal satin and gauze, with embroidery of gold appliqué, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and appliqué of coloured satin, and studded with jewels; a ceinture and pendant were of white satin, with cerise appliqué and embroidery, and she wore a jewelled headdress."<ref>“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.</ref>{{rp|p. 3, Col. 3c}} * "Lovely Lady Cynthia Graham was one [Queen of Sheba], in white satin embroidered in gold and silver and bright rose."<ref>“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.</ref>{{rp|42, Col. 1b}} * According to the ''Carlisle Patriot'', reprinting the ''Evening Standard'' description (perhaps because Lady and Lord Graham were local), "Lady Cynthia Graham of Netherby also personated the famous Eastern Queen, wearing a lovely robe of white Bengal satin and gauze, with embroidery of gold applique, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and applique of coloured satin, and studded with jewels; a ceinture and pendent were of white satin, with cerise applique and embroidery, and she wore a jewelled headdress."<ref>"Fancy Dress Ball: Unparalleled Splendour." ''Carlisle Patriot'' Friday 9 July 1897: 7 [of 8], Col. 4a–b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000365/18970709/084/0007.</ref> * "The other Queen of Sheba, who was Lady Cynthia Graham, was charmingly attired in white and silver and rose red."<ref>“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|p. 32, Col. 2c}} Lady Cynthia Graham's original costume appeared in the Drury Lane production of ''The White Heather''.<ref>"The Morning’s News." London ''Daily News'' 18 September 1897, Saturday: 5 [of 8], Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970918/027/0005.</ref> [[File:Sir Edward John Poynter - The visit of the Queen of Sheba to King Solomon - Google Art ProjectFXD.jpg|thumb|alt=Large oil painting showing a woman climbing some shallow steps to a man standing at the top in a commanding pose, both dressed in flowing robes|Sir Edward Poynter, ''The Visit of the Queen of Sheba to King Solomon'']] ==== The Queen of Sheba ==== Stories about the Queen of Sheba appear in Jewish, Christian and Islamic traditions. She visited King Solomon with gifts and tested his wisdom. Sir Edward John Poynter's 1890 ''The Visit of the Queen of Sheba to King Solomon'' (right) is in the collection of the Art Gallery of New South Wales, which accessioned it in 1892, so it would have been available for viewing until then. The Queen of Sheba's clothing here, such as there is of it, is unlikely to have been an original for the costumes worn by Lady Cynthia Graham or Daisy, Princess Pless, but her headdress has some similarities to the one worn by [[Social Victorians/People/Goelet|May Goelet]] dressed as Scheherazade. == Demographics == === Nationality === *British === Residences === * Lady Cynthia and Sir Richard Graham: Netherby Hall in the Carlisle district of Cumbria (which is why the ''Carlisle Patriot'' coverage is so thorough)<ref>{{Cite journal|date=2021-05-08|title=Arthuret|url=https://en.wikipedia.org/w/index.php?title=Arthuret&oldid=1022099353|journal=Wikipedia|language=en}} [[wikipedia:Arthuret|https://en.wikipedia.org/wiki/Arthuret#Netherby Hall]].</ref> == Family == *Charles Duncombe, 1st Baron Feversham of Duncombe Park (5 December 1764 – 16 July 1841)<ref name=":8">"Charles Duncombe, 1st Baron Feversham of Duncombe Park." {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25757|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> *Lady Charlotte Legge ( – 5 November 1848)<ref>"Lady Charlotte Legge." {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25758|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> #Hon. Frances Duncombe (– 15 June 1881) #Hon. Louisa Duncombe ( – 18 November 1852) #Charles Duncombe (1795 – 1819) #'''William Duncombe, 2nd Baron Feversham of Duncombe Park''' (14 January 1798 – 11 February 1867) #Reverend Henry Duncombe (25 August 1800 – 1 October 1832) #Admiral Hon. Arthur Duncombe (24 March 1806 – 6 February 1889) #Very Rev. Augustus Duncombe (2 November 1814 – 26 January 1880) #Hon. Octavius Duncombe (8 April 1817 – 3 December 1879) *William Duncombe, 2nd Baron Feversham of Duncombe Park (14 January 1798 – 11 February 1867)<ref name=":9">"William Duncombe, 2nd Baron Feversham of Duncombe Park." {{Cite web|url=https://www.thepeerage.com/p1242.htm#i12415|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> *Lady Louisa Stewart ( – 5 March 1889)<ref>"Lady Louisa Stewart." {{Cite web|url=https://www.thepeerage.com/p1348.htm#i13478|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> #Hon. Gertude Duncombe ( – 24 February 1916) #Hon. Jane Duncombe ( – 3 April 1901) #Hon. Helen Duncombe ( – 22 November 1896) #Hon. Albert Duncombe (11 February 1826 – 14 September 1846) #'''William Ernest Duncombe, 1st Earl Feversham of Ryedale''' (28 January 1829 – 13 January 1915) #Hon. Cecil Duncombe (27 May 1832 – 20 May 1902) *William Ernest Duncombe, 1st Earl of Feversham (28 January 1829 – 13 January 1915)<ref name=":6">"William Ernest Duncombe, 1st Earl of Feversham of Ryedale." {{Cite web|url=https://thepeerage.com/p1873.htm#i18721|title=Person Page|website=thepeerage.com|access-date=2020-11-22}}</ref> *Mabel Violet Graham Duncombe (15 February 1833 – 28 August 1915)<ref name=":0" /> #Lady Ulrica Duncombe (1874? [based on presentation at Queen's drawing-room May 1892] – 27 April 1935) #William Reginald Duncombe, [[Social Victorians/People/Helmsley | Viscount Helmsley]] (1 August 1852 – 24 December 1881) #Hon. James Henry Duncombe (20 October 1853 – 10 January 1886) #Hon. Hubert Ernest Valentine Duncombe (14 February 1862 – 21 October 1918) #Lady Hermione Wilhelmina Duncombe (30 March 1864 – 19 March 1895) #'''Lady Helen Venetia Duncombe''' (1866 – 16 May 1954) #'''Lady Cynthia (Mabel Cynthia) Duncombe''' (1869 – 25 April 1926) *Lady Helen Venetia Duncombe ( – 16 May 1954)<ref name=":1" /> *Edgar Vincent, 1st and last Viscount D'Abernon (19 August 1857 – 1 November 1941)<ref name=":2" /> * Sir Richard James Graham, 4th Bt. (24 February 1859 – 26 August 1932)<ref>"Sir Richard James Graham, 4th Bt.." {{Cite web|url=https://thepeerage.com/p7148.htm#i71471|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> * Olivia Baring (14 May 1863 – 21 March 1887)<ref>"Olivia Baring." {{Cite web|url=https://thepeerage.com/p7148.htm#i71472|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> * Lady Cynthia (Mabel Cynthia) Duncombe (1869 – 25 April 1926)<ref>"Lady Mabel Cynthia Duncombe." {{Cite web|url=https://thepeerage.com/p1604.htm#i16038|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> *# Lt.-Col. Sir Fergus Frederick Graham, 5th Bt. (10 March 1893 – 1 August 1978) *# Richard Preston Graham-Vivian (10 August 1896 – 30 September 1979) *# Daphne Graham (17 March 1903 – ) *Charles William Reginald Duncombe, 2nd Earl of Feversham (8 May 1879 – 15 September 1916)<ref name=":7">" Charles William Reginald Duncombe, 2nd Earl of Feversham of Ryedale." {{Cite web|url=https://thepeerage.com/p2288.htm#i22880|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> *Marjorie Blanche Eva Greville Duncombe (25 October 1884 – 25 July 1964)<ref>"Lady Marjorie Blanche Eva Greville." {{Cite web|url=https://thepeerage.com/p2289.htm#i22881|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> #Lady Mary Diana Duncombe (19 March 1905 – October 1943) #Charles William Slingsby Duncombe, 3rd Earl of Feversham (2 November 1906 – 4 September 1963) #Hon. David William Ernest Duncombe (8 February 1910 – September 1927) == Also Known As == *Family name: Duncombe *Earl Feversham of Ryedale **William Ernest Duncombe, 1st Earl of Feversham (25 July 1868 – 13 January 1915)<ref name=":6" /> **Charles William Reginald Duncombe, 2nd Earl of Feversham (13 January 1915 – 15 September 1916)<ref name=":7" /> *[[Social Victorians/People/Helmsley | Viscount Helmsley]] **William Ernest Duncombe (25 July 1868 – 1881)<ref name=":6" /> **Charles William Reginald Duncombe, 2nd Earl of Feversham (24 December 1881 – 13 January 1915)<ref>{{Cite journal|date=2020-09-12|title=Charles Duncombe, 2nd Earl of Feversham|url=https://en.wikipedia.org/w/index.php?title=Charles_Duncombe,_2nd_Earl_of_Feversham&oldid=978075739|journal=Wikipedia|language=en}}</ref> *Baron of Feversham **William Ernest Duncombe (11 February 1867 – )<ref name=":6" /> *Baron Feversham of Duncombe Park **Charles Duncombe, 1st Baron Feversham of Duncombe Park ( – 16 July 1841)<ref name=":8" /> **William Duncombe, 2nd Baron Feversham of Duncombe Park (16 July 1841 – 11 February 1867)<ref name=":9" /> *Other [[Social Victorians/People/Duncombe | Duncombe]] families existed as well. == Questions and Notes == #The newspapers call the Earl and Countess Feversham ''Lord and Lady Feversham''. #The ''Times'' article lists Sir R. and Lady C. Graham<ref name=":3" />: if Lady C. Graham is Lady Cynthia, then Sir R. Graham is Sir Richard James Graham. #Also present at the ball and accounted for on the [[Social Victorians/People/Duncombe | Duncombe page]] are the following: Alicia Duncombe, Lady and Mr. Florence Duncombe. #Present at other social events and not accounted for were the following: Caroline Duncombe and the Misses Duncombe. #William Duncombe, 1st Earl of Feversham is #443 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who attended]] the Duchess of Devonshire's 2 July 1897 fancy-dress ball; Mabel, Countess Feversham is #444; Lady Helen Vincent is #215; Sir Edgar Vincent is #226; Sir Edgar Vincent is #226; Lady Cynthia Graham of Netherby is #220; Sir Richard James Graham is #464. == Footnotes == {{reflist}} 0tqzrn9peln0lbfckgbr846o8lovjet 2684006 2683987 2024-11-11T22:13:34Z Scogdill 1331941 /* Lady Cynthia Graham and Sir Richard Graham */ 2684006 wikitext text/x-wiki == Overview == [[File:Vincent E Vanity Fair 1899-04-20.jpg|thumb|alt=Old colored drawing of a man in a 19th-century black suit with grey and black striped trousers standing very erect, his hands behind his back and a full beard and moustache, looking to his left|"Eastern finance" (Sir Edgar Vincent) ''Vanity Fair'', 20 April 1899]] [[Social Victorians/People/Helmsley | Viscount Helmsley]] was the courtesy title for the eldest son and heir apparent of the Earl of Feversham (during the second half of the 19th century). The people who attended the [[Social Victorians/1897 Fancy Dress Ball |Duchess of Devonshire's fancy-dress ball]] from this family are the Earl and Countess of Feversham, their two youngest daughters and their husbands. == Acquaintances, Friends and Enemies == == Timeline == '''1851 August 7''', William Duncombe (at that time 2nd Baron Feversham of Duncombe Park) and Mabel Graham married.<ref name=":0">"Mabel Violet Graham." {{Cite web|url=https://thepeerage.com/p2288.htm#i22879|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1881 July 14, Thursday afternoon, beginning about 2 p.m.''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1881-07-14 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1881 July 22, Friday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to — and likely attended — [[Social Victorians/1881-07-22 Marlborough House Party|the party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1882 July 13, Thursday''', William, Earl of Feversham, Mabel, Countess of Feversham and Lady Hermione Duncombe were invited to a [[Social Victorians/1882-07-13 Marlborough House Garden Party|Garden Party at Marlborough House for Queen Victoria]] hosted by the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1884 July 03''', William, Earl of Feversham and Mabel, Countess of Feversham attended [[Social Victorians/1884-07-03 Munster Reception|Count Münster's Reception at the German Embassy]], Carlton House Terrace. '''1886 July 21, Wednesday''', the Earl and Countess of Feversham and the Ladies Duncombe were invited to — and likely attended — [[Social Victorians/1886-07-21 Ball at Marlborough House|the Ball at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]]. '''1888 March 8''', Sir Richard James Graham's father died, so he succeeded as the 4th Baronet Graham of Netherby.<ref>"Sir Frederick Ulric Graham, 3rd Bt." {{Cite web|url=https://thepeerage.com/p5396.htm#i53954|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1889 June 27''', Lady Cynthia Duncombe and Sir Richard James Graham, 4th Baronet of Netherby married. '''1890 September 24''', Lady Helen Venetia Duncombe and Edgar Vincent married.<ref name=":1">"Lady Helen Venetia Duncombe." {{Cite web|url=https://thepeerage.com/p23311.htm#i233108|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1891 July 9, Thursday''', William, Earl of Feversham seems to have been invited to a [[Social Victorians/1891-07-09 Garden Party|Garden Party at Marlborough House]] hosted by [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], to which about 3,000 people were invited. '''1892 May 18, Wednesday''', Mabel, Countess of Feversham attended [[Social Victorians/Timeline/1892#18 May 1892, Wednesday18 May 1892, Wednesday|the Queen's Drawing-room at Buckingham Palace]] and presented Lady Ulrica Duncombe to her Royal Highness Princess Christian of Schleswig-Holstein, who held the drawing-room on behalf of Queen Victoria. '''1894 July 19, Thursday''', William, Earl of Feversham and Lady Ulrica Duncombe attended [[Social Victorians/Timeline/1894#19 July 1894, Thursday|a ball hosted by the Duke and Duchess of Devonshire at Devonshire House that followed a dinner for the Prince and Princess of Wales]], some of their children, the Russian Ambassador, the Portuguese Minister [is this de Soveral?] and a few British dignitaries and aristocratic friends and family. '''1897 June 28, Monday''', William, Earl of Feversham and Mabel, Countess of Feversham were invited to [[Social Victorians/Diamond Jubilee Garden Party|Queen Victoria's immense Diamond Jubilee garden party at Buckingham Palace]]. '''1897 July 2, Friday''', Lady Helen and Sir Edgar Vincent attended the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]] at Devonshire House as did Lord and Lady Feversham, the Earl and Countess Feversham. Sir R. and Lady C. Graham were also present. '''1897 July 31, Saturday''', William, Earl of Feversham and Mabel, Countess of Feversham gave Mabel Wombwell a "silver-gilt inkstand and candlesticks"<ref>"Marriage of Mr. H. R. Hohler and Miss Wombwell." ''Morning Post'' 2 August 1897, Monday: 6 [of 8], Col. 3a–c [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970802/067/0006 (accessed June 2019).</ref> for [[Social Victorians/Timeline/1897#31 July 1897, Saturday|her wedding to Henry R. Hohler]]. '''1899 April 20''', a caricature portrait (above right) by Leslie Ward ("Spy") of "Eastern Finance" (Sir Edgar Vincent) appeared in this issue of ''Vanity Fair'', as Number 746 in its "Men of the Day" series.<ref>{{Cite journal|date=2024-01-14|title=List of Vanity Fair (British magazine) caricatures (1895–1899)|url=https://en.wikipedia.org/w/index.php?title=List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899)&oldid=1195518024|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/List_of_Vanity_Fair_(British_magazine)_caricatures_(1895%E2%80%931899).</ref> (Note the differences between the figure and the shadow in this caricature.) '''1926 February 20''', Edgar Vincent was created 1st Viscount D'Abernon, of Esher and Stoke D'Abernon, County Surrey.<ref name=":2">"Edgar Vincent, 1st and last Viscount D'Abernon." {{Cite web|url=https://thepeerage.com/p23310.htm#i233094|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> '''1936 March 2''', Edgar Vincent succeeded as the 16th Baronet Vincent, of D'Abernon, County Surrey.<ref name=":2" /> [[File:Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.jpg|thumb|alt=Black-and-white photograph of a standing woman richly dressed in an historical costume with a tiara and a black feather plume on top of her head|Helen Vincent as a Genoese Lady, after Vandyck. ©National Portrait Gallery, London.]] == Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball == === William, Earl of Feversham and Mabel, Countess of Feversham === William Ernest Duncombe, 1st Earl of Feversham and Mabel Violet Graham Duncombe, Countess Feversham were present at the [[Social Victorians/1897 Fancy Dress Ball | Duchess of Devonshire's fancy-dress ball]], as were their daughters Lady Helen Vincent and Lady Cynthia Graham and their husbands. Nothing is known about the costumes of the Earl and Countess of Feversham. === Lady Helen Vincent === [[File:Den Haag - Mauritshuis - Anthony van Dyck (1599-1641) - Portrait of Anna Wake (1605-before 1669), wife of Peter Stevens 1618.jpg|thumb|left|alt=Old portrait of a woman richly dressed in black and white, with jewelry, in a gold frame|Portrait of Anna Wake, wife of Peter Stevens, by Antony Van Dyke (1618)]] Lady Helen Vincent sat at Table 12 for the first seating for supper and was dressed as Contessa Valentina Gateago in the 17th-century procession.<ref name=":3">"Ball at Devonshire House." The ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref><ref name=":4">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4a–8 Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref> Lady Helen's high status among the group of people attending the ball is revealed by her presence in the first supper seating. Henry Van der Weyde's portrait (above right) of "Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck" in costume is photogravure #83 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.<ref name=":5">"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.</ref> The printing on the portrait says, "Lady Helen Vincent as a Genoese Lady, after Vandyck."<ref>"Helen Venetia (née Duncombe), Viscountess D'Abernon as a Genoese Lady, after Vandyck." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158441/Helen-Venetia-ne-Duncombe-Viscountess-DAbernon-as-a-Genoese-Lady-after-Vandyck.</ref> Van Dyke's 1628 portrait of Anna Wake (left) does not look like the original of Lady Helen Vincent's dress, but it shows the painter's treatment of a similar subject. ==== Commentary on Lady Vincent's Costume ==== * No newspapers described or commented on Lady Helen's dress. * Lady Vincent's dress is a hodgepodge of elements, many Victorian but with an approximately 17th-century collar and ruffled peplum. The waist is the most notable Victorian element. The ruffles (or little puffs) at the bottom of the bodice and the pearl belt emphasize and flatter her waist, as do the broad shoulders and collar. Similar ruffles (or little puffs or ruches) also appear at the neckline. * Lady Helen's sleeves are Victorian in how short and high they are. Although the slashed puff is a 17th-century element, its silhouette echoes the shape of sleeves popular in the 1890s. The treatment of the sleeve below the single puff is odd, difficult to know what on earth the designer was thinking, how it was constructed and what keeps it above the elbow. * Lady Helen has pulled her skirts to the front on both sides for the photograph, distorting the front panel of the skirt slightly. The skirt appears to have stripes made by stitching strips of the same satin fabric cut from the crosswise grain, which gives this very plain skirt more texture. The center piece of the skirt is reminiscent of an underskirt. This black-and-white photograph is too dark to permit clear analysis of the features of the skirt. * The border at the bottom of the skirt and train is stiffened — probably with horsehair — preventing the fabric from hanging straight down, resulting in an A-line. In the 1890s,<blockquote>Skirts were lined with cambric or taffeta and trained gowns were weighted and disciplined by facings of horsehair which might be as deep as eighteen inches at center back.<ref>Payne, Blanche. ''History of Costume: From the Ancient Egyptians to the Twentieth Century''. Harper & Row, 1965.</ref> (532)</blockquote> * This costume lacks the sophistication that would have been present in a dress designed by [[Social Victorians/People/Dressmakers and Costumiers#Mrs. Mason|Mrs. Mason]], for example, [[Social Victorians/People/Dressmakers and Costumiers#Mr. Charles Alias|Mr. Charles Alias]] or the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]]. Aesthetically, the [[Social Victorians/Terminology#Frou-frou|frou-frou]] on the top is not balanced by the simplicity of the design on the skirt and train, although, because of the stripes the costume might have looked more interesting in motion than it does in this photograph. *The photograph appears to have been retouched on the right side of Lady Helen's waist, under her right arm, a common practice. *Lady Helen's headdress looks like a crown because of the points made by the pearls. A single black plume rises straight up from the center of the headdress. *Lady Helen's jewelry is primarily strands of pearls with two brooch ornaments, one pendant from one of the necklaces and the other at the center of the neckline of her bodice. Besides the several strands of pearls at her neck and on her headdress are pearls on her sleeves and at her waist. *Lady Vincent's jewels do not display the kind of wealth that someone like the Duchess of Devonshire or Mrs. Arthur Paget, for example, had. * The wired collar should be standing up behind her head to frame her face, but the wires cannot hold up the center back because of the cut of the lace, which should have been attached differently. [[File:Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.jpg|thumb|alt=Black-and-white photograph of a standing man richly dressed in an historical costume with a large ruff around his neck, a large hat, and a sword|Edgar Vincent as a Dutch Stadtholder, after Frans Hals. ©National Portrait Gallery, London.]] === Sir Edgar Vincent === [[File:Frans Hals 042.jpg|thumb|left|alt=Old portrait of a proud gentleman with a big white ruff, big hat, and sword|Frans Hals, ''Willem van Heythuyzen'']] According to the newspapers, Sir Edgar Vincent was dressed as II Conte Oravio<ref name=":4" /> or Orayio<ref name=":3" /> in the 17th-century procession. He is not listed as having been in the first supper seating although Lady Helen Vincent is. Henry Van der Weyde's portrait (right) of "Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals" in costume is photogravure #84 in the album presented to the Duchess of Devonshire and now in the National Portrait Gallery.<ref name=":5" /> The printing on the portrait says, "Sir Edgar Vincent as a Dutch Stadtholder after Frans Hals."<ref>"Edgar Vincent, Viscount d'Abernon as a Dutch Stadtholder after Frans Hals." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158442/Edgar-Vincent-Viscount-dAbernon-as-a-Dutch-Stadtholder-after-Frans-Hals.</ref> Van der Weyde's photograph of Sir Edgar Vincent is similar enough to Frans Hals's 1625-1630? portrait of Willem van Heythuyzen (left) that Hals's seems to be the original. Sir Edgar Vincent is striking a very similar pose, and even the photographer's drapery and set seem to refer to the Hals painting. ==== Commentary on Sir Edgar Vincent's Costume ==== The photograph of Sir Edgar is a close copy of the portrait of Willem van Heythuyzen by Frans Hals, but the clothing worn by the Victorian has been modified, as always, for the people at this ball, to accommodate standards of beauty contemporary to their own time. The painting is very dark, affecting our sense especially of the black-on-black details. * In spite of the similarity between the two portraits, the doublet worn by Sir Edgar reflects Victorian rather than Elizabethan fashion. * Sir Edgar's collar is not stiffened. The folds are more limp, suggesting a [[Social Victorians/Terminology#Cavalier|Cavalier]] collar, unlike the stiffened folds on the Hals portrait. But more important is that the collar in the Hals portrait has a lot of fabric, which alone can account for the fullness. Sir Edgar's collar may be starched, but it lies flatter because the costumier used so much less fabric. * The ornament below the collar on Sir Edgar is large and probably made of lace, as is van Heythuyzen's. We cannot tell what it is or what it symbolizes. * The fabric used for Sir Edgar's doublet and knee breeches appears to be textured, possibly a brocade or a velvet brocade. While the cloak is black like the doublet and breeches, the fabric is a more subtle, less textured brocade. Yet another fabric was used for the lining of the cloak. The textures in the fabrics are what makes this costume so sophisticated: the color is all the same. * Sir Edgar's sleeves were made to look like they were tied to the doublet, as Elizabethan sleeves would be, but were probably sewn to it. * The bodice of Sir Edgar's doublet is not stiffened and pointed, which changes the line of the garment, making it looser and more Victorian than Elizabethan. * The level (rather than pointed) bodice changes the waistline and the [[Social Victorians/Terminology#Peplum|peplum]] as well. * The garments in both portraits have decorated belts or braid at the waist. Aglets are suspended from ribbon at the waistline on both portraits. * Sir Edgar's knee breeches and sleeves are full, so they might be padded. * Sir Edgar's white cuffs fold back from the wrists and have tiny starched pleats and lace edging (like the cuffs in Van den Weyde's portrait), but they are not as stiffly starched. The tiny tucks or pleats in van Heythuyzen's cuffs give them stiffness and texture; Sir Edgar's cuffs are looser and less controlled. * The buttons on the sides of the breeches look decorative rather than functional. * The ornament at the bottom of the knee breeches actually appears to be similar in size in both portraits, but Sir Edgar's is a simple bow that is less decorative than what looks like lacy, beaded trim on van Heythuyzen. * The shoes are dominated by the bows, which may be velvet, in the Hals portrait. Sir Edgar's bows are placed below the tongue and are smaller. * Sir Edgar's shoes have flat heels, and the tongue rises above the bow. Van Heythuyzen's shoes appear to have wooden pattens beneath the soles. * The metal tips attached to ribbons at the waists of the men in both portraits are [[Social Victorians/Terminology#Aglet, Aiglet|aglets or aiglets]]. Historically, breeches could be tied to the doublet with ribbons or cords whose ends were tipped with aglets. Sir Edgar's ribboned aglets are definitely decorative, but it is not clear whether Van Heythuyzen's are decorative or functional. * Sir Edgar and Van Heythuyzen are carrying ornate cavalier rapiers. Early cavalier rapiers were long like these are, later becoming smallswords. In the portraits, the rapiers are in scabbards. Hanging from the waist of Sir Edgar's doublet is a rapier belt to hold the rapier in its scabbard. Van Heythuyzen's scabbard is quite ornate, but Sir Edgar's is simple. Both rapiers have very ornate hand guards, which is what makes them look like cavalier weapons. * The two swords — especially the hand guards — are so like each other, did Sir Edgar find the same sword? or have this one made? Is the sword in a collection somewhere? ==== The Historical William van Heythuyzen ==== While the ''Times'' and the ''Morning Post'' say that Sir Edgar Vincent was in the 17th-century Italian procession, the description in the [[Social Victorians/1897 Fancy Dress Ball/Photographs#The Album of Photographs|commemorative album]] associates his costume with a painting rather than a person. The man in the painting is Willem van Heythuyzen, Dutch cloth merchant and , dressed in early [[Social Victorians/Terminology#Cavalier|Cavalier style]].<ref name=":10">{{Cite journal|date=2023-08-27|title=Willem van Heythuysen|url=https://en.wikipedia.org/w/index.php?title=Willem_van_Heythuysen&oldid=1172477813|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Willem_van_Heythuysen.</ref> Van Heythuyzen was the founder of Hofje van Willem Heythuijsen. (A hofje is a group of almshouses surrounding an open courtyard in which poor, elderly people, especially women, can live.<ref>{{Cite journal|date=2023-08-09|title=Hofje|url=https://en.wikipedia.org/w/index.php?title=Hofje&oldid=1169559641|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Hofje.</ref>) Hofje van Willem Heythuijsen — the hofje founded by Willem van Heythuyzen — is still in existence.<ref name=":10" /> === Lady Cynthia Graham and Sir Richard Graham === Lady Cynthia Graham of Netherby and [[Social Victorians/People/Pless|Princess Henry of Pless]] were dressed as the Queen of Sheba and led the [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#"Oriental" Procession|"Oriental" Procession]].<ref name=":3" /><ref name=":4" />{{rp|p. 7, Col. 5b}} At this time, no photograph of Lady Cynthia Graham in this costume exists. (Lady Cynthia Graham is the Earl of Feversham's youngest daugther and Sir Richard Graham's second wife.) ==== Newspaper Accounts ==== Three actual accounts of Lady Cynthia's costume exist, two reprinted elsewhere. * Lady Cynthia Graham "was in white satin and gauze, embroidered in gold and silver and bright rose."<ref>"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." London ''Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and https://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|p. 5, Col. 7c}} * "Lady Cynthia Graham appeared as Queen of Sheba, in a robe of white Bengal satin and gauze, with embroidery of gold appliqué, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and appliqué of coloured satin, and studded with jewels; a ceinture and pendant were of white satin, with cerise appliqué and embroidery, and she wore a jewelled headdress."<ref>“The Ball at Devonshire House. Magnificent Spectacle. Description of the Dresses.” London ''Evening Standard'' 3 July 1897 Saturday: 3 [of 12], Cols. 1a–5b [of 7]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000183/18970703/015/0004.</ref>{{rp|p. 3, Col. 3c}} * "Lovely Lady Cynthia Graham was one [Queen of Sheba], in white satin embroidered in gold and silver and bright rose."<ref>“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.</ref>{{rp|42, Col. 1b}} * According to the ''Carlisle Patriot'', reprinting the ''Evening Standard'' description (perhaps because Lady and Lord Graham were local), "Lady Cynthia Graham of Netherby also personated the famous Eastern Queen, wearing a lovely robe of white Bengal satin and gauze, with embroidery of gold applique, satin white and cerise. The manteau was of crepon de chine, covered with embroidered gauze and applique of coloured satin, and studded with jewels; a ceinture and pendent were of white satin, with cerise applique and embroidery, and she wore a jewelled headdress."<ref>"Fancy Dress Ball: Unparalleled Splendour." ''Carlisle Patriot'' Friday 9 July 1897: 7 [of 8], Col. 4a–b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000365/18970709/084/0007.</ref> * "The other Queen of Sheba, who was Lady Cynthia Graham, was charmingly attired in white and silver and rose red."<ref>“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|p. 32, Col. 2c}} Lady Cynthia Graham's original costume appeared in the Drury Lane production of ''The White Heather''.<ref>"The Morning’s News." London ''Daily News'' 18 September 1897, Saturday: 5 [of 8], Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970918/027/0005.</ref> [[File:Sir Edward John Poynter - The visit of the Queen of Sheba to King Solomon - Google Art ProjectFXD.jpg|thumb|alt=Large oil painting showing a woman climbing some shallow steps to a man standing at the top in a commanding pose, both dressed in flowing robes|Sir Edward Poynter, ''The Visit of the Queen of Sheba to King Solomon'']] ==== The Queen of Sheba ==== Stories about the Queen of Sheba appear in Jewish, Christian and Islamic traditions. She visited King Solomon with gifts and tested his wisdom. Sir Edward John Poynter's 1890 ''The Visit of the Queen of Sheba to King Solomon'' (right) is in the collection of the Art Gallery of New South Wales, which accessioned it in 1892, so it would have been available for viewing until then. The Queen of Sheba's clothing here, such as there is of it, is unlikely to have been an original for the costumes worn by Lady Cynthia Graham or Daisy, Princess Pless, but her headdress has some similarities to the one worn by [[Social Victorians/People/Goelet|May Goelet]] dressed as Scheherazade. == Demographics == === Nationality === *British === Residences === * Lady Cynthia and Sir Richard Graham: Netherby Hall in the Carlisle district of Cumbria (which is why the ''Carlisle Patriot'' coverage is so thorough)<ref>{{Cite journal|date=2021-05-08|title=Arthuret|url=https://en.wikipedia.org/w/index.php?title=Arthuret&oldid=1022099353|journal=Wikipedia|language=en}} [[wikipedia:Arthuret|https://en.wikipedia.org/wiki/Arthuret#Netherby Hall]].</ref> == Family == *Charles Duncombe, 1st Baron Feversham of Duncombe Park (5 December 1764 – 16 July 1841)<ref name=":8">"Charles Duncombe, 1st Baron Feversham of Duncombe Park." {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25757|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> *Lady Charlotte Legge ( – 5 November 1848)<ref>"Lady Charlotte Legge." {{Cite web|url=https://www.thepeerage.com/p2576.htm#i25758|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> #Hon. Frances Duncombe (– 15 June 1881) #Hon. Louisa Duncombe ( – 18 November 1852) #Charles Duncombe (1795 – 1819) #'''William Duncombe, 2nd Baron Feversham of Duncombe Park''' (14 January 1798 – 11 February 1867) #Reverend Henry Duncombe (25 August 1800 – 1 October 1832) #Admiral Hon. Arthur Duncombe (24 March 1806 – 6 February 1889) #Very Rev. Augustus Duncombe (2 November 1814 – 26 January 1880) #Hon. Octavius Duncombe (8 April 1817 – 3 December 1879) *William Duncombe, 2nd Baron Feversham of Duncombe Park (14 January 1798 – 11 February 1867)<ref name=":9">"William Duncombe, 2nd Baron Feversham of Duncombe Park." {{Cite web|url=https://www.thepeerage.com/p1242.htm#i12415|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> *Lady Louisa Stewart ( – 5 March 1889)<ref>"Lady Louisa Stewart." {{Cite web|url=https://www.thepeerage.com/p1348.htm#i13478|title=Person Page|website=www.thepeerage.com|access-date=2020-11-23}}</ref> #Hon. Gertude Duncombe ( – 24 February 1916) #Hon. Jane Duncombe ( – 3 April 1901) #Hon. Helen Duncombe ( – 22 November 1896) #Hon. Albert Duncombe (11 February 1826 – 14 September 1846) #'''William Ernest Duncombe, 1st Earl Feversham of Ryedale''' (28 January 1829 – 13 January 1915) #Hon. Cecil Duncombe (27 May 1832 – 20 May 1902) *William Ernest Duncombe, 1st Earl of Feversham (28 January 1829 – 13 January 1915)<ref name=":6">"William Ernest Duncombe, 1st Earl of Feversham of Ryedale." {{Cite web|url=https://thepeerage.com/p1873.htm#i18721|title=Person Page|website=thepeerage.com|access-date=2020-11-22}}</ref> *Mabel Violet Graham Duncombe (15 February 1833 – 28 August 1915)<ref name=":0" /> #Lady Ulrica Duncombe (1874? [based on presentation at Queen's drawing-room May 1892] – 27 April 1935) #William Reginald Duncombe, [[Social Victorians/People/Helmsley | Viscount Helmsley]] (1 August 1852 – 24 December 1881) #Hon. James Henry Duncombe (20 October 1853 – 10 January 1886) #Hon. Hubert Ernest Valentine Duncombe (14 February 1862 – 21 October 1918) #Lady Hermione Wilhelmina Duncombe (30 March 1864 – 19 March 1895) #'''Lady Helen Venetia Duncombe''' (1866 – 16 May 1954) #'''Lady Cynthia (Mabel Cynthia) Duncombe''' (1869 – 25 April 1926) *Lady Helen Venetia Duncombe ( – 16 May 1954)<ref name=":1" /> *Edgar Vincent, 1st and last Viscount D'Abernon (19 August 1857 – 1 November 1941)<ref name=":2" /> * Sir Richard James Graham, 4th Bt. (24 February 1859 – 26 August 1932)<ref>"Sir Richard James Graham, 4th Bt.." {{Cite web|url=https://thepeerage.com/p7148.htm#i71471|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> * Olivia Baring (14 May 1863 – 21 March 1887)<ref>"Olivia Baring." {{Cite web|url=https://thepeerage.com/p7148.htm#i71472|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> * Lady Cynthia (Mabel Cynthia) Duncombe (1869 – 25 April 1926)<ref>"Lady Mabel Cynthia Duncombe." {{Cite web|url=https://thepeerage.com/p1604.htm#i16038|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> *# Lt.-Col. Sir Fergus Frederick Graham, 5th Bt. (10 March 1893 – 1 August 1978) *# Richard Preston Graham-Vivian (10 August 1896 – 30 September 1979) *# Daphne Graham (17 March 1903 – ) *Charles William Reginald Duncombe, 2nd Earl of Feversham (8 May 1879 – 15 September 1916)<ref name=":7">" Charles William Reginald Duncombe, 2nd Earl of Feversham of Ryedale." {{Cite web|url=https://thepeerage.com/p2288.htm#i22880|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> *Marjorie Blanche Eva Greville Duncombe (25 October 1884 – 25 July 1964)<ref>"Lady Marjorie Blanche Eva Greville." {{Cite web|url=https://thepeerage.com/p2289.htm#i22881|title=Person Page|website=thepeerage.com|access-date=2020-11-23}}</ref> #Lady Mary Diana Duncombe (19 March 1905 – October 1943) #Charles William Slingsby Duncombe, 3rd Earl of Feversham (2 November 1906 – 4 September 1963) #Hon. David William Ernest Duncombe (8 February 1910 – September 1927) == Also Known As == *Family name: Duncombe *Earl Feversham of Ryedale **William Ernest Duncombe, 1st Earl of Feversham (25 July 1868 – 13 January 1915)<ref name=":6" /> **Charles William Reginald Duncombe, 2nd Earl of Feversham (13 January 1915 – 15 September 1916)<ref name=":7" /> *[[Social Victorians/People/Helmsley | Viscount Helmsley]] **William Ernest Duncombe (25 July 1868 – 1881)<ref name=":6" /> **Charles William Reginald Duncombe, 2nd Earl of Feversham (24 December 1881 – 13 January 1915)<ref>{{Cite journal|date=2020-09-12|title=Charles Duncombe, 2nd Earl of Feversham|url=https://en.wikipedia.org/w/index.php?title=Charles_Duncombe,_2nd_Earl_of_Feversham&oldid=978075739|journal=Wikipedia|language=en}}</ref> *Baron of Feversham **William Ernest Duncombe (11 February 1867 – )<ref name=":6" /> *Baron Feversham of Duncombe Park **Charles Duncombe, 1st Baron Feversham of Duncombe Park ( – 16 July 1841)<ref name=":8" /> **William Duncombe, 2nd Baron Feversham of Duncombe Park (16 July 1841 – 11 February 1867)<ref name=":9" /> *Other [[Social Victorians/People/Duncombe | Duncombe]] families existed as well. == Questions and Notes == #The newspapers call the Earl and Countess Feversham ''Lord and Lady Feversham''. #The ''Times'' article lists Sir R. and Lady C. Graham<ref name=":3" />: if Lady C. Graham is Lady Cynthia, then Sir R. Graham is Sir Richard James Graham. #Also present at the ball and accounted for on the [[Social Victorians/People/Duncombe | Duncombe page]] are the following: Alicia Duncombe, Lady and Mr. Florence Duncombe. #Present at other social events and not accounted for were the following: Caroline Duncombe and the Misses Duncombe. #William Duncombe, 1st Earl of Feversham is #443 on the [[Social Victorians/1897 Fancy Dress Ball#List of People Who Attended|list of people who attended]] the Duchess of Devonshire's 2 July 1897 fancy-dress ball; Mabel, Countess Feversham is #444; Lady Helen Vincent is #215; Sir Edgar Vincent is #226; Sir Edgar Vincent is #226; Lady Cynthia Graham of Netherby is #220; Sir Richard James Graham is #464. == Footnotes == {{reflist}} kprbsuwoezkog119s11bj5uu8a44ciu Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts 0 264048 2683996 2637242 2024-11-11T21:30:28Z Scogdill 1331941 /* "Oriental" Procession */ 2683996 wikitext text/x-wiki =The Processions and Quadrilles= After they arrived and had been greeted by the 20-year old [[Social Victorians/People/William Angus Drogo Montagu|William, Duke of Manchester]] (grandson of [[Social Victorians/People/Louisa Montagu Cavendish|Louisa, Duchess of Devonshire]]) at the bottom of the famous Devonshire House stairs and the Duke and Duchess of Devonshire at the top, the Royals led the processions into "the White and Gold Saloon," where a dais had been set up for them.<ref name=":0">"Fancy Dress Ball at Devonshire House." ''Morning Post'' Saturday 3 July 1897: 7 [of 12], Col. 4A–8 Col. 2B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970703/054/0007.</ref>{{rp|p. 7, Col. 4c?}} Once the Royals were on the dais, the processions began, perhaps followed by or perhaps including the quadrilles. The ''Gentlewoman'' emphasized the "Oriental" procession, which was the first to be presented (the newspapers used the word ''Oriental'' to refer to what we would now think of as the Middle East and northern Africa as well as what we would now call ''Asian''): <blockquote>First came the Oriental queens, headed by the Duchess of Devonshire herself, who was accompanied by the Duke, as Charles V. of Germany, in black velvet and furs. Among the most magnificent of the Oriental personages was Princess Henry Pless, who, as the Queen of Sheba, was gorgeous to behold. Her dress was of purple and gold-shot gauze, bodice and skirt embroidered nearly to the knees, the train being one mass of jewels encrusted in gold. An Assyrian headdress, with clusters of diamonds over each ear, jewelled feathers, and chains of diamonds and turquoises, which were attached to armlets from shoulder to wrist, completed a costume of dazzling splendour. The other Queen of Sheba, who was Lady Cynthia Graham, was charmingly attired in white and silver and rose red. There were also two Cleopatras — Lady de Grey was one mass of beautiful embroideries, and Mrs. Arthur Paget looked her character to the life, and her jewels were quite the most magnificent in the room. Mr. Gerald Paget walked beside her, attired very effectively as Mark Antony. Among the gods and goddesses was Titania, the Queen of the Fairies; Lady Westmorland who made the prettiest Hebe; the Furies, Lady Lurgan and Lady Sophie Scott; and Lady Archibald Campbell, who elected to appear as Diana.<br /><br />Then came the processions of the various Courts, who afterwards formed into separate quadrilles.<ref name=":8">“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' Saturday 10 July 1897: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|p. 32, Col. 2c}}</blockquote> The reports in the ''Times'' and the ''Gentlewoman'' agree that first the processions were presented to the Prince and Princess of Wales, and then the quadrilles were danced in front of the royals.<ref name=":5" />{{rp|p. 12, Col. 1a}} Dancing quadrilles was a custom at other fancy-dress balls or costume parties as well. (One type of quadrille is the American square dance.) Not everyone was part of a procession, but the quadrilles, some of which had been rehearsed at least to some degree, seem usually to have been smaller groups of people. == The Courts == The processions were made up of the members of the "Courts" of the various monarchs, particularly queens, as well as other groups not led by the 4 queens identified by the ''Times''. The first procession was the "Oriental" one, which included [[Social Victorians/People/Louisa Montagu Cavendish|Louisa, Duchess of Devonshire]] as Zenobia, the Queens of Sheba and the Cleopatras. This procession was followed by the goddesses and gods. Contrasting this ball with the fancy-dress ball hosted by the Prince and Princess of Wales at Marlborough House on 22 July 1874, the ''Times'' says,<blockquote>the innovation of yesterday was the idea of different Courts headed by various well-known ladies and attended by their friends as Princes and courtiers. The Royal party itself fell in very readily with this idea, and attended in historical and mostly Royal costumes of the 16th century. There were four Courts strictly so-called, besides two groups which were separately arranged, but which are only to be called Courts by an extension of the term. The four were the Elizabethan Court, headed by Lady Tweedmouth as Queen Elizabeth with Sir Francis Jeune as Lord Chief Justice, Lord Arran a Cardinal, and [Col. 1a / Col. 1b] Lord Rowton as Archibishop Farrer; the Louis XV. and XVI. Court, with Lady Curzon as Queen Marie Leczinska and Lady Warwick as Marie Antoinette; the Court of Maria Theresa with Lady Londonderry as the Empress, Lord Lansdowne as Prince Kaunitz, and Lady Lansdowne as Lady Keith; and the Court of the Empress Catherine II of Russia, its Imperial centre being Lady Raincliffe. Of equal importance with these Courts were the group of Orientals and the Italian procession, the chief members of the former being the hostess herself, the Duchess of Devonshire as Zenobia, Lady de Grey as Lysistrate, and Lady Cynthia Graham as the Queen of Sheba; while the latter, which covered not only the great period of Italian art but the 17th century as well, was made illustrious both by the beauty of the dresses and by the great distinction of many of those who wore them.<ref name=":5" />{{rp|p. 12, Col. 1a–2b}}</blockquote> Referencing the article on the ball in the ''Times'', both the ''Westminster Gazette'' and the London Evening ''Mail'' say, <blockquote>THE VARIOUS "COURTS." It is twenty-three years (the ''Times'' continues) since a ball of similar design and magnificence was given. We are referring to the famous ball at Marlborough House on July 22, 1874. In one respect there was a considerable difference, for, whereas the Prince of Wales's ball had a number of distinct quadrilles — a Venetian quadrille, a Vandyck quadrille, and a pack-of-cards quadrille — the innovation of yesterday was the idea of different Courts headed by various well-known ladies and attended by their friends as princes and courtiers. ... The dancing was of the most desultory description. In the quadrilles people did their best to vie with the old-fashioned courtliness and grace. Some of their courtesies were quite beautifully done. In the procession everyone saluted the Princess of Wales in appropriate style. The Orientals spread out their hands in the impressive Oriental manner; the gods struck the ground with their sticks, and so on.<ref>“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 2–3}} <ref name=":9">“Ball at Devonshire House.” Evening ''Mail'' 05 July 1897 Monday: 8 [of 8], Col. 1a–4c [of 6]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003187/18970705/070/0008.</ref>{{rp|p. 8, Col. 1a–b}} </blockquote>A report in ''Truth'' emphasizes the queens among the costumed guests. Framed as a letter to "Amy" and referring obliquely to the extensive newspaper coverage of the ball, the report begins,<blockquote>DEAREST AMY, — The historic and fancy ball at Devonshire House outshone, as the moon the stars, every other social event of the week. I must try to describe some of the dresses for you, and am sending a sheaf of newspapers from which you will gather some idea of the splendour of the occasion. In tissue of silver and cloth of gold, and richly jewelled from head to foot, stood the stately Zenobia, Duchess of Devonshire, at the head of her marble stairway, to receive her guests of all the ages: queens who had stepped out of history to grace the scene, queens from the idyllic stories of the long ago, queens from ancient Persia and Abyssinia, and queens from Fairyland. Was not Titania there herself, with glittering wings and lily-wand? And the beautiful fair-haired queen, before whom all bent and performed obeisance as she passed, fair Marguerite de Valois, in gleaming snowy satin and high lace collar, with silver-lined train of cloth of gold, was she not our own Princess, the Queen of Hearts?<ref name=":10" /></blockquote>The Princess of Wales was "our own Princess, the Queen of Hearts." Titania "with glittering wings and lily-wand" may have been one of three women: # [[Social Victorians/People/Arthur Stanley Wilson#Jack and Susanna Wilson Graham Menzies|Susannah Wilson Graham Menzies]], whose costume included "an immense spray of white lilies"<ref name=":1" />{{rp|p. 5, Col. 7b}} as a kind of very large wand or staff; her costume does not, however, seem to have wings. # [[Social Victorians/People/Murray#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Mary Graham Murray]]: neither wings nor wand is mentioned in the scant coverage in the press of her costume.<ref name=":8" /> # [[Social Victorians/People/de Alcalo Galiano#Mademoiselle de Alcalo Galiano|Mademoiselle de Alcalo Galiano]], whose portrait is in the album, although no newspaper descriptions of her costume exist at this time. What Mademoiselle de Alcalo Galiano is wearing on her shoulders could be interpreted as glittering wings, perhaps, but no wand or lilies are present in the portrait, and because her photographer was Bassano, other poses or images of her in costume do not seem to exist at this time. The ''Western Gazette'' describes the quadrilles and processions in the introduction of its story on the ball:<blockquote>The most sumptuous epochs of the most sumptuous Courts were represented, and that with a dazzling completeness which made the times live again all their glitter of precious stuffs, of gold brocades, and imposing arrays of jewels beyond price. There was a noble diversity, yet a satisfying consistency, for the main theory was to reproduce the Courts of princes famous for their love of sumptuary display, and notably the reign of Queen Elizabeth, as perhaps the richest in brave apparel, with the contemporaneous outlook of the French and Spanish Courts of the same era, and these afforded every opportunity for gorgeous display. It might be said that as a panorama of historical costume on these lines no such opportunity has ever occurred of seeing and realising the glories of dress, and the consistent reproduction of historical personages in all their traditional bravery to the fullest advantage.<ref name=":2">"The Duchess of Devonshire's Great Ball. Remarkable Social Function. Crowds of Mimic Kings & Queens. Panorama of Historical Costume. An Array of Priceless Jewels." ''Western Gazette'' 9 July 1897: 2 [of 8], Col. 7A–C. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000407/18970709/009/0002.</ref>{{rp|p. 2, Col. 7a}}</blockquote> === How the Courts Were Organized === The suggestion that some of the women form courts, which may have come from the Duchess of Devonshire herself,<ref>Wilson, Verity. ''Dressing Up: A History of Fancy Dress in Britain''. Reaktion, 2022: 62.</ref> caused the ball to be visually organized in a way that it would not have been otherwise, because so many of the costumes were from the same time periods. Dressing as a queen was not only not unusual, but, at the many fancy-dress balls and Gothic revival tournaments, “One of the most common costumes for a lady of the Victorian period was … that of a Queen.”<ref>Thrush, Nanette. "Clio's Dressmakers: Women and the Uses of Historical Costume." In Meaghan Clarke, ed. ''Fashionability, Exhibition Culture and Gender Politics: Fair Women''. Routledge, 2020: 258-277.</ref>{{rp|270}} There were actual royals present — the Prince of Wales and his family as well as expatriate royals living in London and dignitaries from the Empire. Put on the dais and the object of formal presentations by the processions and quadrilles, [[Social Victorians/1897 Fancy Dress Ball/Quadrilles Courts#The Royals On the Dias|the actual royals]] mostly did not assert their royalty fictionally. The highest fictional rank among the royals was Alexandra, Princess of Wales, who was dressed as Marguerite de Valois. The total number of women dressed as queens is large but, according to the ''Times'', only 4 defined the courts, "strictly so-called."<ref name=":5" />{{rp|p. 12, Col. 1a–2b}} The first 4 — Marie Thérèse of Austria, Catherine II of Russia, Marie Antoinette and Queen Elizabeth — were the most important and organized in the ball, and their "courts" accounted for many of the other guests who attended. Of the 700 or so people who attended the ball, 134–137 are accounted for by the first 4 queens and 263–267 by all the various kinds of courts, processions and quadrilles. (The numbers of people in the various courts are not perfectly stable: not all the newspapers that treat the courts agree on who was in them; these numbers are based on the typeset visualizations in the ''Morning Post''.) Just because of chance and the individual choice of whom to personate, many of the others at the ball who came as individuals or part of much smaller groups and who were not in processions would have contributed to the number of people dressed in that time period and looking as if they could have been part of the courts. A large number of individuals, including almost all the royals ('''check Princess Louise, Faust costume, opera?'''), were also in Elizabethan dress. The ''Western Gazette'' says that "the French and Spanish Courts [were] of the same era."<ref name=":2" />{{rp|p. 2, Col. 7a}} These additional costumes from the time periods of the major courts probably made the ball look more coherent, although one newspaper account describes the effect of random and unrelated people seen side by side in conversation ('''find this'''). Also, individuals dressed as ancestors represent belonging to a kinship group rather than a social network of friends. Nearly fifty women came as historical, Biblical, and occasionally fictional queens, empresses and other regents. They were # [[Social Victorians/People/Louisa Montagu Cavendish|Louise, Duchess of Devonshire]], dressed as Zenobia, Queen of Palmyra and functioning as an individual, maybe but not probably part of the "Oriental" procession # [[Social Victorians/People/Tweedmouth|Fanny Marjoribanks, Lady Tweedmouth]], dressed as Elizabeth, Queen of England and leading 40 people # Theresa Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry|Marchioness of Londonderry]], dressed as Marie Thérèse of Austria, Queen and Holy Roman Empress and leading a procession of between 34 and 37 people # Grace Denison, [[Social Victorians/People/Londesborough|Viscountess Raincliffe]], dressed as Catherine II, Queen of Russia and leading the Russia procession of 31 people plus trumpeters and "Black Attendants" # [[Social Victorians/People/Warwick|Daisy, Countess Warwick]], dressed as Marie Antoinette, Queen of France and leading 29 Louis XV and XVI royals and courtiers, not counting pages # [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], dressed as Marguerite de Valois and with a court of 7 or 8 people, all family members, plus 2 attendants # [[Social Victorians/People/Mar and Kellie|Violet, Countess of Mar and Kellie]], dressed as Beatrice and leading the Venetians procession of 47 people # [[Social Victorians/People/Gerard|Lady Mary Gerard]], dressed as Astarte, Goddess of the Moon, not exactly a queen but in this list because she led the 7-person procession of goddesses from mythology # [[Social Victorians/People/Zetland|Lilian, Marchioness of Zetland]], dressed as Henrietta Maria, Queen of Charles I of England and leading 12 people in the courts of Charles I and Charles II # Elizabeth [[Social Victorians/People/Ormonde|Butler]], the [[Social Victorians/People/Ormonde|Marchioness of Ormonde]], dressed as Queen Guinevere and leading 21 people in the Knights of the Table of King Arthur procession #[[Social Victorians/People/Rodney|Corisande Evelyn Vere, Lady Rodney]], dressed as Queen Guinevere, was not listed as being in the procession; she attended with her husband, who was dressed as King Arthur. #Daisy Cornwallis-West, [[Social Victorians/People/Pless|Princess Henry of Pless]], dressed as Queen of Sheba and leading a procession of “Oriental” queens (23 people) with Lady Cynthia Graham #[[Social Victorians/People/Feversham|Lady Cynthia Graham]], dressed as Queen of Sheba and leading a procession of “Oriental” queens (23 people) with Daisy, Princess Henry of Pless #Katherine Osborne, [[Social Victorians/People/Leeds|Duchess of Leeds]], not a queen but in this list because she led the 17-person procession of Duchesses with Georgina, Dowager Countess of Dudley #Georgina, [[Social Victorians/People/Dudley|Dowager Countess of Dudley]], not a queen but in this list because she led the 17-person procession of Duchesses with Katherine, Duchess of Leeds # [[Social Victorians/People/Paget Family|Lady Minnie Paget]], dressed as Cleopatra in the "Oriental" procession; attended with her husband and her brother-in-law, who was dressed as Marc Anthony # [[Social Victorians/People/Gwladys Robinson|Gwladys Robinson]], Marchioness of Ripon (when Countess de Grey), dressed as Cleopatra #[[Social Victorians/People/Newcastle|Kathleen Pelham-Clinton, Duchess of Newcastle]], dressed as Princess Dashkova # [[Social Victorians/People/Connaught|Princess Louise, Duchess of Connaught]], dressed as Anne of Austria, Queen of France # [[Social Victorians/People/Francis Duke of Teck|Princess Mary Adelaide, Duchess of Teck]], dressed as Princess Sophia Electress of Luneberg and Hanover, mother of George I # Madame [[Social Victorians/People/Baudon de Mony|Baudon de Mony]], dressed as Princess of Navarre # [[Social Victorians/People/Santurce|Jesusa Murrieta del Campo Mello y Urritio, Marquisa de Santurce]], dressed as the Infanta of Spain # [[Social Victorians/People/Clary Aldringen|Thérèse née Kinsky, Countess Clary-Aldringen]], dressed as the Queen of Naples, Napoleon's sister # [[Social Victorians/People/Kinsky|Princess of Löwenstein-Wertheim-Rosenberg]], née Countess Josephine Kinsky, dressed as Princess Pauline Borghese, Napoleon's sister # [[Social Victorians/People/Fitzgerald|Amelia, Lady Fitzgerald]], dressed as Marie Joséphe, Queen of Poland, A.D. 1737 # [[Social Victorians/People/Jersey|Margaret Child-Villiers, Countess of Jersey]], dressed as Anne of Austria, Queen of France # [[Social Victorians/People/Katharine Mary Montagu Douglas Scott|Katharine Montagu-Douglas-Scott]], dressed as Marie Stuart, Mary Queen of Scots # [[Social Victorians/People/Minto|Mary, Countess of Minto]], dressed as '''Princess Andrillon''' # [[Social Victorians/People/Muriel Wilson|Muriel Wilson]], dressed as Queen Vashti # [[Social Victorians/People/Tweeddale|Candida Louise, Marchioness of Tweeddale]], dressed as Empress Josephine # Aileen, Countess of Meath, dressed as Queen Hortense # [[Social Victorians/People/Buckingham and Chandos|Alice, Duchess of Buckingham and Chandos]], dressed as Caterina Cornaro, Queen of Cyprus # [[Social Victorians/People/Lathom|Alice, Countess of Lathom]], dressed as Catherine of Aragon # [[Social Victorians/People/Leslie|Leonie Blanche Jerome, Lady Leslie]], dressed as Brunhild # Helena, Countess of Stradbroke, dressed as Delilah # Ethel, Lady Knaresborough, dressed as Elizabeth, Queen of Bohemia # [[Social Victorians/People/Churchill|Jennie, Lady Randolph Churchill]], dressed as Empress Theodora, wife of Justinian # [[Social Victorians/People/Essex|Adela, Countess of Essex]], dressed as Berenice, Queen of Palestine # Hon. Julia Beatrice Maguire, dressed as Dido, Queen of Carthage # [[Social Victorians/People/Bischoffsheim|Clarisse Bischoffsheim]], dressed as Anne of Austria, queen with Louis XIII of France # [[Social Victorians/People/de Trafford|Violet, Lady de Trafford]], dressed as Semiramis, Queen of Assyria # [[Social Victorians/People/Hartopp|Millicent, Lady Cradock-Hartopp]], dressed as the Empress Josephine # [[Social Victorians/People/Cadogan|Beatrix, Countess Cadogan]], dressed as Elizabeth, Queen of Bohemia # [[Social Victorians/People/Somerset|Susan Margaret, Duchess of Somerset]], dressed as Jane, Queen of England, wife to King Henry VIII and mother of King Edward VI # [[Social Victorians/People/Ampthill|Emily Theresa, Lady Ampthill]], dressed as the Princess de Lamballe # [[Social Victorians/People/Gordon-Lennox|Blanche, Lady Gordon-Lennox]], dressed as the Princess de Lamballe # [[Social Victorians/People/Dudley|Rachel, Countess of Dudley]], dressed as Queen Esther # Mademoiselle de Alealo Galiano, dressed as the Queen of the Fairies # Susannah Graham Menzies, dressed as Titania, Queen of the Fairies Some women came as goddesses: # [[Social Victorians/People/de Courcel|Marie, Baroness de Courcel]], dressed as Night # Florence, Lady Terence Blackwood, dressed as Flora Goddess of Flowers # Probably (Sybil Aimée) Geraldine Webber (née Magniac), dressed as Dawn # [[Social Victorians/People/Fanny Ronalds|Fanny Ronalds]], dressed as Euterpe # [[Social Victorians/People/Borthwick|Alice, Lady Glenesk]], dressed as Egeria # [[Social Victorians/People/Gosford|Louisa Augusta Beatrice (née Montagu), Countess of Gosford]], dressed as Minerva (period of Louis XV) # [[Social Victorians/People/Westmorland|Sybil Mary (née St Clair-Erskine), Countess of Westmorland]], dressed as Hebe # [[Social Victorians/People/Gerard|Mary Emmeline Laura (née Milner), Lady Gerard]], dressed as Astarte, Goddess of the Moon # [[Social Victorians/People/Hope-Vere|Marie Elizabeth Françoise Hope-Vere]] (née Guillemin), dressed as Medusa # [[Social Victorians/People/Herschell|Agnes Adela (née Kindersley), Lady Herschell]], dressed as Night # Dorothy Blanche ('Doreen', née Boyle), Viscountess Long, dressed as Urania, Goddess of Astronomy # [[Social Victorians/People/Wolverton|Edith Amelia (née Ward), Lady Wolverton]], dressed as Britannia # [[Social Victorians/People/Stanley#Lord Stanley and Lady A. Stanley|Lady Alice Stanley]], dressed as Diana Men also came as kings and emperors: # [[Social Victorians/People/Spencer Compton Cavendish|Spencer Compton, Duke of Devonshire]], dressed as the Emperor Charles V # [[Social Victorians/People/Boulatzell|N. Boulatzell]], dressed as Prince of Mingrelia # [[Social Victorians/People/Wolverton|Frederic Glyn, 4th Baron Wolverton]], dressed as King Richard Coeur de Lion # [[Social Victorians/People/Duleep Singh|Prince Victor Albert Jay Duleep Singh]], dressed as Akbar # [[Social Victorians/People/Londonderry#Castlereagh|Charles Stewart Henry Vane-Tempest-Stewart, 7th Marquess of Londonderry]] when Viscount Castlereagh as the Emperor Francis Joseph of Austria, dressed as # [[Social Victorians/People/Rodney|George Rodney, 7th Baron Rodney]], dressed as King Arthur of the Round Table # [[Social Victorians/People/Dunville|John Dunville]], dressed as the Emperor Yuan of China # [[Social Victorians/People/Reuben David Sassoon|Reuben David Sassoon]], dressed as a Persian Prince # [[Social Victorians/People/Crewe-Milnes|Robert Offley Ashburton Crewe-Milnes, 1st Marquess of Crewe]], dressed as Philip II of Spain # Sir Ralph Barrett Macnaghten, 9th Bt., dressed as Jerome Buonaparte, King of Westphalia # [[Social Victorians/People/Rothschild Family|Alfred Charles de Rothschild]], dressed as King Henry III # [[Social Victorians/People/Cavendish Bentinck|Lord Henry Cavendish-Bentinck]], dressed as the King of Poland # [[Social Victorians/People/Hartopp|Sir Charles Edward Cradock-Hartopp, 5th Bt.]], dressed as Napoleon I The courts or groupings are subnetworks within the network at this ball: there are other women dressed as goddesses, for example, than the ones included in the procession, suggesting that the ones who organized into groups did it based on relationships with each other than with a preference for a particular time or person. At this ball, women were “arbiters” of cultural, social and political power. Even though both the Duke and Duchess of Devonshire hosted the ball, it was and has since always been called her ball. As social organizers, they were the gatekeepers to the aristocracy, granting some admittance and denying others.<ref name=":11" /> As accomplished beauties and leaders of fashion, they were cultural arbiters.<ref>Clarke, Meaghan. ''Fashionability, Exhibition Culture and Gender Politics: Fair Women''. Routledge, 2020.</ref> Costumed as queens, they presented themselves as “makers of history."<ref>Felber, Lynette, ed. ''Clio's Daughters: British Women Making History, 1790-1899''. Associated University Presses, 2007.</ref> Their portraits taken in costume, which can be found in the National Portrait Gallery today, were a performance of wealth and privilege, and, with the identities personated, power. === The Courts in Performance === We know almost nothing about how these processions or quadrilles were formed, except that the Duchess of Devonshire may have been encouraged these women to form courts: # Theresa Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] as Marie Thérèse of Austria # Grace Denison, [[Social Victorians/People/Londesborough|Viscountess Raincliffe]], dressed as Catherine II, Queen of Russia # [[Social Victorians/People/Warwick|Daisy, Countess Warwick]], dressed as Marie Antoinette, Queen of France # [[Social Victorians/People/Tweedmouth|Fanny Marjoribanks, Lady Tweedmouth]] as Elizabeth, Queen of England We know that the groups doing quadrilles would have been expected to have rehearsed, and we know that the Elizabethan procession, at least, did do so at a dinner party the night before the ball. == The Quadrilles == "[T]he quadrilles took place" after or as part of the procession.<ref name=":0" />{{rp|p. 7, Col. 4C}} A quadrille is a choreographed "square" dance. (The very specific kind of dance called a square dance in the U.S. is a quadrille, but not all quadrilles are American square dances.) Typically, quadrilles were made up of four couples. Apparently fancy-dress balls often included quadrilles, especially those with costumes of the past and ''bals poudres'' (typically balls with 18th-century costumes and powdered hair). The ''Western Gazette'' describes the quadrilles under "The Dancing":<blockquote>The dancing was of the most desultory description. There was the Royal quadrille and there were the quadrilles danced by the Venetians, and the Russian quadrille. In the quadrilles the dancers did their best to vie with the old-fashioned courtliness and grace. Some of their courtesies were quite beautifully done. If all did not fall in with the spirit of their times it was excusable, as there were no rehearsals. Not until the chaperons and those who merely went to see had left or gone down to supper was there space for ordinary dancing, and even then so few of the dresses were fitted for the waltz and the gardens were so temptingly cool with all their coloured lights that the latter attracted the majority.<ref name=":2" />{{rp|p. 2, Col. 7c}}</blockquote> This article suggests that there was a "Royal quadrille," suggesting that the Royals danced at some point as a group, and that the people did not rehearse their quadrilles. == The Royals On the Dias == The Royals who were on the dais were likely the immediate family of the Prince of Wales, including his siblings and children as well as the Princess of Wales, but a number of people who were — or had been — royals in other countries were also present at the ball. === The Prince and Princess of Wales's Children and Their Families === *[[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] as Grand Master of the Knights Hospitalier of Malta in the court of Queen Elizabeth *[[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] as Margaret of Valois *Prince George of Wales, [[Social Victorians/People/George and Mary#George, Duke of York|Duke of York]] as George Clifford, 3rd Earl of Cumberland and thus in Elizabethan dress *Mary of Teck, [[Social Victorians/People/George and Mary#Mary, Duchess of York|Duchess of York]] as a lady in attendance on Margaret of Valois (Alexandra, Princess of Wales) *Princess Louise, [[Social Victorians/People/Fife|Duchess of Fife]] as one of the ladies of the court of Margaret of Valois (Alexandra, Princess of Wales) *Alexander Duff, [[Social Victorians/People/Fife|Duke of Fife]] as a courtier of late Elizabethan Period, the time of Henri II *[[Social Victorians/People/Prince Charles of Denmark|Maud of Wales, Princess Charles of Denmark]] accompanying the Princess of Wales as one of the ladies of the court of Margaret of Valois *[[Social Victorians/People/Prince Charles of Denmark|Prince Charles of Denmark]] accompanying the Prince and Princess of Wales as a gentleman of the Court of Denmark in the time of Elizabeth *[[Social Victorians/People/Princess Victoria of Wales|Princess Victoria of Wales]] === The Prince of Wales's Siblings and Their Families === *[[Social Victorians/People/Christian of Schleswig-Holstein|Princess Helena, or Princess Christian of Schleswig-Holstein]] as Sophia Charlotte, daughter of the Electress Sophia of Hanover and sister of George I *[[Social Victorians/People/Christian of Schleswig-Holstein|Prince Christian of Schleswig-Holstein]] as the Earl of Lincoln in the time of Elizabeth *[[Social Victorians/People/Victoria of Schleswig-Holstein|Princess Victoria of Schleswig-Holstein]], daughter of Helena and Christian of Schleswig-Holstein, as a lady or princess of the Elizabethan Court *[[Social Victorians/People/Princess Louise|Princess Louise]], Marchioness of Lorne as a character from the opera ''Faust'' or the Tudor period *John Campbell, [[Social Victorians/People/Argyll|Marquis of Lorne]] as a Tudor *[[Social Victorians/People/Connaught|Prince Arthur, Duke of Connaught and Strathearn]] as an Elizabethan military commander *[[Social Victorians/People/Connaught|Princess Louise, Duchess of Connaught]] as Ann of Austria *[[Social Victorians/People/Alfred of Edinburgh|Alfred, Hereditary Prince of Saxe-Coburg and Gotha]], nephew of the Prince of Wales and son of Alfred of Edinburgh and Grand Duchess Maria Alexandrovna Romanova, as Duke Robert of Normandy, A.D. 1060 Many of these costumes are from the Elizabethan period, but the royals wearing them would not have been in the Elizabethan procession or quadrille. One newspaper report noticed this as well. === Other Royals Possibly on the Dais === These people were closely related but not of Victoria's immediate family and thus perhaps not eligible for the same obeisances? So perhaps they were not on the dais. Also, they are not listed as having marched in a procession or danced in a quadrille. * [[Social Victorians/People/Francis Duke of Teck|Francis, Duke of Teck]] as Capitaine Garde du Roi, 1660 * Princess [[Social Victorians/People/Francis Duke of Teck|Mary Adelaide, Duchess of Teck]] as Princess Sophia, Electress of Luneburg and Hanover * Prince [[Social Victorians/People/Francis Duke of Teck|Alexander of Teck]] as a Dragoon Guard with a blue coat, Queen Anne's period * Prince [[Social Victorians/People/Francis Duke of Teck|Francis of Teck]] as a Dragoon Guard with a red coat, Queen Anne's period * Prince [[Social Victorians/People/Francis Duke of Teck|Adolphus of Teck]] ==Processions== Speaking of the processions before the [[Social Victorians/People/Albert Edward, Prince of Wales|Albert Edward, Prince of Wales]] and [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]] the ''Morning Post'' describes the scene:<blockquote>One after the other they entered by one door, advanced up the middle of the ball room, made obeisance, and left by another door. Those who did not belong to any particular group lined the room and crowded the doorways. After this the quadrilles took place.<ref name=":0" />{{rp|7, Col. 4C}}</blockquote>The ''Graphic'' published an illustration by W. Hatherell and J. Gulich showing a member of one of the processions bowing before the Prince and Princess of Wales, who is inclining her head in return. The guest has two train-bearers who look like children, which if this illustration is true to life means that the woman bowing is probably ("Duchess of Devonshire's Costume Ball, The: The Procession of Guests Bowing to the Royal Group in the White and Gold Saloon. Drawn by W. Hatherell and J. Gulich." The Graphic 10 July 1897: 17–18 [of 34]. [https://www.britishnewspaperarchive.co.uk/viewer/BL/0000057/18970710/021/0017?browse=true https://www.britishnewspaperarchive.co.uk/viewer/BL/0000057/18970710/021/0017].) It seems that the processions came in to the White and Gold Saloon and then formed in front of the Royals to do their quadrilles, so any group might be called a procession or a quadrille, depending on what exactly they did. According to the ''Morning Post'', which in this list apparently mixes up "courts" and processions, "The following processions were formed shortly after the assembling of the guests, and passed through the ball-room": # "Oriental" (their word for it, and repeated twice more later in the list) # Goddesses and gods #Duchess # Venetians # Austrian # Russian, led by the "Trumpeters of the Imperial Guard" # Louis XVI # Elizabethan The ''Morning Post'' story highlighted the "Oriental" procession, which was the first procession to dance before the Prince and Princess of Wales. The story in the ''Gentlewoman'' also emphasizes this procession by listing it first and describing it in detail. Also, the ''Morning Post'' article attempted to illustrate how people were arranged in the processions by the way their names were typeset. The ''Times'' listed people in the various processions and courts, but did not attempt a typeset visualization the way the ''Morning Post'' did. === "Oriental" Procession === What the newspapers called the "Oriental" procession was "the Oriental Queens of an era previous to Christianity, with their suites," who were permitted to assemble in a different place than everybody else before leading the rest of the processions and quadrilles.<ref>“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|5, Col. 2c}} <ref name=":8" />{{rp|32, Col. 2a}} One newspaper, the ''Times'', says that [[Social Victorians/People/Louisa Montagu Cavendish|Louisa, Duchess]] and [[Social Victorians/People/Spencer Compton Cavendish|Spencer Cavendish, Duke of Devonshire]] took part in the "Oriental" group.<ref name=":5" />{{rp|Col. 1b}} The ''Gentlewoman'' says,<blockquote> First [to present themselves to the Royals] came the Oriental queens, headed by the Duchess of Devonshire herself, who was accompanied by the Duke, as Charles V. of Germany, in black velvet and furs.<ref name=":8" />{{rp|32, Col. 2c}}</blockquote> This sentence from the ''Daily Telegraph'' occurs at the end of the description of the Duchess of Devonshire's costume, suggesting but not saying that the "Oriental" queens got this special treatment because she was one of them:<blockquote>Masters of the Ceremonies in Louis Seize military uniforms passed the guests through into inner rooms, only the Oriental Queens of an era previous to Christianity, with their suites, assembling in the white and gold saloon, with its fine pictures in the panels, and brilliantly-lighted by hundreds of wax candles in crystal chandeliers, as were all the rooms.<ref>“Historic Ball at Devonshire House. Brilliant Scene.” The ''Daily Telegraph'' 3 July 1897, Saturday: 9 [of 14], Col. 6a–7c [of 7]. ''British Newspaper Archive''  https://www.britishnewspaperarchive.co.uk/viewer/bl/0001112/18970703/094/0009.</ref>{{rp|9, Col. 6a}}</blockquote> The people in the "Oriental Procession" assembled in the white-and-gold saloon.<ref name=":8" />{{rp|32, Col. 2a}} The presentations to the Royals took place in the saloon or ballroom, which was "particularly magnificent, being a splendid harmony of white and gold."<ref name=":8" />{{rp|32, Col. 2a}} Besides having the white-and-gold saloon in which to assemble, the queens and suites of the "Oriental Procession" lined the "centre of the saloon" for the procession of the Prince and Princess of Wales to their place on the dais. According to the ''Gentlewoman'', <blockquote>About half-past eleven the Blue Hungarian Band, which was stationed in a small ante-room, announced the Prince of Wales' arrival with the stirring strains of "God Save the Queen," and His Royal Highness led the Princess up the centre of the saloon, which was lined by ladies dressed as Oriental queens and their suites.<ref name=":8" />{{rp|32, Col. 2a}}</blockquote> Besides the account in the ''Gentlewoman'', most newspapers that mention it say the "Oriental" procession was led by Lady Cynthia Graham and [[Social Victorians/People/Pless|Daisy Cornwallis-West, Princess of Pless]], as Queens of Sheba.<ref name=":5" /> <ref name=":0" />{{rp|7, Col. 5b}} In the newspaper reports, Lady Cynthia Graham's name is listed first in spite of the Princess of Pless's higher rank. In the visualization in the ''Morning Post'', which is an enumeration, Lady Cynthia's name is first, followed by the Princess of Pless, at the same level. Then the suites of ladies and gentlemen follow, indented to show they accompanied either the Princess of Pless or, perhaps, both Queens of Sheba. ==== The Attendants for the Queens of the "Oriental" Procession ==== Some of the Duchess of Devonshire's attendants and hired staff for the ball were people of color, probably boys and men. Some of the people in attendance on some of the queens at the ball were people of color, again probably boys and men. While not all of these queens were in the "Oriental" procession, several were. ==== The "Oriental" Queens ==== ''Truth'' says that 3 women came dressed as Queen of Sheba but names only Lady Cynthia Graham and Daisy Cornwallis-West, the same 2 named by the ''Morning Post'' and ''Times'': "There were three Queens of Sheba, and Paris himself could scarcely have decided to which the apple of beauty should have been awarded."<ref name=":10" />{{rp|42, Col. 1b}} This procession included the following people: # [[Social Victorians/People/Feversham|Lady Cynthia Graham]], as the Queen of Sheba # Daisy (Mary Theresa) [[Social Victorians/People/Cornwallis-West|Cornwallis-West]], [[Social Victorians/People/Pless|Princess Henry of Pless]], as the Queen of Sheba # The Suite of Ladies following Daisy, Princess of Pless (or perhaps both the two Queens of Sheba) ## Miss West: Miss Cornwallis West, [[Social Victorians/People/Cornwallis-West|Shelagh Cornwallis-West]], as her "Ethiopian attendant"<ref name=":1" />{{rp|p. 5, Col. 7c}} ## Miss Mary [[Social Victorians/People/Goelet|Goelet]] ## [[Social Victorians/People/Westminster#Lady C. Grosvenor|Lady C. Grosvenor]] ## Miss [[Social Victorians/People/Oppenheim|Rosalinda Oppenheim]] # The Suite of Men following Daisy, Princess of Pless (less likely both the two Queens of Sheba) ## The [[Social Victorians/People/Keppel|Hon. George Keppel]], as King Solomon, in the Suite of Men following the two Queens of Sheba (Lady Cynthia Graham and Princess Henry of Pless)<ref name=":5" /><ref name=":0" />{{rp|p. 7, Col. 5b}} ## [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Wilfred Wilson]] ## [[Social Victorians/People/Portman|Arthur Portman]] ##[[Social Victorians/People/Halifax|Gordon Wood]] ## The [[Social Victorians/People/Bourke#Hon. Algernon Bourke|Hon. A. Bourke]]: Hon. Algernon Bourke ## [[Social Victorians/People/Cornwallis-West#George Cornwallis-West|George Cornwallis-West]], not mentioned in any newspaper report # [[Social Victorians/People/Duncombe|Lady Alicia Duncombe]], as a Greek Slave # [[Social Victorians/People/Bourke#Hon. Guendoline Bourke|Hon. Mrs. A. Bourke]]: Hon. Guendoline Bourke, as Salambo # Minnie Paget, [[Social Victorians/People/Paget Family|Mrs. Arthur Paget]], as Cleopatra # Gerald [[Social Victorians/People/Paget Family|Paget Paget]], likely Gerald Cecil Stewart Paget, as Marc Antony #Lady Randolph Churchill, according to the London Evening ''Mail''<ref name=":9" />{{rp|p. 8, Col. 1c}}, as Empress Theodora of Byzantium # Lady [[Social Victorians/People/de Trafford|Violet de Trafford]] #Alexandra Harriet Paget, [[Social Victorians/People/Colebrooke|Lady Colebrooke]] # Two women walking together for some reason ## Hon. Mrs. Julia [[Social Victorians/People/Peel Family|Peel Maguire]] (the ''Morning Post'' has her both in the Oriental and the Duchesses processions) ## Miss [[Social Victorians/People/Muriel Wilson#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Muriel Wilson]], as Queen Vashti # [[Social Victorians/People/Fraser#Helena Violet Alice Fraser (Miss Keith Fraser)|Miss Keith Fraser]] # Mary Charteris, [[Social Victorians/People/Charteris|Lady Elcho]] # Mrs. [[Social Victorians/People/Hope-Vere|Hope-Vere]], as Medusa The ''Morning Post'' typeset a visualization of the procession, more or less, like this: Lady Cynthia Graham .................. Queen of Sheba. Princess Pless ....................... Queen of Sheba. Miss West .................. ) Miss Goelet ................ ) Lady C. Grosvenor .......... ) Suite of Ladies. Miss Oppenheim ............. ) The Hon. G. Keppel ......... ) Wilfred Wilson ............ ) Arthur Portman ............. ) Suite of Men. Gordon Wood ................ ) The Hon. A. Bourke ......... ) Lady Alicia Duncombe ................ Greek Slave. Hon. Mrs. A. Bourke .................. Salambo. Mrs. Arthur Paget .................... Cleopatra. Gerald Paget Paget ................... Marc Antony. Lady De Trafford Hon. Mrs. Maguire ................ ) Miss Muriel Wilson ................ ) Miss Keith Fraser Lady Elcho Mrs. Hope-Vere ===Goddesses=== The women who walked in the procession of goddesses included these women listed in the ''Morning Post'' list: *[[Social Victorians/People/Gerard|Lady Mary Gerard]] (at 256), as Astarte, Goddess of the Moon *Sybil Vane, [[Social Victorians/People/Westmorland|Countess of Westmorland]] (at 219), as Hebe *[[Social Victorians/People/Lurgan|Lady Emily Lurgan]] (at 56), a Fury *[[Social Victorians/People/Cadogan|Lady Sophie Scott]] (at 57), a Fury *[[Social Victorians/People/Shrewsbury|Mrs. Talbot]] (probably not the wife of [[Social Victorians/People/Talbot|Edmund Talbot]], as two other Mrs. Talbots were there, both wives of higher ranking men) *Miss de Brienen (at 259) *[[Social Victorians/People/Leslie|Mrs. Leonie Leslie]] (at 260) went as Brunhilde in the Goddesses procession The ''Gentlewoman'' says, "Among the gods and goddesses was Titania, the Queen of the Fairies; Lady Westmorland who made the prettiest Hebe; the Furies, Lady Lurgan and Lady Sophie Scott; and Lady Archibald Campbell, who elected to appear as Diana."<ref name=":8" />{{rp|p. 32, Col. 2c}} Others dressed as goddesses — likely dressed as individuals and not part of an organized group — include the following: *Alice [[Social Victorians/People/Borthwick|Borthwick, Lady Glenesk]] (at 88) as Egeria (although Algernon Borthwick, Baron Glenesk did walk in the Elizabethan procession) *Mrs. [[Social Victorians/People/Fanny Ronalds|Fanny Ronalds]] (at 92), as Euterpe, Goddess of Music *[[Social Victorians/People/Argyll|Lady Archibald Campbell]] (at 377), as Artemis, goddess of the chase *Mrs. Susannah [[Social Victorians/People/Arthur Stanley Wilson|Wilson Graham Menzies]] (at 378), as Titania. *Lady A. Stanley: Lady Alice Maud Olivia [[Social Victorians/People/Stanley|Montagu Stanley]] (at 157) as Diana. The ''Morning Post'' typeset a visualization of the procession, more or less, like this<ref name=":0" />{{rp|p. 7, Col. 5B}}: Goddesses were: Lady Gerard. Lady Westmorland. Lady Lurgan. Lady S. [Sophie?] Scott. Mrs. Talbot. Miss de Brienen. Mrs. Leslie. ===The Duchesses Procession=== The members of this procession included the following: # Katherine Osborne, the [[Social Victorians/People/Leeds|Duchess of Leeds]] (at 35), as the fictional Persian character Lalla Rookh. While the ''Morning Post'' says she walked in the Duchesses Procession, she might have walked in the "Oriental" one instead. # [[Social Victorians/People/Dudley|Lady Dudley]]: Georgina, Dowager Countess of Dudley (at 198) # [[Social Victorians/People/Ripon|Gwladys, Countess de Grey]] (at 136), possibly as Cleopatra (according to the ''Carlisle Patriot'', she headed the "Oriental" procession, but the ''Morning Post'' visualization puts her with the Duchesses)<ref>"Fancy Dress Ball: Unparalleled Splendour." ''Carlisle Patriot'' Friday 9 July 1897: 7 [of 8], Col. 4a–b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000365/18970709/084/0007.</ref> #[[Social Victorians/People/Churchill|Lady Randolph Churchill]] (at 132), as Empress Theodora of Byzantium # Mrs. Maguire (the ''Morning Post'' has her both in the Oriental and the Duchesses processions) # [[Social Victorians/People/Adele Grant Capell|Adele Grant Capell, Countess Essex]] (at 194) # [[Social Victorians/People/Asquith|Margot Asquith]] (at 217), as a snake charmer # Mrs. Leo (at 246) # [[Social Victorians/People/Gosford|Louisa Acheson, Lady Gosford]] (at 140), as a lady in Charles V.'s Court(?) # Edith Glyn, [[Social Victorians/People/Wolverton|Baroness Wolverton]] (at 130), as Britannia # [[Social Victorians/People/Stanley|Lady Alice Maude Olivia Montagu Stanley]] (at 157) (but she seems more likely to have walked in the Goddess procession) # Mr. [[Social Victorians/People/Brassey|L. Brassey]] (at 252), as Apollo # [[Social Victorians/People/Gosford|Lady A. Acheson]] — Lady Alexandra Louise Elizabeth Acheson — (at 254), in Hunting Costume, period of Louis XV # [[Social Victorians/People/Gosford|Lord Acheson]], Archibald Charles Montagu Brabazon Acheson (at 255), as Mignon Henri III. or Raoul di Nangis # Lady J. Stanley (at 250) # W. Stanley: [[Social Victorians/People/Stanley#Lord William Stanley and Lady Alexandra Stanley|Hon. Frederick William Stanley]] (at 473), in hunting dress (period of Louis XVI) or as Chasseur à Louis XV The ''Morning Post'' typeset a visualization of the procession, more or less, like this, suggesting that everybody except Lady de Grey and Lady Wolverton was walking or perhaps dancing side by side in pairs. Duchess of Leeds. Lady Dudley. Lady de Grey. Lady Randolph Churchill. Lady Colebrooke. Mrs. Maguire. Lady Essex. Mrs. Asquith. Mrs. Leo. Lady Gosford. E. Stanley. Lady Wolverton. Lady A. Stanley. L. Brassey. Lady A. Acheson. Lord Acheson. Lady J. Stanley. W. Stanley. ===Italian Procession=== The Venetians Procession is variously called the Venetian or 17th-century or Italian Procession or Quadrille in the newspapers. This group is also made up of subgroups: the Italian Procession, the Venetians and the 17th Century, each smaller procession with its own leader. The ''Westminster Gazette'' says, "The Venetian group might indeed have been called a 'dream of fair women,' as it numbered more decidedly beautiful women than any other at the ball."<ref>“The Duchess’s Costume Ball.” ''Westminster Gazette'' 03 July 1897 Saturday: 5 [of 8], Cols. 1a–3b [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002947/18970703/035/0005.</ref>{{rp|p. 5, Col. 1}} The ''Gentlewoman'' says,<blockquote>The Venetian Court was most picturesque, led by the Duchess of Portland, who looked magnificent in white brocade embroidered with silver, a diamond crown, and ropes of diamonds and pearl, round her neck. One of the most noticeable ladies of her Court was Lady Mar and Kellie, in white and green and silver, embroidered with gold.<ref name=":8" />{{rp|p. 32, Col. 3a}}</blockquote>''Truth'' says something quite similar:<blockquote>The Venetian group was highly picturesque. Lord Lathom was Doge, and among the ladies and gentlemen of Venice were the Duchess of Portland, Countess of Mar and Kellie, Lady Alington, Mr. and Mrs. W. H. Grenfell, and Lord and Lady St. Oswald.<ref name=":10">“Girls’ Gossip.” ''Truth'' 8 July 1897, Thursday: 41 [of 70], Col. 1b – 42, Col. 2c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0002961/18970708/089/0041.</ref>{{rp|41, Col. 2c}}</blockquote> These are the names in the visualization in the ''Morning Post'' story. ==== Italian Procession ==== # The [[Social Victorians/People/Mar and Kellie|Countess Mar and Kellie]] (at 160), as Beatrice # Lloyd Tyrell-Kenyon, 4th [[Social Victorians/People/Lloyd Kenyon|Baron Kenyon]] (at 167) as Guido Cavalcanti # Mabel Winn, [[Social Victorians/People/Saint Oswald|Lady St. Oswald]] (at 284), as Duchessa di Caluria in the Italian procession or a Venetian lady of the 14th century # Mr. [[Social Victorians/People/Wyndham|George Wyndham]] (at 221), as Signor di Samare # [[Social Victorians/People/Forbes|Miss Blanche Forbes]] (at 285), as Donna Lucrezia Arcella # Mr. [[Social Victorians/People/Schreiber|Schreiber]] (at 286), as Duca d'Iripolda # [[Social Victorians/People/Higgins|Mrs. Higgins]] (at 287), as Donna Valeria Bodessa # Mr. [[Social Victorians/People/Grenfell|William Henry Grenfell]] (at 222), as Signor di Argentina or as [[Social Victorians/People/Grenfell|Mercutio]] # Mrs. Mary [[Social Victorians/People/Von Andre|Von André]] (at 289), as Desdemona # Mr. [[Social Victorians/People/Walter Murray Guthrie|Murray Guthrie]] (at 290), as Otello # [[Social Victorians/People/Montagu|Lady Alice Montagu]] (at 292), as Laura and escorted by Giles Fox-Strangways # Giles Fox-Strangways (at 78), [[Social Victorians/People/Ilchester|Lord Stavordale]], as Petrarch # Miss [[Social Victorians/People/Arthur Stanley Wilson#Enid Wilson|Enid Wilson]] (at 293), as Giulietta # Lord Hyde: George Herbert Hyde [[Social Victorians/People/Villiers|Villiers]] (at 294), as Romeo ==== Venetians ==== # The [[Social Victorians/People/Lathom|Earl of Lathom]] (at 125), as Il Doge, Giovannino de Medici #Mr. [[Social Victorians/People/Williams#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Hwfa Williams]] (was unable to attend), as Cardinale Giovanni Bembo #Mrs. [[Social Victorians/People/Williams#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Hwfa Williams]] (was unable to attend), as Caterina Cornaro (Regina di Cipri) # [[Social Victorians/People/Guest|Hon. Ivor Guest]] (at 295), as Marco (Re di Cipri) # Mildred Cadogan, [[Social Victorians/People/Cadogan|Viscountess Chelsea]] (at 162), Venditrice di Fiori, a Veronese lady # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Clarence Wilson]] (at 300), as Buffone #[[Social Victorians/People/Fortescue|Hon. Seymour Fortescue]] (at 296), as Avocato #[[Social Victorians/People/Warwick#Hon. Sir Sidney Robert Greville|Hon. S. Greville]] (at 297), as Cipriano # The [[Social Victorians/People/Curzon|Hon. Mrs. George (Mary) Curzon]] (at 301), as Marchesa Malaspina # [[Social Victorians/People/Peel Family#Hon. George Peel|Hon. George Peel]] (at 302), as Luigi Giorgi # Ettie (Mrs. W.) [[Social Victorians/People/Grenfell|Grenfell]] (at 200), as Contessa Maria Cicogna or Maria de Medici # The [[Social Victorians/People/Charteris|Hon. Evan Charteris]] (at 303), as Cavaliere Vittorio # [[Social Victorians/People/Grosvenor|Lady Lettice Grosvenor]] (at 304), as Bianca Capelli # Lord [[Social Victorians/People/Thynne|Alexander Thynne]] (at 305), as Marino Grimani # Mrs. [[Social Victorians/People/Portland|Cavendish Bentinck]] (at 264), as Grandezza degli Antenati # [[Social Victorians/People/Lurgan#Hon. Cecil Brownlow|Hon. Cecil Brownlow]] (at 305), as Nicolo Danabi # Mrs. [[Social Victorians/People/Walter Murray Guthrie|Olive Guthrie]] (at 291), as Marguerita Grimani # [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Mr. Herbert Wilson]] (at 307), as Antonio Priali (misspelled as Briali) ==== 17th-Century Procession ==== # [[Social Victorians/People/Arthur Sassoon|Louise (Mrs. Arthur) Sassoon]] (at 202), as La Dogaressa, led the 17th-century procession, with two nephews as attendants: ##[[Social Victorians/People/Rothschild Family|Evelyn Achille de Rothschild]] (at 669), as a page to the Doge's Wife ##[[Social Victorians/People/Rothschild Family|Anthony Gustav de Rothschild]] (at 670), as a page to the Doge's Wife # Arthur Wellesley Peel, 1st [[Social Victorians/People/Peel Family|Viscount Peel]] (at 74), as Il Doge # Winifred, [[Social Victorians/People/Portland|Duchess of Portland]] (at 29), as Duchessa di Savoia # William, [[Social Victorians/People/Portland|Duke of Portland]] (at 28), as Duca Filiberto di Savoia (or possibly the Duke of Buckingham) # [[Social Victorians/People/Feversham|Lady Helen Vincent]] (at 215), as Contessa Valentina Gateago # [[Social Victorians/People/Feversham|Sir Edgar Vincent]] (at 226), as II Conte Oravio or Orayio # Mrs. Gerard Leigh (at 308), as Lucrezia de Rossi # [[Social Victorians/People/Higgins|Mr. Higgins]] (at 288), as Sanchio di Sedilla # Mrs. [[Social Victorians/People/Drummond|Katherine Mary Drummond]] (at 309), as Donna Caranado # [[Social Victorians/People/Henry White|Mr. Henry White]] (at 310), as Giovanni Felici (or possibly Henri de Lorraine, Duc de Guise) # Miss [[Social Victorians/People/Mildred Grenfell|Mildred Grenfell]] (at 30), as Bianca di Piacoma, accompanying Winifred, [[Social Victorians/People/Portland|Duchess of Portland]] # Mr. Norton (at ), as Guyman di Silva (the ''Times'' and hence the Evening ''Mail'' says Morton) # [[Social Victorians/People/Fraser#Captain Hugh Fraser|Captain Fraser]] (at 244), as Duca di Tarsis Visitors to the Court of Savoia # Windham, [[Social Victorians/People/Dunraven|Earl of Dunraven]] (at 199), as Cardinal Mazzarin # Consuelo, [[Social Victorians/People/Manchester|Duchess of Manchester]] (at 175), as Anne d'Autriche [this isn't right: she's in the Russian Procession with the Duke of Marlborough, as the French Ambassador to the Court of Catherine II and his wife.] # Mr. [[Social Victorians/People/Beraud|Jean Béraud]] (at 312), as Cinq Mars ==== Not Listed in the ''Morning Post'' story, But Still ==== ... said somewhere to have been in the Italian Procession or might logically have processed with them. #[[Social Victorians/People/Salisbury|Lady Edward Cecil]], probably Violet Georgina Maxse Gascoyne-Cecil (at 102) ==== The Morning Post Visualization ==== In the ''Morning Post'' visualization of the procession, Beatrice, the Countess of Mar and Kellie led the procession. The typeset visualization looks, more or less, like this: ITALIAN PROCESSION ''Beatrice'', ''Guido Cavalcanti'', The Countess of Mar and Kellie. Lord Kenyon. ''Duchessa di Caluria'', ''Signor di Samare'', Lady St. Oswald. Mr. George Wyndham. ''Donna Lucrezia Arcella'', ''Duca d'Iripolda'', Miss Blanche Forbes. Mr. Schreiber. ''Donna Valeria'' ''Bodessa'', ''Signor di Argentina'', Mrs. Higgins. Mr. W. Grenfell. ''Desdemona'', ''Otello'', Mrs. Von André. Mr. Murray Guthrie. ''Laura'', ''Petrarch'', Lady Alice Montagu. Lord Stavordale. ''Giulietta'', ''Romeo'', Miss Enid Wilson. Lord Hyde. Venetians ''Il Doge (Giovannino de Medici)'', ''Marco (Redi Cipri)'', The Earl of Lathom. Hon. Ivor Guest. Avocato, Venditrice di Fiori, Cipriano, Hon. Seymour Fortescue Viscountess Chelsea. Hon. S. Greville. Buffone, Mr. Clarence Wilson. ''Marchesa Malaspina'', ''Luigi Giorgi'', Hon. Mrs. George Curzon. Hon. George Peel. ''Contessa Maria Cicogna'', ''Cavaliere Vittorio'', Mrs. W. Grenfell. Hon. Evan Charteris. ''Bianca Capelli'', ''Marino Grimani'', Lady Lettice Grosvenor. Lord Alexander Thynne. ''Grandezza degli Autenati'', ''Nicolo Danabi'', Mrs. Cavendish Bentinck. Hon. Cecil Brownlow. ''Marguerita Grimani''. ''Antonio Priali'', Mrs. Guthrie. Mr. Herbert Wilson. 17th CENTURY ''La Dogaressa'', ''Il Doge'', Mrs. Arthur Sassoon. Viscount Peel. ''Duchessa di Savoia'', ''Duca Filiberto di Savoia'', The Duchess of Partland. The Duke of Portland. ''Contessa Valentina Gateago'', ''II Conte Oravio'', Lady Helen Vincent. Sir Edgar Vincent. ''Lucrezia de Rossi'', ''Sanchio di Sedilla'', Mrs. Gerard Leigh. Mr. Higgins. ''Donna Caranado'', ''Giovanni Felici'', Mrs. Drummond. Mr. H. White. ''Bianci di Piacoma'', ''Guyman di Silva'', Miss Mildred Grenfell. Mr. Norton. ''Duca di Tarsis'', Captain Fraser. Visitors to the Court of Savoia. ''Cardinal Mazzarin'', ''Anne d'Autriche'', ''Cinq Mars'', The Earl of Dunraven. The Duchess of Manchester. Mr. Jean Bérand. ===Austrian=== The ''Gentlewoman'' says, "The Austrian Court was a wonderful procession, headed by the Marchioness of Londonderry as the Empress Marie Thérèse. She wore the famous Londonderry diamonds, which included a diamond crown copied exactly from one worn by the Empress Marie Thérèse on her powdered hair. She was followed by four young Archduchesses, in white and silver and pale blue ribbons."<ref name=":8" />{{rp|p. 32, Col. 2c–3a}} The Austrian procession and quadrille were headed up by Theresa Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] as Marie Thèrése of Austria. Most accounts say it had 4 archduchesses in attendance, even though the Guernsey ''Star'' reported 5 and the ''Belfast News-Letter'' adds [[Social Victorians/People/Somerset|Miss Seymour]] (at 406): * "four beautiful young Archduchesses in white and silver with pale blue ribbons, and wearing white plumes in their powdered hair"<ref name=":1">"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." ''London Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and http://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|p. 5, Col. 7A}} *"four young Archduchesses, in white and silver and pale blue ribbons. These ladies were impersonated by Lady Helen Stewart, Lady Beatrice Butler, Lady Beatrix FitzMaurice, and Lady Alexandra Hamilton."<ref name=":8" />{{rp|p. 32, Col. 2c–3a}} * "five Archduchesses and five Archdukes. The former, all attired exactly alike in white and silver brocade, were Lady Helen Stewart, Lady Beatrice Butler, Lady Beatrix FitzMaurice, Lady Alexandra Hamilton, and Miss Stirling."<ref name=":3">"Duchess of Devonshire's Fancy-Dress Ball. Brilliant Spectacle." The [Guernsey] ''Star'' 6 July 1897, Tuesday: 1 [of 4], Col. 1–2. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000184/18970706/003/0001.</ref> Possibly this quite-large group had subsections: the ''Morning Post'' and the ''Times'' mention for example "the Archduchess Marie-Karoline and Emperor Joseph II section of the Austrian Court of Maria Theresa Quadrille."<ref name=":0" />{{rp|p. 7, Col. 6b}} <ref name=":5">"Ball at Devonshire House." ''Times'' Saturday 3 July 1897: 12, Cols. 1a–4c ''The Times Digital Archive''. Web. 28 Nov. 2015.</ref> # Section 1 ## Theresa Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry|Marchioness of Londonderry]] (at 42), as Marie Thérèse of Austria ## Henry Petty-FitzMaurice, [[Social Victorians/People/Lansdowne|Marquis of Lansdowne]] (at 52), as Prince Kaunitz ## Maud Hamilton Petty-Fitzmaurice, [[Social Victorians/People/Lansdowne|Marchioness of Lansdowne]] (at 51), as Lady Keith, wife of the British Ambassador at the Court of Marie Thérèse ##[[Social Victorians/People/Winchester|Augustus, Marquis of Winchester]], as a Coldstream Guard at Vienna # Section 2: Archduchess Marie-Karoline and Emperor Joseph II section of the Austrian Court of Maria Theresa Quadrille ## Archduchesses ###[[Social Victorians/People/Ormonde|Lady Beatrice Butler]] (at 45), Archduchess Marie-Karoline ###[[Social Victorians/People/Abercorn|Lady Alexandra Hamilton]] (at 46), Archduchess Marie-Josepha ###[[Social Victorians/People/Lansdowne|Lady Beatrix Petty-FitzMaurice]] (at 44), as Archduchess Marie Anna ### Lady Helen Stewart ([[Social Victorians/People/Londonderry|Vane-Tempest-Stewart]]) (at 43), as the Archduchess Marie Christine of Austria ## Charles Stewart Henry Vane-Tempest-Stewart, [[Social Victorians/People/Londonderry|Viscount Castlereagh]] (at 73), attended as Maria Thérèse's son Emperor Joseph II (Charles Vane-Tempest-Stewart, Viscount Castlereagh, was the [[Social Victorians/People/Londonderry|Marchioness of Londonderry]]'s son.) ## Mr. [[Social Victorians/People/Gathorne-Hardy|Gathorne-Hardy]] (at 352), as Archduke Leopold ## Charles William Reginald Duncombe, [[Social Victorians/People/Helmsley|Viscount Helmsley]] (at 353), as Archduke Charles ##[[Social Victorians/People/Lurgan|Lord William Lurgan]] (at 165), as Duke Albert von Sachsen-Texhen or Sachsentexhen # Small Group of 4 ## [[Social Victorians/People/Magheramorne|Lady Magheramorne]] (at 355), as Maria-Amelia, Princess of Lorraine ## Lady [[Social Victorians/People/Beaumont|Aline Beaumont]] (at 356), as as Marie Josephe of Austria or Queen of Sardinia ## Lord Ava: Archibald Hamilton-Temple-Blackwood, [[Social Victorians/People/Hamilton Temple Blackwood#Archibald Hamilton-Temple-Blackwood, Earl of Ava|Earl of Ava]] (at 357), as Archduke Maximilian ## Mr. [[Social Victorians/People/Ancaster|C. Willoughby]] (at 358), as Grand Duke Charles of Tuscany # Small Group of 4 ## Mrs. [[Social Victorians/People/Grimthorpe#Mr. and Mrs. Gervase BeckettMr. and Mrs. Gervase Beckett|Mabel (G. Gervase) Beckett]] (at 359), as Princess Elenora of Lichtenstein ## Siegfried, [[Social Victorians/People/Clary Aldringen|Count Clary]] (at 205), as General Count Nadasdy ## Mrs. [[Social Victorians/People/Grimthorpe#Mr. and Mrs. R. Beckett|Muriel Beckett]] [sic Mrs. R. Beckeet] (at 482), as Princess Isabella of Parma ## [[Social Victorians/People/Hadik|Count Hadik]] (at 361), as Field-Marshal Hadik # Small Group of 4 ## Cicely Gascoyne-Cecil, [[Social Victorians/People/Salisbury|Viscountess Cranborne]] (at 196), as Princess Josepha of Bavaria ## Schomberg McDonnell, [[Social Victorians/People/Antrim|Mr. Schomberg M'Donnell]] (at 104), as Duke Ferdinand of Modena ## [[Social Victorians/People/Midleton|Lady Hilda Charteris Brodrick]] (at 362, Lady H. Brodrick), as Princess Marie Künigunde of Saxony ## Mr. Jack [[Social Victorians/People/Arthur Stanley Wilson|Graham Menzies]] (at 362), as Freiherr von Bartenstein # Small Group of 4 ## Mrs. [[Social Victorians/People/William James|Evelyn James]] (at 364), as Archduchess Elizabeth ## [[Social Victorians/People/Lansdowne|Lady C. FitzMaurice]] (at 365), as Secretary to Kaunitz, personated as listed above by Henry Petty-FitzMaurice, [[Social Victorians/People/Lansdowne|Marquis of Lansdowne]] (at 558) ## Muriel Duncombe, [[Social Victorians/People/Helmsley|Viscountess Helmsley]] (at 354), as Princess Charlotte of Lorraine ## Henry Petty-FitzMaurice, [[Social Victorians/People/Kerry|Earl of Kerry]] (at 72), as Count Mercy d'Argentau # Small Group of 4 ## [[Social Victorians/People/Cavendish|Lady E. Cavendish]] (probably Lady Evelyn Cavendish, at 164), as Countess Trautmannsdorf ##[[Social Victorians/People/Mildmay|Mr. F. B. Mildmay]] (at 95), as "Field-Marshal Count Charles of Batthyany" ## (Lady M.) [[Social Victorians/People/Cavendish|Lady Moyra Cavendish]] (at 366) ## James Somerville, [[Social Victorians/People/Athlumney|Lord Athlumney]] (at 367), as Prince Metternich # Small Group of 2? (or they belong above, her with the Archduchesses?) ##[[Social Victorians/People/Stirling|Miss Stirling]] (at 47), as Countess Kinskey in the Austrian Court of Maria Theresa Quadrille ## [[Social Victorians/People/Midleton#St. John Broderick|Mr. St. John Brodrick]] (at 368), as Count Kinskey # People not in the ''Morning Post'' visualization but elsewhere said to have been in this procession: ## Charles Vane-Tempest-Stewart, the [[Social Victorians/People/Londonderry|Marquess of Londonderry]] (at 511), in the procession according to the ''Morning Post'' story ## [[Social Victorians/People/Lansdowne|Edmond Fitzmaurice]] (at 627), a Courtier of the Empress Marie Thérèse ##Miss [[Social Victorians/People/Ellis|Alexandra Ellis]] (at 655), in a Thérèse costume The ''Morning Post'' typeset a visualization of the procession, more or less, like this<ref name=":0" />{{rp|p. 7, Col. 6b}}: Lady Londonderry . . . . . Empress Maria Theresa. Lord Lansdowne . . . . . . Prince Kaunitz. Lady Lansdowne . . . . . . Lady Keith. Lord Winchester . . . . . A Coldstream Guard at Vienna. Lady B. Butler . . . . . . Archduchess Marie-Karoline. Lord Castlereagh . . . . . Emperor Joseph II. Lady A. Hamilton . . . . . Archduchess Marie-Josepha. Mr. Gathorne-Hardy . . . . Archduke Leopold. Lady B. FitzMaurice . . . Archduchess Marie Anna. Lord Helmsley . . . . . . Archduke Charles. Lady Helen Stewart . . . . Archduchess Marie Christine. Lord Lurgan . . . . . . . Duke Albert von Sachsen-Texhen. Lady Magheramorne . . . . . Maria-Amelia, Princess of Lorraine. Lady Aline Beaumont . . . . Queen of Sardinia. Lord Ava . . . . . . . . . Archduke Maximilian. Mr. C. Willoughby . . . . . Grand Duke Charles of Tuscany. Mrs. G. Beckett . . . . . . Princess Elenora of Lichtenstein. Count Clary . . . . . . . . General Count Nadasdy. Mrs. R. Beckeet [sic] . . . Princess Isabella of Parma. Count Hadik . . . . . . . . Field-Marshal Hadik. Lady Cranborne . . . . . . Princess Josepha of Bavaria. Mr. M'Donnel . . . . . . . Duke Ferdinand of Modena. Lady H. Brodrick . . . . . Princess Marie Künigunde of Saxony. Mr. Menzies . . . . . . . . Freiherr von Bartenstein. Mrs. James . . . . . . . . Archduchess Elizabeth. Lady C. FitzMaurice . . . . Secretary to Kaunitz. Lady Helmsley . . . . . . . Princess Charlotte of Lorraine. Lord Kerry . . . . . . . . Count Mercy d'Argentau. Lady E. Cavendish . . . . . Countess Trautmannsdorf. Mr. Mildmay . . . . . . . . Field-Marshal Count Charles of Batthyany. Lady M. Cavendish . . . . . Countess Lützau (A Lady-in-Waiting to Maria Theresa). Lord Athlumney . . . . . . Prince Metternich. Miss Stirling . . . . . . . Countess Kinskey. Mr. Brodrick . . . . . . . Count Philip Kinsky. ===Russian=== According to the ''Gentlewoman'',<blockquote>The Russian Court formed a dazzling procession, headed by Lady Raincliffe, as the Empress Catherine; her gown of white satin was studded with rubies, emeralds, and turquoises, and across her bodice she wore a blue ribbon with the Orders of the Star and Eagle, and upon her head a Russian crown of diamonds. Beside her was Prince Orloff, represented by Prince Henry Pless, in a costume of red cloth with heavy gold embroideries; he also wore the Order of St. Catherine. There were eight officers of the Imperial Court accompanying the Empress, whilst Lady Henry Bentinck and Lady Yarborough impersonated ladies of her suite, amongst which one of the most striking figures was Mr. Cresswell, as her Chamberlain, in a costume of cerise velvet, covered with the double-headed eagle of Russia in gold, which embroidery was repeated on his pink satin vest, his white satin breeches, and his silk stockings.<ref name=":8" />{{rp|p. 32, 3b}}</blockquote> ''Truth'' says,<blockquote>Lady Raincliffe as Catherine of Russia was a marvel of millinery in yellow / and gold, ermine and rubies. Her lords and ladies emulated her splendour, and among the most successful were the Duchesses of Marlborough and Newcastle, Lady Yarborough, Lady Henry Bentinck, Lord Raincliffe, and Mr. Cresswall.<ref name=":10" />{{rp|41, Col 2c – 42, Col. 1a}}</blockquote> # The "Trumpeters of the Imperial Guard" led the procession # The first group, if they did break into subgroups ## Lord Henry Bentinck (probably [[Social Victorians/People/Cavendish Bentinck|Lord Henry Cavendish Bentinck]]) (at 262), as Count Poneatowski (afterwards King of Poland) ## Grace Denison, [[Social Victorians/People/Londesborough|Viscountess Raincliffe]] (at 75), as Catherine II of Russia (after the picture by Lambi) ## [[Social Victorians/People/Heeren|Count Heeren]] (at 265), as Duc de Ligne ## [[Social Victorians/People/Cresswell|Addison Francis Baker-Cresswell]] (Mr. A. F. B. Cresswell) (at 103), as Count Lausköi, Chamberlain of the Empress Catherine II of Russia # The second group ## [[Social Victorians/People/Pless|Prince Henry of Pless]] (at 40), as Count Orloff ## Mrs. H. T. [[Social Victorians/People/Barclay|Barclay]] (at 266), Princess Shakofsky ## Mr. [[Social Victorians/People/Myddleton-Biddulph|Biddulph]] (at 268), as Count Soltykoff # The third group, with the 8 "Imperial Guard" walking along the outside (or at least typeset that way) of the "Ladies and Gentlemen of the Court" ## Imperial Guards: left side ### William Denison, [[Social Victorians/People/Londesborough|Viscount Raincliffe]] (at 76) ### Captain [[Social Victorians/People/Cook|E. B. Cook]] (at 269) ### Hon. [[Social Victorians/People/Dudley#Hon.%20Gerald%20Ernest%20Francis%20Ward|Gerald Ward]] (at 271) ###[[Social Victorians/People/Forbes|James Stewart Forbes]] (at 273)<ref name=":1" />{{rp|p. 5, Col. 7a}} ## Imperial Guards: right side ### Lord [[Social Victorians/People/Romilly|Romilly]] (at 269) ### Mr. H. T. [[Social Victorians/People/Barclay|Barclay]] (at 267) ### The Hon. [[Social Victorians/People/Campbell|Cecil Campbell]] (at 272) ### Mr. [[Social Victorians/People/Arthur Stanley Wilson|C. Wellesley Wilson]] (at 274) ## Ladies and Gentlemen of the Court ###[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill|Consuelo Vanderbilt Spencer-Churchill]], the [[Social Victorians/People/Marlborough|Duchess of Marlborough]] (at 174) ### Sunny (Charles Richard John) Spencer-Churchill, the [[Social Victorians/People/Marlborough|Duke of Marlborough]] (at 142), one of the Gentlemen of the Court of Catherine II of Russia ### Kathleen Florence May Candy Pelham-Clinton, [[Social Victorians/People/Newcastle|Duchess of Newcastle]] (at 150) ### Charles Anderson-Pelham, [[Social Victorians/People/Yarborough|Earl of Yarborough]] (at 61), with Lady Yarborough, was among Ladies and Gentlemen of the Court ### Marcia Anderson-Pelham, [[Social Victorians/People/Yarborough|Countess of Yarborough]] (at 54) ### [[Social Victorians/People/Buchan|Lord Shipley Cardross]] (at 275) ### [[Social Victorians/People/Buchan|Lady Rosalie Cardross]] (at 276) ### [[Social Victorians/People/Stourton|Herbert Marmaduke Joseph Stourton]] (at 277) ### the [[Social Victorians/People/Buchan|Hon. M. (Muriel) Erskine]] (at 278), as La Marquise de Vintimille du Luc ### Mr. Elliot: [[Social Victorians/People/Minto|Sir Henry George Elliot]] (at 279) ### Lady Henry Bentinck ([[Social Victorians/People/Cavendish Bentinck|Lady Henry Cavendish Bentinck]]) (at 263) ### N. [[Social Victorians/People/Boulatzell|Boulatzell]] (at 280), as Prince of Mingrelia, one of the Gentlemen of the Court in the procession of the Empress Catherine II of Russia ### [[Social Victorians/People/Spicer|Lady Margaret Spicer]] (at 281), as Countess Soltykoff ### M. [[Social Victorians/People/Gourko|Nicholas Gourko]] (at 108) ###[[Social Victorians/People/Londesborough|Lady Mildred Denison]] (at 283) ### Charles Henry John Chetwynd-Talbot, 20th [[Social Victorians/People/Shrewsbury|Earl of Shrewsbury]] (at 101), as a member of the Court of Catherine II of Russia ### "Black Attendants" The ''Guernsey Star'' suggests that the Hon. Mrs. Erskine's daughter was in this procession, but the ''Morning Post'' does not list her.<ref name=":3" /> The [[Social Victorians/People/Durham#Hon. Cecil Lambton|Hon. Cecil Lambton]] (at 628) was also there, apparently, and sold his costume to theatre director Arthur Collins, who directed ''The White Heather''.<ref>"The Morning’s News." London ''Daily News'' 18 September 1897, Saturday: 5 [of 8], Col. 2b. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970918/027/0005.</ref> The ''Morning Post''<nowiki/>'s visualization of the procession looks more or less like this<ref name=":0" />{{rp|p. 7, Col. 5b}}: Trumpeters of the Imperial Guard. ''Count Poneatowski'' ''Empress Catherine II. of Russia'' ''Duc de Ligne,'' ''(afterwards King'' ''of Poland),'' ''(after the picture by Lambi)'', Count Heeren. Lord Henry Bentinck. Lady Raincliffe. ''Count Lausköi'', Mr. Cresswell. ''Count Orloff'', ''Princess Shakofsky'', ''Count Soltykoff'', Prince Henry of Pless. Mrs. H. T. Barclay. Mr. Biddulph. ["Imperial Guard." — typeset vertically up the left and down the right side of the column, with 2 vertical rules separating the two columns of names.] Lord Raincliffe. | | Lord Romilly. Captain Cook. | | Mr. H. T. Barclay. Hon. Gerald Ward. | | Hon. Cecil Campbell. Mr. J. Forbes. | | Mr. T. W. Wilson. Ladies and Gentlemen of the Court. Duchess of Marlborough. Duke of Marlborough. Duchess of Newcastle. Earl of Yarborough. Countess of Yarborough. Lord Cardross. Lady Cardross. Mr. Stourton. Hon. M. Erskine. Mr. Elliot. Lady Henry Bentinck. M. Botalzell. Lady Margaret Spicer. M. Gourko. Lady Mildred Denison. Earl of Shrewsbury. Black Attendants. ===Louis XV and XVI Period=== Louis XV was King of France 1715–1774, although his reign began when he reached maturity in 1724. Louis XVI reigned 1774–1792. Daisy, Countess Warwick, as Marie Antoinette, was widely regarded as the center of this group rather than any of the Louis. ''Truth'' says,<blockquote>The Countess of Warwick, as Marie Antoinette, in white and blue, with golden fleur-de-lys upon her velvet train, was the centre of a picturesque group, among whom was the Earl of Essex, dressed as his ancestor of that period, and the Earl of Mar and Kellie as Sir Walter Raleigh.<ref name=":10" />{{rp|42, Col 1a}}</blockquote> The ''Morning Post'' calls this one a ''quadrille'' rather than a ''procession'', the quadrille of the Louis XV and XVI Period,<ref name=":0" />{{rp|7, Col. 6B}} This procession or quadrille was organized and led by Daisy, Countess of Warwick<ref>"Duchess of Devonshire's Fancy Ball. A Brilliant Spectacle. Some of the Dresses." ''London Daily News'' Saturday 3 July 1897: 5 [of 10], Col. 6a–6, Col. 1b. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970703/024/0005 and http://www.britishnewspaperarchive.co.uk/viewer/BL/0000051/18970703/024/0006.</ref>{{rp|p. 5, Col. 9c}}. # Headed by [[Social Victorians/People/Warwick|Daisy, Countess Warwick]] (at 53) as Marie Antoinette<ref name=":3" />, as La Reine Marie Antoinette<ref name=":0" /> ## Plus 4 boys dressed as pages<ref>“The Duchess of Devonshire’s Ball.” ''Chelmsford Chronicle''9 July 1897, Friday: 2 of 8. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000322/18970709/008/0002.</ref> # Georgiana Elizabeth Spencer-Churchill Curzon, [[Social Victorians/People/Howe|Viscountess Curzon]] (at 168), as La Reine Marie Leszuiska in the quadrille of the period of Louis XV and XVI # Nellie, [[Social Victorians/People/Kilmorey|Countess Kilmorey]] (at 207), as Madame du Barry # [[Social Victorians/People/Gordon-Lennox|Lady Algernon Gordon-Lennox]] (at 333), as Princesse de Lamballe # Lady [[Social Victorians/People/Burton#Lady Burton|Harriet Burton]] (at 334), as Madame de Tençin # Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336), as Comtesse d'Artois # The Hon. Mrs. Greville (at 299), as Madame Elizabeth de France #[[Social Victorians/People/Keppel|Alice (the Hon. Mrs. George) Keppel]] (at 231), as Madame de Polignac # Lady Rose Leigh (at 337), as Duchesse de Villars # [[Social Victorians/People/Farquharson|Mrs. Farquharson]] (at 338), as L'Archiduchesse Louise # Miss [[Social Victorians/People/Naylor|Mary Naylor]] (at 339), as Comtesse de Charny # The [[Social Victorians/People/Sackville West|Hon. Mrs. Sackville West]] (at 340), as Duchess of Dorset # Henry Arthur Cadogan, [[Social Victorians/People/Cadogan|Viscount Chelsea]] (at 163), as Le Roi Louis XV in the quadrille of the Louis XV. and Louis XVI. Period # Lord Camden: John Pratt, [[Social Victorians/People/Camden|4th Marquess Camden]] (at 341), as Duc de Richelieu # The [[Social Victorians/People/Alington|Hon. Humphrey Sturt]], M.P. (at 120), as an Abbé de l'Epoque # Lord [[Social Victorians/People/Burton#Lord Burton|Michael Burton]] (at 335), as Cardinal Dubois # Mousquetaires et Militaires de l'Epoque ## Luke White, [[Social Victorians/People/Annaly|Lord Annaly]] (at 342) ## Lord Tullibardine: John George Stewart-Murray, [[Social Victorians/People/Atholl|Marquess of Tullibardine]] (at 343) ## Lord [[Social Victorians/People/Atholl|George Stewart-Murray]] (at 344) ## Frederick Edward Guest, the [[Social Victorians/People/Guest|Hon. F. Guest]] (at 345), as one of the Mousquetaires et Militaires de l'Epoque in the Quadrille of the Louis XV. and Louis XVI. ## [[Social Victorians/People/Cadogan|Sir Samuel Scott]], Bart., (at 99) one of the Mousquetaires et Militaires de l'Epoque in the Quadrille of the Louis XV. and Louis XVI ## [[Social Victorians/People/Sarah Spencer-Churchill Wilson|Captain Gordon Wilson]] (at 96), one of the Mousquetaires et Militaires de l'Epoque in the Quadrille of the Louis XV. and Louis XVI ## [[Social Victorians/People/Durham#Captain the Hon. W. Lambton|Captain the Hon. W. Lambton]] (at 346), likely [[Social Victorians/People/Durham|Hon. Sir William Lambton]], one of the Mousquetaires et Militaires de l'Epoque in the Quadrille of the Louis XV. and Louis XVI. ## [[Social Victorians/People/Elliot|Captain Gilbert Elliot]] (at 347) ## [[Social Victorians/People/Warwick|Mr. Frank Dugdale]] (at 348) ##Carlo Ermes Visconti, [[Social Victorians/People/San Vito|Marchese di San Vito]] (at 691), as one of the Mousquetaires # [[Social Victorians/People/Muriel Wilson|Mr. Clive Wilson]] (at 349) as Le Comte de Ferson in the Quadrille of the Louis XV. and Louis XVI # Mr. [[Social Victorians/People/Lowe|W. M. Lowe]] (at 350), as Gentilhomme de la Cour Louis XVI # [[Social Victorians/People/Morley|Rt. Hon. Arnold Morley]] (at 351), was dressed as a Gentilhomme de la Cour Louis XV in the Quadrille of the Louis XV. and Louis XVI. or Duc de Choiseul. Not listed in the visualization in the ''Morning Post'' and probably not a member of the quadrille but mentioned elsewhere as having been dressed in a costume of this period: # Millicent, [[Social Victorians/People/Sutherland|Duchess of Sutherland]] (at 33), "belonged to the Louis Seize group of the Countess of Warwick"<ref name=":3" /> # The R[[Social Victorians/People/Chamberlain|ight Hon. Joseph Chamberlain]] (at 93), as a gentleman of the Louis XVI period #[[Social Victorians/People/Sarah Spencer-Churchill Wilson|Lady Sarah Wilson]] (at 392), as Madame de Pompadour # Mr. [[Social Victorians/People/Loder|Gerald Loder]], M.P. (at 100), as a Gentleman of the Court of Louis XVI #[[Social Victorians/People/Stanley|Sir George Frederick Stanley]] (at 249), as Maro (period of Louis XVI) #[[Social Victorians/People/Stanley|Lady Isobel Stanley]] (at 645), in hunting costume, period of Louis XVI #[[Social Victorians/People/Alva|Jacobo Fitz-James Stuart y Falcó, Lord Alva]] (at 405), as as a courtier of Louis XV #[[Social Victorians/People/Carrington|Charles Carington, the Earl Carington]] (at 69), as Louis Seize #Charles Chetwynd-Talbot, [[Social Victorians/People/Shrewsbury|Earl of Shrewsbury]] (at 101), either a Gentleman of the Court of Lois XV. or a Gentleman of the Court of the Empress Catherine II of Russia The ''Morning Post'' typeset a visualization of the procession, more or less, like this: Louis XV. and Louis XVI. Period. Lady Warwick . . . . . . . . . . La Reine Marie Antoinette. Lady Curzon . . . . . . . . . . La Reine Marie Leszuiska. Lady Kilmorey . . . . . . . . . Madame du Barry. Lady Algernon Gordon-Lennox . . Princesse de Lamballe. Lady Burton . . . . . . . . . . Madame de Tençin. Lady Garvagh . . . . . . . . . . Comtesse d'Artois. The Hon. Mrs. Greville . . . . . Madame Elizabeth de France. The Hon. Mrs. George Keppell . . Madame de Polignac. Lady Rose Leigh . . . . . . . . Duchesse de Villars. Mrs. Farquharson . . . . . . . . L'Archiduchesse Louise. Miss Naylor . . . . . . . . . . Comtesse de Charny. The Hon. Mrs. Sackville West . . Duchess of Dorset. Lord Chelsea . . . . . . . . . . Le Roi Louis XV. Lord Camden . . . . . . . . . . Duc de Richelieu. The Hon. Humphrey Sturt . . . . Abbé de l'Epoque. Lord Burton . . . . . . . . . . Cardinal Dubois. Lord Annaly . . . . . . . . . . ) Lord Tullibardine . . . . . . . ) Lord George Murray . . . . . . . ) The Hon. F. Guest . . . . . . . ) Sir Samel Scott . . . . . . . . ) Mousquetaires et Mili- Captain Gordon Wilson . . . . . ) taires de l'Epoque. Captain the Hon. W. Lambton . . ) Captain Gilbert Elliot . . . . . ) Mr. Dugdale . . . . . . . . . . ) Mr. Clive Wilson . . . . . . . . Le Comte de Ferson. Mr. W. M. Lowe . . . . . . . . . Gentilhomme de la Cour Louis XVI. Mr. Arnold Morley . . . . . . . Gentilhomme de la Cour Louis XV.<ref name=":0" />{{rp|p. 7, Col. 6B}} ===Elizabethan=== Elizabethan costumes seem to have been very popular, even outside the Elizabethan procession, in part because the Royals were costumed in Renaissance styles as well. In this description the ''Gentlewoman'' includes Anne of Austria and the Electress of Luneberg and Hanover, not to mention Napoleon, who would not have been in Elizabeth's court. They could conceivably have walked in the Elizabeth procession, although Anne of Austria, while Renaissance, might have walked with the French procession if it included Louis XIII. The Duchess of Connaught and the Duchess of Teck were very closely related to Queen Victoria's immediate family and thus might be grouped here because many of the Royals wore Elizabethan dress. <blockquote>A Court, the details of which were perfectly carried out, was that of Elizabeth of England. Lady Tweedmouth took the part of Her Majesty, and her costume was an exact reproduction of Queen Elizabeth's portrait in the National Portrait Gallery. Her skirt of rich old white and gold brocade was held in place by the old-fashioned hoops, the bodice and front of gold tissue embroidered in old jewels were finished by stiffened cuffs and large wired collar of old lace wrought with gold. Four yeomen held a canopy over Her Majesty's head. Their uniforms were exactly copied from the picture of the Field of the Cloth of Gold at Hampton Court. These were the Duke of Roxburghe, the Hon. Dudley Marjoribanks, Captain Maunde Thompson, and Mr. Rose attired in scarlet and black. The two heralds who preceded the Queen were Mr. Harold Brassey and Mr. E. Villiers, while Lord Rothschild, in a splendid costume of the time, walked between them. Among her Majesty's Court were Sir Walter Raleigh (Mr. Ernest Beckett), Sir Philip Sidney (Mr. H. Warrender), Sir Francis Drake (Sir Charles Hall), the Lord Chief Justice (Sir Francis Jeune), the Lord of Burleigh (the Earl of Sandwich), while Lord Lonsdale, who carried a hooded falcon on his wrist, represented Sir Richard Lowther. The Duchess of Roxburghe, and the Countess of Powis, as the Countess of Shrewsbury and Lady Herbert of Cherbury, looked very effective. Countess Spencer, Mrs. Habington, Lady de Ramsay, and the Archbishop of Canterbury, represented by Lord Rowton, made up the Court. Then followed Mary Queen of Scots, in the person of Lady Edmonstone, wonderfully attired in turquoise-blue velvet with pearls and white satin; Mary Hamilton, in white satin and gold, and Mary Seaton, in white, followed in her wake as did the Countess of Lonsdale (Lady Hunsdon), Lord Glenesk, and many others. H.R.H. the Duchess of Connaught, as Anne of Austria, and H.R.H. the Duchess of Teck, as Electress of Luneberg and Hanover, looked their characters very well, and a very effective trio was formed by the Countess Clary d'Aldringen, Countess Isabel Deym, and Countess Kinsky, as the three sisters of Napoleon. The Duchess of Somerset as Lady Jane Seymour, after a picture by Holbein, was dressed in gold brocade with a wonderful headdress; superbly jewelled, white gloves and Holbein ornaments embroidered on her gown. Margaret of Orleans, impersonated by the Duchess of Manchester, in white satin and silver, was a great success. Josephine, the wife of Napoleon, copied from the picture of her coronation, was impersonated by the Marchioness of Tweeddale, who wore white satin wrought with gold, and a train of geranium-red velvet, trimmed with ermine. Lady Lathom as Catherine of Arragon was splendidly dressed in bronze-green velvet worked in gold designs.<ref name=":8" />{{rp|p. 32, Col. 3c – 34, Col. 1a}}</blockquote> ''Truth'' describes the procession like this:<blockquote>Lady Tweedmouth was gorgeously arrayed as Queen Elizabeth, and was surrounded by a numerous Court, including Lord Tweedmouth, Lord Battersea, the Earl of Sandwich, and Lord Frederick Hamilton, to say nothing of six stalwart halberdiers, one of whom was the Duke of Roxburghe, whose Duchess was also bravely attired as an Elizabethan lady of high degree.<ref name=":10" />{{rp|41, Col 2c}}</blockquote>The Elizabethan procession was "led" by Fanny Marjoribanks, [[Social Victorians/People/Tweedmouth|Lady Tweedmouth]] (at 85) as Queen Elizabeth, but she did not come first in the procession. # Heralds # Row of 3 men #* Mr. E. ([[Social Victorians/People/Grimthorpe|Ernest) Beckett]] (at 313), as Sir Walter Raleigh #* Mr. H. (Hugh) Warrender (at 314), as Sir Philip Sydney #* [[Social Victorians/People/Charles Hall|Sir Charles Hall]], Q.C., M.P. (at 127), as Sir Francis Drake at the head of the Queen Elizabeth procession # Row of 3 men #* Sir F. ([[Social Victorians/People/Jeune|Francis) Jeune]] (at 315), as Lord Chief Justice #* Edward Montagu, [[Social Victorians/People/Sandwich|8th Earl of Sandwich]] (at 71), as Lord Burleigh #* [[Social Victorians/People/Lowther|Earl of Lonsdale]], Sir Richard Lowther (at 225), as Lord High Falconer # Row of 3 women #* Violet [[Social Victorians/People/Powis|Countess Powis]] (at 316), as Lady Herbert of Cherbury in the Queen Elizabeth procession #*Anne [[Social Victorians/People/Roxburghe|Duchess of Roxburghe]] (at 22), as Countess of Shrewsbury or Bess of Hardwicke #*Charlotte, [[Social Victorians/People/Spencer|Countess Spencer]] (at 192), as the Countess of Lennox # Row of 2 women #* Grace, [[Social Victorians/People/Lowther|Countess Lonsdale]] (at 211), as the Countess of Essex #*Mrs. [[Social Victorians/People/Cavendish Bentinck#Mrs. and Mr. Arthur James|Mary (Arthur) James]] (at 318), as Elisabeth Cavendish # [[Social Victorians/People/Leslie|Colonel John Leslie]] (at 261) was dressed as "Lord Darnley (carrying Sword of State)" in the Queen Elizabeth procession<ref>"Leslie as Earl Darnley." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158503/Sir-John-Leslie-2nd-Bt-as-Earl-Darnley.</ref> # Row of 2 men #* Edward Marjoribanks, [[Social Victorians/People/Tweedmouth|Lord Tweedmouth]] (at 109) as the Earl of Leicester #* George Capell, 7th [[Social Victorians/People/Essex|Earl Essex]] (at 64), as his ancestor, Robert Devereux, 2nd Earl of Essex * Yeomen ** The [[Social Victorians/People/Roxburghe|Duke of Roxburghe]] (at 49), a halberdier attending on Queen Elizabeth ** Dudley Marjoribanks (at 319), son of [[Social Victorians/People/Tweedmouth|Lord and Lady Tweedmouth]], as a Yeoman bearing the canopy, possibly, with the Duke of Roxburghe and two "brother officers in the Royal Horse Guards" * Row before the queen, with canopy ** [[Social Victorians/People/Ephrussi|Mr. Ephrussi]] (at 320), as the Spanish Envoy ** Canopy ** H. E. M. [[Social Victorians/People/de Courcel|Alphonse Chodron de Courcel]] (at 133), as the French Ambassador * Fanny Marjoribanks, [[Social Victorians/People/Tweedmouth|Lady Tweedmouth]] (at 85), as Queen Elizabeth *More Yeomen (possibly the two "brother officers in the Royal Horse Guards" of Dudley Marjoribanks (at 319) **[[Social Victorians/People/Mann Thomson|Captain Mann Thomson]] (at 321), as a Yeoman **[[Social Victorians/People/Rose|Mr. Rose]] (at 322), as a Yeoman *Row behind the queen **[[Social Victorians/People/Edmonstone|Sir A. Edmonstone]] (at 323), as Duc d'Alencon **[[Social Victorians/People/Holden|Henry Holden]] (at 325), as Will Somers (Court Jester) **John Spencer, 5th [[Social Victorians/People/Spencer|Earl Spencer]] (at 145), as Sir A. Brown, First Viscount Montagu (None of the sources agree on who he personated; this is the ''Morning Post'') *More Yeomen (possibly the two "brother officers in the Royal Horse Guards" of Dudley Marjoribanks (at 319) ** [[Social Victorians/People/Villiers Schott|Mr. E. Villiers]] (at 326), as a Yeoman **[[Social Victorians/People/Brassey|Harold Brassey]] (at 253), as a Yeoman * Row behind the yeomen ** Arthur [[Social Victorians/People/Arran|Earl of Arran]] (at 327), as Cardinal Loraine ** Nathan Mayer de Rothschild, [[Social Victorians/People/Rothschild Family|Lord Rothschild]] (at 216), as Swiss Burgher ** Montagu Lowry-Corry, [[Social Victorians/People/Rowton|1st Baron Rowton]] (at 189), as Archbishop Parker, the Archbishop of Canterbury *Row of 3 women **Margaret (the [[Social Victorians/People/Greville|Hon. Mrs. Ronald) Greville]] (at 298), as Mary Seaton **[[Social Victorians/People/Edmonstone|Lady Edmonstone]] (at 324), as Mary Queen of Scots **Mary Louise Douglas-Hamilton, [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Duchess of Hamilton]] (at 166), as Mary of Hamilton *Row of 2 women **Constance de Rothschild Flower, [[Social Victorians/People/Rothschild Family|Lady Battersea]] (at 328), as Lady Hunsdon **Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329), as Lady Burleigh *Row of 3 men **[[Social Victorians/People/Rothschild Family|Baron Ferdinand de Rothschild]] (at 330), as Casimir Count Patatine of Bavaria, an Austrian noble of the 16th century **George, [[Social Victorians/People/Powis|Earl of Powis]] (at 317), as Lord Herbert of Cherbury **Cyril Flower, 1st [[Social Victorians/People/Rothschild Family|Baron Battersea]] (at 110) as Lord Hunsdon *Row of 3 men **Mr. [[Social Victorians/People/Webb|Godfrey Webb]] (at 331), as Martin Frobisher **Algernon [[Social Victorians/People/Borthwick|Borthwick, Baron Glenesk]] (at 87) as Lord James Murray **The Hon. S. (George William [[Social Victorians/People/Lyttelton|Spencer) Lyttelton]] (at 332), as Sir Thomas Gresham *[[Social Victorians/People/Peel Family|Rochfort Maguire]] (at 241) was C. Maguire, Lord of Fermanagh The royals were mostly dressed in Elizabethan dress but are properly considered their own group. Besides them, these people were in Elizabethan dress at the ball but not listed as being in the Elizabeth procession or quadrille: *[[Social Victorians/People/Abercorn|Lord Frederick Hamilton]] (at 84), a Gentleman of the Court of Queen Elizabeth *[[Social Victorians/People/Abercorn|Mr. Ronald Hamilton]] (at 105), a Gentleman of the Court of Queen Elizabeth * Walter, [[Social Victorians/People/Mar and Kellie|Earl of Mar and Kellie]] (at 58), as an Elizabethan or perhaps as Sir Walter Scott * Henry Lascelles, 5th [[Social Victorians/People/Harewood|Earl Harewood]] (at 62), as Philip II of Spain *[[Social Victorians/People/Crewe-Milnes|Robert Offley Ashburton Crewe-Milnes]] (at 169), also as Philip II of Spain * [[Social Victorians/People/Jarvis|Weston (Mr. A. W.) Jarvis]] (at 106), as Sir Francis Walsingham * Emma Louise von Rothschild, [[Social Victorians/People/Rothschild Family|Lady Rothschild]] (at 112), as Anne of Cleves * Lady Alice Villiers Bootle-Wilbraham, the [[Social Victorians/People/Lathom|Countess of Lathom]] (at 213), as Catharine of Aragon *[[Social Victorians/People/Prince Charles of Denmark|Prince Charles of Denmark]] accompanied the Prince and Princess of Wales as a gentleman of the Court of Denmark in the time of Elizabeth *Susan St. Maur, [[Social Victorians/People/Somerset|Duchess of Somerset]] (at 209), as Jane Seymour *[[Social Victorians/People/Katharine Mary Montagu Douglas Scott|Lady Katharine Montagu-Douglas-Scott]] (at 25), as Mary Queen of Scots; perhaps she walked in this procession. * Algernon St. Maur, [[Social Victorians/People/Somerset|Duke of Somerset]] (at 27), as Somerset the Protector, older brother of Jane Seymour. (The ''Gentlewoman'' lists the Duchess of Somerset as a member of the Queen Elizabeth procession, but the ''Morning Post'' and the ''Times'' do not '''double check this'''.) Georgiana, [[Social Victorians/People/Hindlip|Baroness Hindlip]] was supposed to be part of the Elizabethan procession, but she and Samuel, [[Social Victorians/People/Hindlip|Baron Hindlip]] did not attend, as he was quite ill and in fact died less than two weeks later. The ''Morning Post'' typeset a visualization of the procession, more or less, like this: QUEEN ELIZABETH PROCESSION. ''Heralds''. ''Sir Walter Raleigh'', ''Sir P. Sydney'', ''Sir F. Drake'', Mr. E. Beckett. Mr. H. Warrender. Sir C. Hall. ''Lord Chief Justice'', ''Lord Burleigh'', ''Sir Richard Lowther'' Sir F. Jeune. Earl of Sandwich. ''(Lord High Falconer)'', Earl of Lonsdale. ''Lady Herbert of Cherbury, Countess of Shrewsbury, Countess of Lennox,'' Countess of Powis. Duchess of Roxburghe. Countess Spencer. ''Countess of Essex, Elisabeth Cavendish.'' Countess of Lonsdale. Mrs. A. James. [p. 7, Col. 5–6] ''Lord Darnley'' ''(carrying Sword of State),'' Colonel Leslie. ''Lord Leicester, Earl of Essex,'' Lord Tweedmouth. Earl of Essex. ''Yeoman, Yeoman,'' Duke of Roxburghe. Hon. D. Marjoribanks. ''Spanish Envoy,'' <u>| CANOPY. |</u> ''French Ambassador,'' Mr. Ephrussi. H. E. M. de Courcel. ''Queen Elizabeth,'' Lady Tweedmouth. ''Yeoman, Yeoman,'' Captain Mann Thomson. Mr. Rose. ''Duc d'Alençon, Will Somers Sir A. Brown, First'' Sir A. Edmonstone. ''(Court Jester). Viscount Montagu.'' Mr. Holden. Earl Spencer. ''Yeoman, Yeoman,'' Mr. E. Villiers. Mr. Harold Brassey. ''Cardinal Loraine, Swiss Burgher, Archbishop of Canterbury.'' Earl of Arran. Lord Rothschild. Lord Rowton. ''Mary Seaton, Mary Queen of Scots, Mary Hamilton'', Hon. Mrs. Greville. Lady Edmonstone. Duchess of Hamilton. ''Lady Hunsdon, Lady Burleigh,'' Lady Battersea. Lady de Ramsey. ''Casimir Count Patatine of Bavaria Lord Herbert of Cherbury, Lord Hunsdon,'' Baron F. de Rothschild. Earl of Powis. Lord Battersea. ''Martin Frobisher, Lord James Murray, Sir Thomas Gresham,'' Mr. Godfrey Webb. Lord Glenesk. Hon. S. Lyttelton. ''C. Maguire (Lord of Fermanagh),'' Mr. R. Maguire.<ref name=":0" />{{rp|7, Col. 5C–6B}} ==Other Groups== Other processions or quadrilles existed, not captured fully by the ''Morning Post'' but mentioned in, for example, the London ''Daily News'' story about the ball.The ''Morning Post'' is not complete in other ways as well, judging by other newspaper accounts or even descriptions from later in the big ''Morning Post'' story. Both the Knights of the Round Table of King Arthur procession and the Cosway Quadrille are examples of processions or quadrilles not detailed in the ''Morning Post''. === The Court of Marguerite de Valois === Theoretically, the court of Marguerite de Valois could have been included among the Elizabeth procession, but some of the people in this court, which was led by the Alexandra, Princess of Wales, might have been on the dais with her, so perhaps it could be imagined as a court but not a procession. * [[Social Victorians/People/Alexandra, Princess of Wales|Alexandra, Princess of Wales]], as Marguerite Valois *[[Social Victorians/People/Alington|Evelyn, Lady Alington]] (at 41), as Duchesse de Nevers * Princess Charles of Denmark (Princess Maud of Wales) * Prince Charles of Denmark was in this court? He was photographed with Princess Charles of Denmark and Princess Victoria of Wales; this photograph is in the Album.<ref name=":6">"Devonshire House Fancy Dress Ball (1897): photogravures by Walker & Boutall after various photographers." 1899. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait-list.php?set=515.</ref> * [[Social Victorians/People/George and Mary|Mary Teck, Duchess of York]], attended by ** [[Social Victorians/People/Beauchamp|Lady Mary Lygon]] (at 547), as Marie de Lorraine, a lady of the Court of Marguerite de Valois ** Sir Charles Cust (at 152) * Princess Louise, [[Social Victorians/People/Fife|Duchess of Fife]] (at 177) * [[Social Victorians/People/Princess Victoria of Wales|Princess Victoria of Wales]] (at 370) * Princess Victoria of Schleswig-Holstein (at 10) ===Queen Guinevere and the Knights of the Round Table of King Arthur procession=== A procession represented King Arthur's Round Table. This court is mentioned in the story in the ''Times'' as well as the Evening ''Mail'', which seems to have reprinted the story from the ''Times''.<ref name=":5" /><ref name=":9" />{{rp|p. 9, Col. 1c}} The ladies included Lady Ormonde, Lady Constance Butler, Lady Ashburton and Miss Chaplin. According to the ''Morning Post'' and the ''Gentlewoman'', the Knights of the Round Table were George, [[Social Victorians/People/Rodney|Baron Rodney]]; [[Social Victorians/People/Grosvenor|Hon. R. Grosvenor]]; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]]; and Hon. Grosvenor [[Social Victorians/People/Hood|Hood]].<ref name=":0" />{{rp|p. 8, Col. 1b}} <ref name=":8" />{{rp|p. 40, Col. 1c}} According to the ''Daily News,'' the Knights of the Table Round were "[[Social Victorians/People/Ashburton|Lord Ashburton]], Lord Rodney, [[Social Victorians/People/Bathurst|Lord Bathurst]], [[Social Victorians/People/Ampthill#Oliver Russell, Lord Ampthill|Lord Ampthill]], and [[Social Victorians/People/Beauchamp|Lord Beauchamp]]";<ref name=":1" />{{rp|p. 5, Col. 7a}} the newspaper accounts disagree on Lord Beauchamp in particular. George, Baron Rodney was 40 years old at the time of the ball; Seymour Henry Bathurst, [[Social Victorians/People/Bathurst|7th Earl Bathurst]] was nearly 33; Hon. Grosvenor [[Social Victorians/People/Hood|Hood]] was 29;  [[Social Victorians/People/Ashburton|Lord Francis Ashburton]] was nearly 31; [[Social Victorians/People/Ampthill|Lord Ampthill]] was 28; [[Social Victorians/People/Beauchamp|Lord Beauchamp]] was 25. We can see what they wore because some of them had their portraits taken in their costume. # Elizabeth [[Social Victorians/People/Ormonde|Butler]], the [[Social Victorians/People/Ormonde|Marchioness of Ormonde]] (at 373), was dressed as Guinevere #Lord [[Social Victorians/People/Westminster#Lord Gerald Grosvenor|Gerald Grosvenor]] (at 618), as Sir Launcelot (listed in the ''Times'' and the Evening ''Mail'', not in the ''Morning Post'') #Lord [[Social Victorians/People/Westminster#Lord Arthur Grosvenor|Arthur Grosvenor]] (at 619), Arthur Hugh Grosvenor, as King Arthur (listed in the ''Times'', not in the ''Morning Post'') # [[Social Victorians/People/Rodney|Corisande, Baroness Rodney]] (at 472) was also dressed as Queen Guinevere, according to her portrait in the Album in the National Portrait Gallery,<ref>"Corisande Evelyn Vere." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158471/Corisande-Evelyn-Vere-ne-Guest-Lady-Rodney-as-Queen-Guinevere.</ref> but she may not have been in this procession, although George, Baron Rodney was, as a Knight of the Round Table. # [[Social Victorians/People/Ormonde|Lady Constance Butler]] (Elizabeth Butler's daughter, at 374) was Lynette or Elaine # Mabel, [[Social Victorians/People/Ashburton|Lady Ashburton]] (at 375), as Enid # [[Social Victorians/People/Henry Chaplin|Miss Chaplin]] (probably Hon. Edith Helen Chaplin, at 407), as Elaine #Mr. [[Social Victorians/People/Henry Chaplin|Eric Chaplin]] (at 616), as Sir Gareth # John [[Social Victorians/People/Lister-Kaye|Lister Kaye]] (at 97), as Sir Kay #[[Social Victorians/People/Tilney|Mr. Tilney]] (at 615), as Sir Galahad # [[Social Victorians/People/Peel Family|Captain R. Peel]] (at 614), as Sir Bedivere # [[Social Victorians/People/Ampthill#Margaret Russell, Lady Ampthill|Margaret Russell, Lady Ampthill]] (at 419), as a Lady in Waiting at the Court of King Arthur #Mr. J. B. ([[Social Victorians/People/Leigh|John Blundell) Leigh]] (at 602), as Sir Tristram #Captain [[Social Victorians/People/Milner|George Francis Milner]] (at 617), as Sir Percevale [sic] # Knights of the Round Table (first four, ''Morning Post''; first two plus last three are London ''Daily News'') ##[[Social Victorians/People/Rodney|Lord Rodney: George, Baron Rodney]] (at 80) ##[[Social Victorians/People/Bathurst|Earl Bathurst]] (at 82) ##[[Social Victorians/People/Grosvenor|Hon. R. Grosvenor]] (at 81) ## [[Social Victorians/People/Hood|Hon. G. Hood]] (at 83). The printing on the portrait that was in the Album presented to the Duchess of Devonshire says, "The Hon. Grosvenor Hood as Sir Galahad."<ref>"Grosvenor Hood as Sir Galahad." ''Diamond Jubilee Fancy Dress Ball''. National Portrait Gallery https://www.npg.org.uk/collections/search/portrait/mw158513/Grosvenor-Arthur-Alexander-Hood-5th-Viscount-Hood-as-Sir-Galahad.</ref> ## Francis, [[Social Victorians/People/Ashburton|Lord Ashburton]] (at 376) ##[[Social Victorians/People/Ampthill|Oliver Russell, Baron Ampthill]] (at 77) ## William Lygon, 7th [[Social Victorians/People/Beauchamp|Earl Beauchamp]] (at 60) ===The Cosway Quadrille=== The "Cosway quadrille," with the [[Social Victorians/People/Roxburghe|Ladies Innes-Ker]] and the [[Social Victorians/People/Villiers|Ladies Villiers]], is not mentioned in the ''Morning Post'' article. This description from the London ''Daily News'' suggests that there were two Ladies Ker and two Ladies Villiers: "Very artistic was the "Cosway" quadrille, in which the Ladies Ker and the Ladies Villiers took part. The long clinging gowns of Oriental cream satin were veiled in pink muslin, and had very short waists and coloured silk sashes — two of blue and two of pink."<ref name=":1" />{{rp|6, Col. 1a}} These costumes seem to have been based on portraits by Richard rather than Maria Cosway. The Ladies Innes-Ker had the blue and the Ladies Villiers had the pink sashes. [[Social Victorians/People/Roxburghe|Lady Margaret Innes-Ker]] (at 23) and [[Social Victorians/People/Roxburghe|Lady Victoria Innes-Ker]] (at 383) are in the album given to the Duke and Duchess of Devonshire by some of the people attending the ball.<ref name=":6" /> [[Social Victorians/People/Villiers|Lady Edith Villiers]] (at 282) was dressed after Cosway and may have been in the Quadrille. The other Lady Villiers is not likely to be [[Social Victorians/People/Jersey|Lady Margaret Childs-Villiers]] (at 433), called Lady M. Villiers. We know Lady Margaret Villiers was already at the ball: her portrait as Madame Henriette Duchess d'Orleans is in the Album. She is not part of the same family Lady Edith came from, which was that of the [[Social Victorians/People/Villiers|Earl of Clarendon]]; Lady Margaret Childs-Villiers is part of the family of the [[Social Victorians/People/Jersey|Earl of Jersey]]. Another young woman from that family was [[Social Victorians/People/Jersey|Lady May Julia Child-Villiers]], who may in fact be the second of the Ladies Villiers in the Quadrille. Since a quadrille is usually a dance for four couples, this list would make up the Cosway quadrille if indeed four women took part: # [[Social Victorians/People/Roxburghe|Lady Margaret Innes-Ker]] (at 23) # [[Social Victorians/People/Roxburghe|Lady Victoria Innes-Ker]] (at 383) # [[Social Victorians/People/Villiers|Lady Edith Villiers]] (at 282) # [[Social Victorians/People/Jersey|Lady May Julia Childs-Villiers]] (at 372) Two other women were dressed after Cosway, neither from any of the Villiers families. Both Miss [[Social Victorians/People/Stanley#Madeline%20Stanley|Madeline Stanley]] (at 552) and [[Social Victorians/People/Marion Margaret Violet Lindsay Manners|Violet Manners, Marchioness of Granby]] (at 448) were in the Album. Miss Stanley was dressed as Lady Eliza Hopeton, "after a miniature by Cosway," and Lady Violet was dressed "after Cosway" as well. ==== People Whose Costumes Were "After Cosway" ==== * 2 Ladies Ker (if the London Daily News article is right) ** [[Social Victorians/People/Roxburghe|Lady Margaret Innes-Ker]] (at 23) ** [[Social Victorians/People/Roxburghe|Lady Victoria Innes-Ker]] (at 383) * 2 Ladies Villiers (if the London ''Daily News'' article is right) ** L[[Social Victorians/People/Villiers|ady Edith Villiers]] (at 282) ** [[Social Victorians/People/Jersey|Lady May Julia Child-Villiers]] (at 372)? ** [[Social Victorians/People/Jersey|Lady Margaret Childs-Villiers]] (at 433), as Madame Henriette Duchess d'Orleans * [[Social Victorians/People/Marion Margaret Violet Lindsay Manners|Violet Manners, Marchioness of Granby]] (at 448) * Miss [[Social Victorians/People/Stanley#Madeline Stanley|Madeline Cecilia Carlyle Stanley]] (at 552) === Courts of Charles I (and Henrietta Maria, Queen) and Charles II === A number of people were identified as being a member of the courts of Charles I or Charles II, even though no such group is directly discussed in the major stories. This is Charles II of England; the Duke of Devonshire was dressed as Charles V, Holy Roman Emperor of Germany, so this was not a group forming around him. Relevant people would be Cromwell, the Roundheads, and so on. #[[Social Victorians/People/Zetland|Lilian, Marchioness of Zetland]] (at 48), Henrietta Maria, wife of Charles I, after Van Dyck #[[Social Victorians/People/Manchester|Lord Charles Montagu]] (at 161), as Charles I, after Van Dyck #[[Social Victorians/People/Harcourt#Elizabeth Harcourt|Lady Elizabeth Harcourt]] (at 94), as a Lady of the Court of Henrietta Maria # Lord Edward Cecil (Edward Herbert [[Social Victorians/People/Salisbury|Gascoyne-Cecil]]) (at 411), as a courtier of Charles I #[[Social Victorians/People/Chaine|Colonel William Chaine]] (at 98), as a Gentleman of the Court of Charles II # Mr. [[Social Victorians/People/Portland|Cavendish-Bentinck]] (at 113), as a Gentleman of the Court of Charles II # Sir [[Social Victorians/People/Donald Mackenzie Wallace|Donald Mackenzie Wallace]] (at 114), as a Gentleman of the Court of Charles II # Sir Henry [[Social Victorians/People/Meysey-Thompson|Meysey-Thompson]] (at 116), in the Costume of a gentleman of the period of Charles II # Herbert Gardner, [[Social Victorians/People/Burghclere|Lord Burghclere]] (at 129) as a Puritan # William, [[Social Victorians/People/Portland|Duke of Portland]] (at 28), as "Steenie" Villiers, 1st Duke of Buckingham, according to the London ''Daily News''<ref name=":1" /> and the ''Pall Mall Gazette''<ref name=":7">“The Devonshire House Ball. A Brilliant Gathering.” The ''Pall Mall Gazette'' 3 July 1897, Saturday: 7 [of 10], Col. 2a–3a. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000098/18970703/019/0007.</ref>; the ''Morning Post''<ref name=":0" /> and the ''Times''<ref name=":5" /> say he went as Duca Filiberto di Savoia in the 17th-century section of the Venetians procession, where he is listed as well. # [[Social Victorians/People/Portland#George Cavendish-Bentinck|George (William George) Cavendish-Bentinck]] (at 666), as William, Baron Bentinck, A.D. 1643 # [[Social Victorians/People/Zetland|Lawrence Dundas, Marquis of Zetland]] (at 59), as the Duke of Buckingham (probably at the time of Charles I or II) == People Not Listed as Part of a Procession or Quadrille == === Subnetworks === '''Probably more than half''' the people who came in costume were not part of an organized procession or quadrille. Made up largely of courts of monarchs, and particularly women who were monarchs or leaders, the processions have a kind of internal coherence as people attending this ball were able to find people from those courts whom they were willing and able appear as. Because it would have taken communication and negotiation for people to determine and claim their place in the courts, the processions and quadrilles suggest that they make up subnetworks of people within the larger network of those who attended. The quadrilles would have been expected to rehearse, and we know that at least the Queen Elizabeth court met the night before the ball for dinner. Newspaper articles about the ball, the people who attended, and the costumes they wore reveal how this social world was dominated and organized by women's identities and practices. Most obviously, the party is called the Duchess of Devonshire's ball by everyone, then and now. The highest-status women present were queens or princesses in history, biblical stories, and legends, from Louisa, the Duchess of Devonshire's Zenobia to Queen Elizabeth, Empress Marie-Thérèse, and Catherine II of Russia. The courts were organized around these women. Leonore Davidoff discusses some of the implications of women's roles as gatekeepers in this social world at this time in her ''The Best Circles: Society Etiquette and the Season''.<ref name=":11">Davidoff, Leonore. The ''Best Circles: Society Etiquette and the Season''. Intro., Victoria Glendinning. The Cressett Library (Century Hutchinson), 1986 (orig ed. 1973).</ref> The fact that the courts were led by women is made clear in the newspaper reportage, sometimes in spite of overt language to the contrary. For example, what the newspapers call the courts of '''Louis XIV???''' are in fact the court of Marie Antoinette, led by Daisy, Countess of Warwick. Outside of this kind of organized coherence, of whatever degree, small groups of people decided to dress to reflect relationships, most often husbands and wives. Inevitably, working independently from each other, more than one person went to the ball dressed as the same person from history or even the same character from a novel, opera, or play. A few were men, but most were women, or at least most of those reported were women. There were multiple * Cleopatras ** [[Social Victorians/People/Pless#Daisy, Princess Henry of Pless|Daisy, Princess Henry of Pless]] (at 38), or as the Queen of Sheba ** [[Social Victorians/People/Paget Family#Minnie Paget|Minnie Paget]], Mrs. Arthur Paget (at 90) * Princesses de Lamballe ** Countess [[Social Victorians/People/Deym#Countess Isabel Deym|Isabel Deym]] (at 67) ** [[Social Victorians/People/John Milton Hay#Mr. John and Mrs. Clara Hay|Mrs. Clara Hay]] (at 153) ** Lady [[Social Victorians/People/Gordon-Lennox#Lady Blanche Gordon-Lennox|Blanche Gordon-Lennox]] (at 333) ** [[Social Victorians/People/Ampthill#Emily, Lady Ampthill|Emily, Lady Ampthill]] (at 420) * Queens of Sheba * Elizabeth, Queens of Bohemia ** [[Social Victorians/People/Cadogan|Beatrix, Countess Cadogan]] (at 55), as Elizabeth, Queen of Bohemia, after a painting by Honthorst ** Lady Ethel [[Social Victorians/People/Meysey-Thompson|Meysey Thompson]] (at 391), as Elizabeth, Queen of Bohemia ** [[Social Victorians/People/Westminster|Katherine Grosvenor, Duchess of Westminster]] (at 34), as Queen Elizabeth of Bavaria (who might not be Elizabethan, but [[Social Victorians/People/Rothschild Family|Baron Ferdinand de Rothschild]], as Casimir Count Patatine of Bavaria was in the Elizabethan procession) * Anne of Austria, Queen of France ** Anne of Austria, Queen of France ([[Social Victorians/People/Connaught|Princess Louise, Duchess of Connaught]]) ** Anne of Austria, Queen of France ([[Social Victorians/People/Jersey|Margaret Child-Villiers, Countess of Jersey]]) *Titania, Queen of the Fairies **Mademoiselle de Alealo Galiano **Susannah Graham Menzies *Night **Agnes, Lady Herschell **Marie, Baroness de Courcel *Napoleons Men are not absent from the reportage, of course, and sometimes, as with the Prince of Wales or men mentioned as part of a couple or when their wives were not. Certainly with the Prince of Wales, a principle other than gender is at work: he is the monarch of this social world of women, in some ways the way his mother was monarch of the political world of men. === Individuals and Their Costumes === The Royals, obviously, would not have been part of any procession or quadrille because they were on the dais instead. Others, whose costumes are described in enough detail for us to know how they were dressed are listed here. # Hon. Oliver [[Social Victorians/People/Borthwick|Borthwick]] (at 89), dressed as Marshal Turenne (reign of Louis XIV) or an officer d'Infanterie #[[Social Victorians/People/Paget Family|Colonel Arthur Paget]] (at 91), dressed as Edward the Black Prince # Arthur Balfour (at 86), the [[Social Victorians/People/Balfour|Right Hon. A. J. Balfour]], in a Dutch costume of 1660 # [[Social Victorians/People/Harcourt#Sir William Harcourt|Sir William Harcourt]] (at 128) as Sir Simon Harcourt, the first Lord Harcourt, in 1712, as Lord Chamberlain #[[Social Victorians/People/Salisbury|Lady Gwendolen Cecil]] (at 404), as Portia # [[Social Victorians/People/Cavendish|Lady Edward Cavendish]] (at 393), as Madame de Maintenon # Alfred [[Social Victorians/People/Rothschild Family|Rothschild]] (at 605), as a French noble of the 16th century # Sir [[Social Victorians/People/Hartopp|Charles Hartopp]] (at 111), as Napoleon I #Lady [[Social Victorians/People/Hartopp|Millicent Hartopp]] (at 488), as the Empress Josephine # Mr. [[Social Victorians/People/Guest|Montague Guest]] (at 115), as Montague Bertie, second Earl of Lindsey # Mr. [[Social Victorians/People/Arthur Stanley Wilson|Arthur Wilson]] (at 118), in a costume from a portrait by Velasquez # Mary (Mrs. Arthur) [[Social Victorians/People/Arthur Stanley Wilson|Wilson]] (at 395) wore a dress in the Georgian period # [[Social Victorians/People/Lathom|Lady Edith Wilbraham]] (at 119), as Peg Woffington # Lord [[Social Victorians/People/Henry James|James of Hereford]] (at 122), as Sir Thomas More # Miss [[Social Victorians/People/Henry James|James]] (at 396), as Eugénie Hortense de Beauharnais, Louis Bonaparte's wife # [[Social Victorians/People/Talbot|Lord Edmund Talbot]] (at 123), as a Gentleman of the Spanish Court of the early 17th Century # [[Social Victorians/People/Wyndham|Colonel Sir Charles Wyndham Murray]], "Mr. C. [[Social Victorians/People/Wyndham|Wyndham]], M.P.," (at 124), as the Emperor John Polaeologus II on his State visit to Venice in 1438. # Lilian Maud [[Social Victorians/People/Marlborough|Spencer-Churchill]] (at 571), as a Watteau shepherdess # Norah Beatrice Henriette [[Social Victorians/People/Marlborough|Spencer-Churchill]] (at 572), also as a Watteau shepherdess # John Lambton, 3rd [[Social Victorians/People/Durham#John Lambton, 3rd Earl of Durham|Earl of Durham]] (at 141), as the Duc de Nemours, period Henri III #[[Social Victorians/People/Howe|Isabella, Countess Howe]] (at 489), as Lady Howe of 1758 #Richard George Penn Curzon, [[Social Victorians/People/Howe|Viscount Curzon]] (at 197), as Admiral Lord Howe, husband of the 1758 Lady Howe, accompanied his mother # Captain [[Social Victorians/People/Holford|George Holford]] (at 385), as Philip IV of Spain # Francis [[Social Victorians/People/Gathorne-Hardy|Gathorne-Hardy]] (at 352), as in either the Archduchess Marie-Karoline and Emperor Joseph II section of the Austrian Court of Maria Theresa Quadrille or as a gentleman of the Court of Louis XV # The [[Social Victorians/People/Grand Duke Michael of Russia|Grand Duke Michael of Russia]] (at 8), as Henri IV of Navarre and France, first married to Marguerite de Valois but father to the children of Gabrielle d'Estrées, personated by [[Social Victorians/People/Grand Duke Michael of Russia|Sophia, Countess de Torby]] (at 184), his morganatic wife. #[[Social Victorians/People/Buccleuch|Louisa Jane, Duchess of Buccleuch]] (at 24), as Elizabeth, Duchess of Buccleuch, after a painting by Sir Joshua Reynolds #[[Social Victorians/People/Buccleuch|William, Duke of Buccleuch]] (at 20), as either William Cavendish, Duke of Newcastle or Charles I #[[Social Victorians/People/Constance Anne Montagu Douglas Scott|Lady Constance Montagu-Douglas-Scott]] (at 26), as a Watteau shepherdess #[[Social Victorians/People/Dudley|William, Earl of Dudley]] (at 63), as Prince Rupert, so he could have been in the Charles I or Charles II procession but is not listed in any of the newspaper reports as being in a procession or quadrille; his wife, Rachel, [[Social Victorians/People/Dudley|Countess of Dudley]] (at 31) is not the Lady Dudley in the Duchesses procession; that's probably his mother, [[Social Victorians/People/Dudley|Georgina, Dowager Countess Dudley]]. #[[Social Victorians/People/Alva|Carlos, 16th Duke of Alba]] (at 32), as his ancestor at the Court of Philip II of Spain #[[Social Victorians/People/Derby|Constance Stanley, Countess of Derby]] (at 36), as Duchess of Orleans. (Members of her family, the Stanleys, are in the Duchesses and the Louis XV and Louis XVI court processions. #[[Social Victorians/People/Forbes|Lady Angela St. Clair-Erskine Forbes]] (at 37), as Queen of Naples # Lawrence Dundas, Earl of [[Social Victorians/People/Zetland|Ronaldshay]] (at 529), as Sir Peter Teazle #[[Social Victorians/People/Warwick|Lady Eva Greville Dugdale]] (at 409), as great-aunt Lady Anne Bingham #[[Social Victorians/People/Ellesmere|Francis Egerton, 3rd Earl of Ellesmere]] (at 68), as James I #[[Social Victorians/People/Deym|Count Franz Deym]] (at 66), as General Wallenstein #[[Social Victorians/People/Deym|Countess Isabel Deym]] (at 67), as the Princesse de Lamballe, one of Napoleon's sisters #[[Social Victorians/People/Clary Aldringen|Thérèse, Countess Clary and Aldringen]] (at 191), as one of Napoleon's sisters #[[Social Victorians/People/Kinsky|Josephine, Countess Kinsky]] (at 394), as one of Napoleon's sisters, though other Princesses de Lamballe, [[Social Victorians/People/Gordon-Lennox|Lady Blanche Gordon-Lennox]] (at 333) appeared in the Louis XV and XVI procession and [[Social Victorians/People/Ampthill#Emily, Lady Ampthill|Emily, Lady Ampthill]] (at 420), also another Princess de Lamballe #[[Social Victorians/People/Ampthill#Emily, Lady Ampthill|Emily, Lady Ampthill]] (at 420), also as the Princess de Lamballe #Miss [[Social Victorians/People/Ampthill#Margaret Russell, Lady Ampthill|Constance Russell]] (at 418), as a flower seller or bouquetière, period Louis XV #[[Social Victorians/People/Selborne|Beatrix Palmer, Countess Selborne]] (at 557), as Lady Percy, after a picture by Vandyk #[[Social Victorians/People/Selborne|William Palmer, 2nd Earl of Selborne]] (at 70), as an officer of the Duke of Marlborough's Army #[[Social Victorians/People/Peel Family|John Seymour Wynne-Finch]] (at 680), as Cosmo, Grand Duke of Tuscany #[[Social Victorians/People/Ilchester|Lady Muriel Fox Strangways]] (at 403), as one of Queen Charlotte's bridesmaids #Frederick, [[Social Victorians/People/Wolverton|Baron Wolverton]] (at 79), as King Richard, Coeur de Lion #[[Social Victorians/People/Harcourt#Lewis Harcourt|Lewis Harcourt]] (at 669), as 1st Viscount Nuneham, c. 1750 #[[Social Victorians/People/Lister-Kaye|Lady Natica Lister-Kaye]] (at 499), as Duchesse de Guise in the time of Henri III #[[Social Victorians/People/Chaine|Maria Chaine]] (at 490) as Madame Sans Gêne, from Victorien Sardou and Émile Moreau's 1893 play ''Madame Sans Gêne'' #[[Social Victorians/People/Shrewsbury|Margaret Jane Stuart-Wortley Chetwynd-Talbot]], Lady Talbot (at 485), as a Valkyrie #[[Social Victorians/People/Salisbury|Lady Robert Cecil]] — Eleanor Lambton Gascoyne-Cecil — (at 450), as Valentina Visconti (XV Century) #[[Social Victorians/People/Cavendish|Hon. Victor Cavendish]] (at 121), as a Tudor or an Elizabethan ambassador, from a Holbein in the National Gallery #[[Social Victorians/People/Cavendish|Mr. S. Cavendish]] (at 700), as Count Chotak #Louisa Montefiore, [[Social Victorians/People/Rothschild Family|Lady de Rothschild]] (at 674), as Lady Vaux, after a picture by Holbein #Mr. [[Social Victorians/People/Rothschild Family|Leopold de Rothschild]] (at 527), as Duc de Sully #Mrs. Leopold ([[Social Victorians/People/Rothschild Family|Marie Perugia) Rothschild]] (at 528), as Zobeida #[[Social Victorians/People/Rothschild Family|Alfred Rothschild]] (at 605), as King Henry III #The [[Social Victorians/People/Long|Right Hon. W. H. Long, M.P.]], (at 117), as a cavalier from the time of Charles II, after a picture by Sir Peter Lely. #[[Social Victorians/People/Long|Mrs. Doreen Long]] (at 484) as Urania, Goddess of Astronomy or an astronomer #[[Social Victorians/People/Argyll|Lady Elspeth Angela Campbell]] (at 621), in white with gold wings #Madame Marie-Elisabeth [[Social Victorians/People/de Courcel|Chodron de Courcel]] (at 182), as Night #Mademoiselle Henriette [[Social Victorians/People/de Courcel|Chodron de Courcel]] (at 371), as a Valkyrie #Mademoiselle [[Social Victorians/People/de Courcel|Chodron de Courcel]] (at 498), as a Valkyrie #[[Social Victorians/People/de Soveral|M. Luis de Soveral]] (at 135), as Count d'Almada, A.D. 1640 #[[Social Victorians/People/Ripon|Frederick Oliver Robinson, Earl de Grey]] (at 656), as Admiral Coligny #[[Social Victorians/People/Rosebery|Archibald, Earl of Rosebery]] (at 139), as Horace Walpole #[[Social Victorians/People/Gosford|Archibald Acheson, 4th Earl of Gosford]] (at 143), as Robert de la Marck (the rest of his family was in the Duchesses procession) #Beatrix Herbert, [[Social Victorians/People/Pembroke|Countess Pembroke]] (at 146), as Mary Sidney, Countess of Pembroke, after the picture by Marcus Gheeraedts #Sidney Herbert, [[Social Victorians/People/Pembroke|Earl Pembroke]] (at 181), as William, 1st Earl of Pembroke after Holbein #[[Social Victorians/People/Pembroke|Lady Beatrix Frances Gertrude Herbert]] (at 648), as Signora Bacelli after Gainsborough #Ana, Countess [[Social Victorians/People/Casa de Valencia|Casa de Valencia]] (at 148), as Nuit d'Espagne #[[Social Victorians/People/Henry White|Daisy (Mrs. Henry) White]] (at 151), as Morosina Morosini Dogaressa of Venice #[[Social Victorians/People/Buckingham and Chandos|Anne (Alice Anne), Duchess of Buckingham]] (at 155), as Caterina Cornaro, Queen of Cyprus #[[Social Victorians/People/Wilbraham Egerton of Tatton|Lord Wilbraham Egerton of Tatton]] (at 591), as the Doge Morosini #Rt. Hon. [[Social Victorians/People/Hamilton|Sir Edward Walter Hamilton]] (at 683), as John of Gaunt #Kathleen, [[Social Victorians/People/Falmouth|Viscountess Falmouth]] (at 471), as Madame Recamier #Albert Count von [[Social Victorians/People/Mensdorff|Mensdorff-Pouilly-Dietrichstein]] (at 180), as Henri III, King of France #Thomas Lister, [[Social Victorians/People/Ribblesdale|4th Baron Ribblesdale]] (at 185), as Lord Ribblesdale, after the Lawrence picture of his grandfather #Charlotte, [[Social Victorians/People/Ribblesdale|Lady Ribblesdale]] (at 206), as Duchess of Parma #[[Social Victorians/People/Dudley|Rachel, Countess of Dudley]] (at 31), as Queen Esther #[[Social Victorians/People/Dunraven|Lady Aileen May Wyndham-Quin]] (at 661), as Queen Hortense #[[Social Victorians/People/Arthur Sassoon|Arthur Sassoon]] (at 553), as Chief of the Janissaries #Mr. R. Sassoon, probably [[Social Victorians/People/Reuben David Sassoon|Reuben David Sassoon]] (at 533), as a Persian Prince #Miss Sassoon, probably Mozelle or Louise Judith [[Social Victorians/People/Reuben David Sassoon|Sassoon]] (at 534), as a "Japanese Lady" #Mary, [[Social Victorians/People/Suffolk|Countess of Suffolk]] (at 538), as a Countess of Suffolk in 1766 #[[Social Victorians/People/Suffolk|Miss Daisy Leiter]] (at 684), in what looks to be an 18th-century dress and headdress #[[Social Victorians/People/Asquith|H. H. Asquith]] (at 381), as a roundhead #Lord St. Oswald, Rowland Winn, [[Social Victorians/People/Saint Oswald|2nd Baron St. Oswald]], (at 641) was dressed as an officer of the Regiment de Pondichery, 1772 #The [[Social Victorians/People/Saint Oswald|Hon. Maud Winn]] (at 642), as Madame La Motte #[[Social Victorians/People/Von Andre|Herr Von André]] (at 386), as Benvenuto Cellini #Lady [[Social Victorians/People/Warrender|Ethel Maud Warrender]] (at 520) as "Duchesse de Lauzun, La Grande Mademoiselle" #Clara ([[Social Victorians/People/John Milton Hay|Mrs. John) Hay]] (at 153), as one of the Princesses de Lamballe #Candida Hay, [[Social Victorians/People/Tweeddale|Marchioness of Tweeddale]] (at 399), as Josephine, wife of Napoleon, with her sons Lord Arthur Vincent Hay and Lord William George Montagu Hay bearing her train (also at 399) #William Montagu Hay, the [[Social Victorians/People/Tweeddale|Marquis of Tweeddale]] (at 400), as Saint Bris from ''Les Huguenots'' #Lady [[Social Victorians/People/Tweeddale|Clementine Hay]] (at 629), as Valentina from ''Les Huguenots'' #Mr. [[Social Victorians/People/Brett|Reginald Balioll Brett]] (at 603), as a gentleman of France #Mrs. [[Social Victorians/People/Brett|Eleanor Frances Brett]] (at 604), as Manon Lescaut #[[Social Victorians/People/Dyke|Lady Emily Hart Dyke]] (at 556), as an Elizabethan lady #[[Social Victorians/People/Dunville|Violet Dunville]] (at 650), as Edith Plantagenet #[[Social Victorians/People/Dunville|John Dunville]] (at 649), as the Emperor Yuan of China #[[Social Victorians/People/Cole-Hamilton|Lucy Charlewood Cole-Hamilton]] (at 652), as Amy Robsart #[[Social Victorians/People/Cole-Hamilton|Claud George Cole-Hamilton]] (at 653), as Edmund Tressilian #[[Social Victorians/People/Cadogan|Hon. Mrs. Cadogan]] (at 668), in Elizabethan costume #[[Social Victorians/People/Belper|Henry, Lord Belper]] (at 512), as Gentleman at Arms, time of Charles II #[[Social Victorians/People/Maurice Baring|Hon. Maurice Baring]] (at 678), as Marlborough #[[Social Victorians/People/Spencer|Mr. R. (Charles Robert) Spencer]] (at 493), in Elizabethan dress #[[Social Victorians/People/Antrim|Hon. Alexander McDonnell]] (at 676), as Mercutio #[[Social Victorians/People/Malcolm|Mr. Ian Malcolm]] (at 692), as a Courtier, time of Henry VIII #[[Social Victorians/People/Marlborough#Lord Churchill|Lord Churchill]] (at 611), as Columbus #[[Social Victorians/People/Leigh|Captain Gerard Leigh]] (at 570), as a member of the Life Guard, time of Charles II #James Hamilton, [[Social Victorians/People/Abercorn|Marquis of Hamilton]] (at 657), in the period of Charles II #Albertha Frances Anne Hamilton Spencer-Churchill, [[Social Victorians/People/Marlborough|Marchioness of Blandford]] (at 601), as a 16th-century Abbess #Mrs. [[Social Victorians/People/Lyttelton|Edith Lyttelton]] (at 580), as a parson's daughter, after a picture by Romney #Georgina Cavendish Coke, [[Social Victorians/People/Leicester|Countess of Leicester]] (at 516), as a Venetian lady #Lady [[Social Victorians/People/Walsh|Clementine Walsh]] (at 523) wore an Empire costume #Lady [[Social Victorians/People/Brassey|Violet Brassey]] (at 531), as Juliet #Mr. [[Social Victorians/People/Brassey|Leonard Brassey]] (at 530), as Apollo #Lord [[Social Victorians/People/Northampton|Alwyne Frederick Compton]] (at 434), as Sir William Compton, time of Charles I #Lady [[Social Victorians/People/Northampton|Mary Compton]] (at 435), as Mme. de Chevreuse, time of Louis XIII #The Hon. Mrs. [[Social Victorians/People/Lowther|Gwendoline Lowther]] (at 672), as Madame de Tallion (Incroyable) #Mr. [[Social Victorians/People/Burton|J. E. Baillie]] (at 666), in a military costume of the early part of the 19th century #The Hon. [[Social Victorians/People/Mar and Kellie#The Hon. William Erskine|William Erskine]] (at 696), as an Incroyable #Mr. [[Social Victorians/People/Portal|William Wyndham Portal]] (at 549) in Court dress, period Marie Thérèse, or Comte de Candale from ''Un Mariage sous Louis XV'' #Florence, [[Social Victorians/People/Portal|Lady Portal]] (at 550), as Comtesse de Candale from ''Un Mariage sous Louis XV'' #Mr. [[Social Victorians/People/Cassel|Ernest Cassel]] (at 462), as Velasquez #Mr. [[Social Victorians/People/Beit|Alfred Beit]] (at 384), as Frederick of Nassau, period 1630 #[[Social Victorians/People/Wombwell|Stephen Frederick Wombwell]] (at 671), as George Villiers, Duke of Buckingham #The Hon. [[Social Victorians/People/Campbell|K. Campbell]] (at 695), as Charles Edward, the Pretender #Mr. [[Social Victorians/People/Chaine|W. R. Chaine]] (at 694), as a gentleman of the Court of Queen Elizabeth #Mr. [[Social Victorians/People/Cavendish|R. Cavendish]], probably Rt. Hon. Lord Richard Cavendish, (at 107), in a costume of the period of Marie Thérèse #The Hon. [[Social Victorians/People/Peel Family|W. G. Peel]] (at 679), in a 15th-century Venetian costume #Lady [[Social Victorians/People/Leicester|Mabel Coke]] (at 644), as a woodland nymph #The Hon. [[Social Victorians/People/Suffield|Bridget Harbord]] (at 398), as the Bride of Abydos #Lady [[Social Victorians/People/Hamilton Temple Blackwood|Florence Blackwood]] (at 637), as Flora, Goddess of Flowers #Lord [[Social Victorians/People/Hamilton Temple Blackwood|Terence Blackwood]] (at 638), as Captain Blackwood, Royal Navy #Hon. [[Social Victorians/People/Maurice Baring|John Baring]] (at 675), as Henry IV #Captain [[Social Victorians/People/Durham#Captain Hedworth Lambton|Hedworth Lambton]] (at 660), as a Roman #Major [[Social Victorians/People/Drummond|Laurence Drummond]] (at 507), as a soldier #Hon. [[Social Victorians/People/Curzon|George Curzon]] (at 495), as a Spanish Admiral #Sir [[Social Victorians/People/Cust|Charles Cust]] (at 152), in a soldier's uniform #[[Social Victorians/People/Dawson|Douglas Dawson]] (at 673), as Raoul de Nangis, Les Huguenots #[[Social Victorians/People/Dawson|Major Vesey Dawson]] (at 521), as a soldier #Pierre, [[Social Victorians/People/Stonor#Pierre, Marquis d'Hautpoul|Marquis d'Hautpoul]] (at 387), in a Vandyck dress #Julia Caroline Stonor, [[Social Victorians/People/Stonor#Julia Caroline Stonor, Marquise of Hautpoul|Marquis d'Hautpoul]] (at 388), as Elsa, in ''Lohengrin'' #Hon. [[Social Victorians/People/Stonor#Hon. Harry Julian Stonor|Harry Julian Stonor]] (at 389), as Lohengrin #[[Social Victorians/People/Adair|Mrs. Adair]] (at 390), as Egyptian Queen Nitocris #Edward Cecil Guiness, [[Social Victorians/People/Iveagh|Lord Iveagh]] (at 382), as a Cavalier, Louis XIII. period #Mr. [[Social Victorians/People/Cavendish Bentinck|Arthur James]] (at 480), as an English gentleman of the fifteenth century #Mr. [[Social Victorians/People/Rothschild Family#Mr. Lewis Flower|Louis Flower]] (at 506), as a French Commissary General, First Empire #Mr. [[Social Victorians/People/William James|William Dodge James]] (at 686), as d'Artagnan #Lady [[Social Victorians/People/Farquhar|Emilie Farquhar]] (at 639), as Duchess de Mailly, Lady in Waiting to Queen Marie Antoinette #Sir [[Social Victorians/People/Farquhar|Horace Brand Farquhar]] (at 380), as Count Egmont or a Dutch burgher after Rembrandt #Colonel [[Social Victorians/People/Swaine|Charles Edward Swaine]] (at 415), as an officer, 11th Dragoons, 1742 #The Right Hon. [[Social Victorians/People/Henry Chaplin|Henry Chaplin]], M.P. (at 379), as General Lefevre, First Empire #Jesusa Murrieta, [[Social Victorians/People/Santurce|Marquisa de Santurce]] (at 633), as the Infanta of Spain #Mr. F. de Murrieta, possibly Don José Murrieta del Campo Mello y Urritio, [[Social Victorians/People/Santurce|Marques de Santurce]] (at 634), as Philip I. of Spain #Miss [[Social Victorians/People/Magniac|Geraldine Magniac]] (at 640), as Dawn or the Sun #Mrs. [[Social Victorians/People/Arthur Stanley Wilson#Mrs. Florence and Mr. Charles Henry Wilson|Charles (Florence) Wilson]] (at 413), as Guinevere #Miss [[Social Victorians/People/Burton|Jane Thornewill]] (at 712), in a costume of the Georgian era #Mr. [[Social Victorians/People/Cork and Orrery|W. Boyle]] (at 504), in an Elizabethan costume #[[Social Victorians/People/Mills|Hon. Violet Mills]] (at 596), in the period of Charles II #Mrs. [[Social Victorians/People/Hartmann|Hartmann]] (at 505), as Madame Sans-Gêne #Mr. [[Social Victorians/People/Shaftesbury|W. W. Ashley]] (at 658), as a soldier #Mr. [[Social Victorians/People/Crichton|Herbert Creighton]] (at 647), as Charles I #Mary [[Social Victorians/People/Murray|Graham Murray]] (at 687), as Titania #Mr. [[Social Victorians/People/Milner|Harry (Marcus Henry) Milner]] (at 612), as a Chasseur of the Louis XV period #Mr. [[Social Victorians/People/Strong|Arthur Strong]] (at 613), as Voltaire at the age of 25 #Mr. [[Social Victorians/People/Longhurst|A. P. Longhurst]] (at 689), as an Egyptian runner #[[Social Victorians/People/Yznaga|Emilia Yznaga]] (at 360), as Cydalise of the Comedie Italienne from the time of Louis XV #Laura, [[Social Victorians/People/Gleichen|Princess Victor of Hohenlohe Langenburg]] (at 16), in a Louis Quinze costume #[[Social Victorians/People/Gleichen|Countess Helena Gleichen]] (at 17), as Joan of Arc #Lady [[Social Victorians/People/Southampton|Hilda Southampton]] (at 402), as Beatrice #[[Social Victorians/People/Henry Irving|Henry Irving]] (at 414), as Cardinal Wolsey #Mrs. [[Social Victorians/People/Bischoffsheim|Clarissa Bischoffsheim]] (at 429), as Anne of Austria #Violet Manners, [[Social Victorians/People/Marion Margaret Violet Lindsay Manners|Marchioness of Granby]] (at 448), as Isabella Marchioness of Granby #[[Social Victorians/People/Neumann|Ludwig Neumann]] (at 452), as Le Duc de Joyeuse #Margaret Montagu-Douglas-Scott, [[Social Victorians/People/Dalkeith|Countess of Dalkeith]] (at 460), as Helen, Countess of Dalkeith #Lord [[Social Victorians/People/Herschell|Farrer Herschell]] (at 496), as Lord Chief Justice Sir Edward Coke #Lady [[Social Victorians/People/Herschell|Agnes Herschell]] (at 497), as Night #The [[Social Victorians/People/Fitzwilliam#Mrs. Edith Fitzwilliam|Hon. Edith Wentworth Fitzwilliam]] (at 635), in a costume based on a painting by Romney #The [[Social Victorians/People/Fitzwilliam#The Hon. Reginald Fitzwilliam|Hon. Reginald Fitzwilliam]] (at 636), as Nelson #Maud Fitzwilliam, [[Social Victorians/People/Fitzwilliam#Lord and Lady Milton|Viscountess Milton]] (at 501), as Madame Le Brun #Catherine (the [[Social Victorians/People/Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor#Hon. Catherine and Mr. Algernon Grosvenor|Hon. Mrs. Algernon) Grosvenor]] (at 510), as Marie Louise #Hardinge Stanley Giffard, [[Social Victorians/People/Halsbury|Lord Halsbury]] (at 147), as George III #Sir [[Social Victorians/People/Poynter|Edward Poynter]] (at 546), as Titian #Hon. [[Social Victorians/People/Dupplin#Hon. Marie Hay|Marie Hay-Drummond]] (at 682), as Mademoiselle Andrée de Taverney, A.D. 1775 #Mrs. [[Social Victorians/People/Walker|Sophie Walker]] (at 584), as Vivien #Mr. [[Social Victorians/People/Walker|Hall Walker]] (at 583), as Merlin #Sir [[Social Victorians/People/Blois|Ralph Blois]] (at 593), as Jerome Buonaparte, King of Westphalia #[[Social Victorians/People/Fitzgerald|Amelia, Lady FitzGerald]] (at 599), as Marie Joséphe, Queen of Poland, A.D. 1737 #Prince [[Social Victorians/People/Duleep Singh|Victor Duleep Singh]] (at 558), as Akbar #[[Social Victorians/People/Kintore|Sydney, Countess Kintore]] (at 608), as Jane, Duchess of Gordon #Lady [[Social Victorians/People/Kintore|Hilda Keith-Falconer]] (at 677), as Lady Susan Gordon #Madame [[Social Victorians/People/Baudon de Mony|Baudon de Mony]] (at 568), as Princess of Navarre #Monsieur [[Social Victorians/People/Baudon de Mony|Baudon de Mony]] (at 567), as a Louis-XIII Musketeer #Mademoiselle [[Social Victorians/People/de Alcalo Galiano|de Alealo Galiano]] (at 631), as the Queen of the Fairies #Mademoiselle [[Social Victorians/People/de Alcalo Galiano|Consuelo de Alealo Galiano]] (at 632), as Veure de Pierrot #Blanche, [[Social Victorians/People/Coventry#Blanche, Countess of Coventry|Countess of Coventry]] (at 559), as an earlier Countess of Coventry #Lady [[Social Victorians/People/Coventry#Lady Anne Coventry|Anne Coventry]] (at 560, as Serena #Lady [[Social Victorians/People/Coventry#Lady Dorothy Coventry|Dorothy Coventry]] (at 561), also as Serena #Rose Towneley-Bertie, [[Social Victorians/People/Norreys|Lady Norreys]] (at 680), as a Paysanne Galante from the time of Louis XVI #[[Social Victorians/People/Lukach|Joseph Harry Lukach]] (at 685), as Henri de Rohan #Alice Emily White Coke, Viscountess Coke (at 643), in 18th-century dress #Hon. [[Social Victorians/People/Stanley#Hon. Ferdinand Charles Stanley|F. C. (Ferdinand Charles) Stanley]] (at 251), as a Grenadier Guard officer, 1660 #Lord [[Social Victorians/People/Stanley#Lord Stanley and Lady A. Stanley|Edward Stanley]] (at 187), as a Grenadier Guard officer, 1660 #[[Social Victorians/People/Jeune#Madeline Cecilia Carlyle Stanley|Madeline Cecilia Carlyle Stanley]] (at 552), accompanying [[Social Victorians/People/Jeune|Sir Francis Jeune]] and [[Social Victorians/People/Jeune|Lady Jeune]], as Lady Hopeton, after a miniature by Cosway #Henry William Crichton, [[Social Victorians/People/Crichton#Lord Crichton|Viscount Crichton]] (at 646), in a costume of the Empire period #[[Social Victorians/People/Ellis#Major-General Ellis|General Ellis]] (at 654), as an Elizabethan noble #Lady [[Social Victorians/People/Durham#Lady Anne Lambton|Anne Lambton]] (at 659), as Mme. de Longueville, Louis XIII period #Mrs. [[Social Victorians/People/Burton#Nellie Lisa Baillie and Colonel James Evan Bruce Baillie of Dochfour|Nellie Lisa Baillie]] (at 667), from the family group by Gainsborough #Mrs. [[Social Victorians/People/Burton#Mr. and Mrs. Hamar Bass|Hamar (Louisa) Bass]] (at 439), from picture at Chesterfield House #Miss [[Social Victorians/People/Burton#Jane Thornewill|Jane Thornewill]] (at 664), in a costume of the Georgian era #Mrs. [[Social Victorians/People/Sneyd|Mary Evelyn Ellis Sneyd]] (at 667), as a Venetian #Mr. [[Social Victorians/People/Foley|Foley]] (at 690), as a Hussar of the Napoleonic era #Mr. [[Social Victorians/People/Crawley|E. Crawley]] (at 692), as a gentleman of the period of Charles I #Mr. [[Social Victorians/People/Carter|J. Carter]] (at 697), as a Courtier of Elizabeth #Lady [[Social Victorians/People/Wolseley|Louisa Wolseley]] (at 541), in an 18th-century dress (?) #Edward Villiers, [[Social Victorians/People/Villiers#Edward Villiers, 5th Earl Clarendon|5th Earl Clarendon]] (at 65), as Villiers, Viscount Grandison, after portrait by Vandyke #[[Social Victorians/People/Souza Correa|M. de Souza Correa]] (at 178), as a Knight Templar, XIV Century #Margaret Child-Villiers, [[Social Victorians/People/Jersey#Lord and Lady Jersey|Countess of Jersey]] (at 432), as Anne of Austria #Mary, Countess Minto (at 544) was Princess [[Social Victorians/People/Minto#Mary, Countess of Minto|Andrillon]] #Lady [[Social Victorians/People/Pembroke#Lady Beatrix Herbert|Beatrix Herbert]] (at 648), as Signora Bacelli after Gainsborough #Mrs. [[Social Victorians/People/Chamberlain#Mrs. Mary Chamberlain|Mary Chamberlain]] (at 491), as Madame d'Epinay #Windham Thomas Wyndham-Quin, [[Social Victorians/People/Dunraven#Earl and Countess Dunraven|4th Earl of Dunraven and Mount-Earl]] (at 199), as Cardinal Mazarin #Lady [[Social Victorians/People/Ancaster#Lady Evelyn Ewart|Evelyn Ewart]] (at 401), as the Duchess of Ancaster, Mistress of the Robes to Queen Charlotte, 1757, after a picture by Hudson #Lady [[Social Victorians/People/Buchan#Lord and Lady Cardross|Rosalie Cardross]] (at 276), as La Duchesse de Lavis #Lady [[Social Victorians/People/Duncombe|Florence Duncombe]] (at 456), as a Lady of the Court of Marie Stuart #Lord [[Social Victorians/People/Gordon-Lennox#Lord Algernon Gordon Lennox|Algernon Gordon Lennox]] (at 623), as a Grenadier Guard officer #Lady [[Social Victorians/People/Cole|Florence Cole]] (at 239), as Hortense Beauharnais #Mr. [[Social Victorians/People/Myddleton-Biddulph|Algernon Myddleton Biddulph]] (at 268), as Count Soltykoff or Saltykov == Notes and Questions == # Work this info in: <blockquote>There is intense excitement (says a lady correspondent) about the Duchess of Devonshire's historical and fancy dress ball to take place to-night. One of the prettiest of Princesses, daughter of a lovely Irish mother, goes as Queen of Sheba, her sister representing an Ethiopian attendant. An illustrious personage is to head the list of old-world knights, and a beautiful Marchioness is to represent Guinevere, her fair young daughter going as Elaine. A most lovely lady is to personate Queen Marie Thérèse, surrounded by her Court. There is to be a procession of young girls dressed after Cosway's miniatures, and an Elizabethan quadrille is to be danced, in which the Virgin Queen herself is to appear, as well as Essex, Raleigh, Shakespeare, and other well-known characters. Another quadrille will be made up of ladies and gentlemen costumed after the style of Catherine II.'s Russian Court, but none will be more pictorially effective than that in which Catherine de Medici will appear, some of the gentlemen representing Henri II., Francis II., Charles IX., Henri III., Gaspard de Collini, Comte de la Marck, and the Duc de Guise.<ref name=":4">"This Morning's News." ''London Daily News'' 2 July 1897, Friday: 5 [of 10], Col. 3B. ''British Newspaper Archive'' http://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970702/026/0005.</ref></blockquote> == Bibliography for Courts == * Drew-Smythe David. "The Duchess of Devonshire's Ball, 1897." ["principal names in the courts"] http://www.zipworld.com.au/~lnbdds/home/rah/dodbcourts.htm (accessed July 2017). Based on the report in the ''Times''. * Ross, Sarah. "The Devonshire House Ball (1897): A Guest-list of Society." ''Pax Victoriana: The Age of Victoria: The Long 19th Century in Literature and Everyday Life'' http://paxvictoriana.tumblr.com/post/101421946818/the-devonshire-house-ball-1897-a-guest-list-of (accessed July 2017). Based on the report in the ''Times''. == Footnotes == {{reflist}} 1icku1k55i3qv1e0hlw22lxmzysjr5t Workings of gcc and ld in plain view 0 285384 2683981 2683435 2024-11-11T20:52:40Z Young1lim 21186 /* Overview */ 2683981 wikitext text/x-wiki === Workings of the GNU Compiler for IA-32 === ==== Overview ==== * Overview ([[Media:Overview.20200211.pdf |pdf]]) ==== Data Processing ==== * Access ([[Media:Access.20200409.pdf |pdf]]) * Operators ([[Media:Operator.20200427.pdf |pdf]]) ==== Control ==== * Conditions ([[Media:Condition.20230630.pdf |pdf]]) * Control ([[Media:Control.20220616.pdf |pdf]]) ==== Function calls ==== * Procedure ([[Media:Procedure.20220412.pdf |pdf]]) * Recursion ([[Media:Recursion.20210824-2.pdf |pdf]]) ==== Pointer and Aggregate Types ==== * Arrays ([[Media:Array.20211018.pdf |pdf]]) * Structures ([[Media:Structure.20220101.pdf |pdf]]) * Alignment ([[Media:Alignment.20201117.pdf |pdf]]) * Pointers ([[Media:Pointer.20201106.pdf |pdf]]) ==== Integer Arithmetic ==== * Overview ([[Media:gcc.1.Overview.20240813.pdf |pdf]]) * Carry Flag ([[Media:gcc.2.Carry.20241111.pdf |pdf]]) * Overflow Flag ([[Media:gcc.3.Overflow.20240724.pdf |pdf]]) * Examples ([[Media:gcc.4.Examples.20240724.pdf |pdf]]) * Borrow ([[Media:Borrow.20230701.pdf |pdf]]) ==== Floating point Arithmetic ==== </br> === Workings of the GNU Linker for IA-32 === ==== Overview ==== * Static Linking Overview ([[Media:Link.3A.StaticLinking.20241112.pdf |pdf]]) * Dynamic Linking Overview ([[Media:Link.3B.DynamicLinking.20241101.pdf |pdf]]) * Shared Library Overview ([[Media:Link.3C.SharedLibrary.20241101.pdf |pdf]]) ==== Library Search Path ==== * Library Search using -L and -l only ([[Media:Link.4A.LibSearch-withLl.20240807.pdf |A.pdf]], [[Media:Link.4B.LibSearch-withLl.20240705.pdf |B.pdf]]) * Library Search Using RPATH ([[Media:Link.5A.LibSearch-RPATH.20241101.pdf |A.pdf]], [[Media:Link.5B.LibSearch-RPATH.20240705.pdf |B.pdf]]) ==== Linking Process ==== * Object Files ([[Media:Link.3.A.Object.20190121.pdf |A.pdf]], [[Media:Link.3.B.Object.20190405.pdf |B.pdf]]) * Symbols ([[Media:Link.4.A.Symbol.20190312.pdf |A.pdf]], [[Media:Link.4.B.Symbol.20190312.pdf |B.pdf]]) * Relocation ([[Media:Link.5.A.Relocation.20190320.pdf |A.pdf]], [[Media:Link.5.B.Relocation.20190322.pdf |B.pdf]]) * Loading ([[Media:Link.6.A.Loading.20190501.pdf |A.pdf]], [[Media:Link.6.B.Loading.20190126.pdf |B.pdf]]) * Static Linking ([[Media:Link.7.A.StaticLink.20190122.pdf |A.pdf]], [[Media:Link.7.B.StaticLink.20190128.pdf |B.pdf]]) * Dynamic Linking ([[Media:Link.8.A.DynamicLink.20190207.pdf |A.pdf]], [[Media:Link.8.B.DynamicLink.20190209.pdf |B.pdf]]) * Position Independent Code ([[Media:Link.9.A.PIC.20190304.pdf |A.pdf]], [[Media:Link.9.B.PIC.20190309.pdf |B.pdf]]) ==== Example I ==== * Vector addition ([[Media:Eg1.1A.Vector.20190121.pdf |A.pdf]], [[Media:Eg1.1B.Vector.20190121.pdf |B.pdf]]) * Swapping array elements ([[Media:Eg1.2A.Swap.20190302.pdf |A.pdf]], [[Media:Eg1.2B.Swap.20190121.pdf |B.pdf]]) * Nested functions ([[Media:Eg1.3A.Nest.20190121.pdf |A.pdf]], [[Media:Eg1.3B.Nest.20190121.pdf |B.pdf]]) ==== Examples II ==== * analysis of static linking ([[Media:Ex1.A.StaticLinkEx.20190121.pdf |A.pdf]], [[Media:Ex2.B.StaticLinkEx.20190121.pdf |B.pdf]]) * analysis of dynamic linking ([[Media:Ex2.A.DynamicLinkEx.20190121.pdf |A.pdf]]) * analysis of PIC ([[Media:Ex3.A.PICEx.20190121.pdf |A.pdf]]) </br> go to [ [[C programming in plain view]] ] [[Category:C programming language]] qfz97esblqif5q9c1shjnna9hxvp5fh Social Victorians/Terminology 0 285723 2683488 2682155 2024-11-11T15:30:04Z Scogdill 1331941 2683488 wikitext text/x-wiki Especially with respect to fashion, the newspapers at the end of the 19th century in the UK often used specialized terminology. The definitions on this page are to provide a sense of what someone in the late 19th century might have meant by the term rather than a definition of what we might mean by it today. In the absence of a specialized glossary from the end of the 19th century in the U.K., we use the ''Oxford English Dictionary'' because the senses of a word are illustrated with examples that have dates so we can be sure that the senses we pick are appropriate for when they are used in the quotations we have. We also sometimes use the French ''Wikipédia'' to define a word because many technical terms of fashion were borrowings from the French. Also, often the French ''Wikipédia'' provides historical context for the uses of a word similar to the way the OED does. == Articles or Parts of Clothing: Non-gender-specific == === Mantle, Cloak, Cape === In 19th-century newspaper accounts, these terms are sometimes used without precision as synonyms. These are all outer garments. '''Mantle''' A mantle — often a long outer garment — might have elements like a train, sleeves, collars, revers, fur, and a cape. A late-19th-century writer making a distinction between a mantle and a cloak might use ''mantle'' if the garment is more voluminous. '''Cloak''' '''Cape''' === Peplum === According to the French ''Wiktionnaire'', a peplum is a "Short skirt or flared flounce layered at the waist of a jacket, blouse or dress" [translation by Google Translate].<ref>{{Cite journal|date=2021-07-02|title=péplum|url=https://fr.wiktionary.org/w/index.php?title=p%C3%A9plum&oldid=29547727|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/p%C3%A9plum.</ref> The ''Oxford English Dictionary'' has a fuller definition, although, it focuses on women's clothing because the sense is written for the present day:<blockquote>''Fashion''. ... a kind of overskirt resembling the ancient peplos (''obsolete''). Hence (now usually) in modern use: a short flared, gathered, or pleated strip of fabric attached at the waist of a woman's jacket, dress, or blouse to create a hanging frill or flounce.<ref name=":5">“peplum, n.”. ''Oxford English Dictionary'', Oxford University Press, September 2023, <https://doi.org/10.1093/OED/1832614702>.</ref></blockquote>Men haven't worn peplums since the 18th century, except when wearing costumes based on historical portraits. The ''Daily News'' reported in 1896 that peplums had been revived as a fashion item for women.<ref name=":5" /> === Revers === According to the ''Oxford English Dictionary'', ''revers'' are the "edge[s] of a garment turned back to reveal the undersurface (often at the lapel or cuff) (chiefly in ''plural''); the material covering such an edge."<ref>"revers, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/164777. Accessed 17 April 2023.</ref> The term is French and was used this way in the 19th century (according to the ''Wiktionnaire'').<ref>{{Cite journal|date=2023-03-07|title=revers|url=https://fr.wiktionary.org/w/index.php?title=revers&oldid=31706560|journal=Wiktionnaire|language=fr}} https://fr.wiktionary.org/wiki/revers.</ref> == Articles or Parts of Clothing: Men's == [[Social Victorians/Terminology#Military|Men's military uniforms]] are discussed below. === À la Romaine === [[File:Johann Baptist Straub - Mars um 1772-1.jpg|thumb|left|alt=Old and damaged marble statue of a Roman god of war with flowing cloak, big helmet with a plume on top, and armor|Johann Baptist Straub's 1772 ''à la romaine'' ''Mars'']] A few people who attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's fancy-dress ball in 1897]] personated Roman gods or people. They were dressed not as Romans, however, but ''à la romaine'', which was a standardized style of depicting Roman figures that was used in paintings, sculpture and the theatre for historical dress from the 17th until the 20th century. The codification of the style was developed in France in the 17th century for theatre and ballet, when it became popular for masked balls. Women as well as men could be dressed ''à la romaine'', but much sculpture, portraiture and theatre offered opportunities for men to dress in Roman style — with armor and helmets — and so it was most common for men. In large part because of the codification of the style as well as the painting and sculpture, the style persisted and remained influential into the 20th century and can be found in museums and galleries and on monuments. For example, Johann Baptist Straub's 1772 statue of Mars (left), now in the Bayerisches Nationalmuseum, Munich, missing part of an arm, shows Mars ''à la romaine''. In London, an early 17th-century example of a figure of Mars ''à la romaine'', with a helmet, '''was''' "at the foot of the Buckingham tomb in Henry VII's Chapel at Westminster Abbey."<ref>Webb, Geoffrey. “Notes on Hubert Le Sueur-II.” ''The Burlington Magazine for Connoisseurs'' 52, no. 299 (1928): 81–89. http://www.jstor.org/stable/863535.</ref>{{rp|81, Col. 2c}} === Cavalier === [[File:Sir-Anthony-van-Dyck-Lord-John-Stuart-and-His-Brother-Lord-Bernard-Stuart.jpg|thumb|alt=Old painting of 2 men flamboyantly and stylishly dressed in colorful silk, with white lace, high-heeled boots and long hair|Van Dyck's c. 1638 painting of cavaliers Lord John Stuart and his brother Lord Bernard Stuart]] As a signifier in the form of clothing of a royalist political and social ideology begun in France in the early 17th century, the cavalier established France as the leader in fashion and taste. Adopted by [[Social Victorians/Terminology#Military|wealthy royalist British military officers]] during the time of the Restoration, the style signified a political and social position, both because of the loyalty to Charles I and II as well the wealth required to achieve the cavalier look. The style spread beyond the political, however, to become associated generally with dress as well as a style of poetry.<ref>{{Cite journal|date=2023-04-25|title=Cavalier poet|url=https://en.wikipedia.org/w/index.php?title=Cavalier_poet&oldid=1151690299|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier_poet.</ref> Van Dyck's 1638 painting of two brothers (right) emphasizes the cavalier style of dress. === Coats === ==== Doublet ==== * In the 19th-century newspaper accounts we have seen that use this word, doublet seems always to refer to a garment worn by a man, but historically women may have worn doublets. In fact, a doublet worn by Queen Elizabeth I exists and '''is somewhere'''. * Technically doublets were long sleeved, although we cannot be certain what this or that Victorian tailor would have done for a costume. For example, the [[Social Victorians/People/Spencer Compton Cavendish#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Duke of Devonshire's costume as Charles V]] shows long sleeves that may be part of the surcoat but should be the long sleeves of the doublet. ==== Pourpoint ==== A padded doublet worn under armor to protect the warrior from the metal chafing. A pourpoint could also be worn without the armor. ==== Surcoat ==== Sometimes just called ''coat''. [[File:Oscar Wilde by Sarony 1882 18.jpg|thumb|alt=Old photograph of a young man wearing a velvet jacket, knee breeches, silk hose and shiny pointed shoes with bows, seated on a sofa and leaning on his left hand and holding a book in his right| Oscar Wilde, 1882, by Napoleon Sarony]] === Hose, Stockings and Tights === Newspaper accounts from the late 19th century of men's clothing use the term ''hose'' for what we might call stockings or tights. In fact, the terminology is specific. ''Stockings'' is the more general term and could refer to hose or tights. With knee breeches men wore hose, which ended above the knee, and women wore hose under their dresses. The ''Oxford English Dictionary'' defines tights as "Tight-fitting breeches, worn by men in the 18th and early 19th centuries, and still forming part of court-dress."<ref>“Tights, N.” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/2693287467.</ref> By 1897, the term was in use for women's stockings, which may have come up only to the knee. Tights were also worn by dancers and acrobats. This general sense of ''tights'' does not assume that they were knitted. ''Clocking'' is decorative embroidery on hose, usually, at the ankles on either the inside or the outside of the leg. It started at the ankle and went up the leg, sometimes as far as the knee. On women's hose, the clocking could be quite colorful and elaborate, while the clocking on men's hose was more inconspicuous. In many photographs men's hose are wrinkled, especially at the ankles and the knees, because they were shaped from woven fabric. Silk hose were knitted instead of woven, which gave them elasticity and reduced the wrinkling. The famous Sarony carte de visite photograph of Oscar Wilde (right) shows him in 1882 wearing knee breeches and silk hose, which are shiny and quite smoothly fitted although they show a few wrinkles at the ankles and knees. In the portraits of people in costume at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the men's hose are sometimes quite smooth, which means they were made of knitted silk and may have been smoothed for the portrait. In painted portraits the hose are almost always depicted as smooth, part of the artist's improvement of the appearance of the subject. === Shoes and Boots === == Articles or Parts of Clothing: Women's == === '''Chérusque''' === According to the French ''Wikipedia'', ''chérusque'' is a 19th-century term for the kind of standing collar like the ones worn by ladies in the Renaissance.<ref>{{Cite journal|date=2021-06-26|title=Collerette (costume)|url=https://fr.wikipedia.org/w/index.php?title=Collerette_(costume)&oldid=184136746|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Collerette_(costume)#Au+xixe+siècle+:+la+Chérusque.</ref> === Corsage === According to the ''Oxford English Dictionary'', the corsage is the "'body' of a woman's dress; a bodice."<ref>"corsage, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/42056. Accessed 7 February 2023.</ref> This sense is well documented in the ''OED'' for the mid and late 19th-century, used this way in fiction as well as in a publication like ''Godey's Lady's Book'', which would be expected to use appropriate terminology associated with fashion and dress making. The sense of "a bouquet worn on the bodice" is, according to the ''OED'', American. === Décolletage === === Girdle === === Mancheron === According to the ''Oxford English Dictionary'', a ''mancheron'' is a "historical" word for "A piece of trimming on the upper part of a sleeve on a woman's dress."<ref>"mancheron, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/113251. Accessed 17 April 2023.</ref> At the present, in French, a ''mancheron'' is a cap sleeve "cut directly on the bodice."<ref>{{Cite journal|date=2022-11-28|title=Manche (vêtement)|url=https://fr.wikipedia.org/w/index.php?title=Manche_(v%C3%AAtement)&oldid=199054843|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Manche_(v%C3%AAtement).</ref> === Petticoat === According to the ''O.E.D.'', a petticoat is a <blockquote>skirt, as distinguished from a bodice, worn either externally or showing beneath a dress as part of the costume (often trimmed or ornamented); an outer skirt; a decorative underskirt. Frequently in ''plural'': a woman's or girl's upper skirts and underskirts collectively. Now ''archaic'' or ''historical''.<ref>“petticoat, n., sense 2.b”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, <https://doi.org/10.1093/OED/1021034245></ref> </blockquote>This sense is, according to the ''O.E.D.'', "The usual sense between the 17th and 19th centuries." However, while petticoats belong in both outer- and undergarments — that is, meant to be seen or hidden, like underwear — they were always under another garment, for example, underneath an open overskirt. The primary sense seems to have shifted through the 19th century so that, by the end, petticoats were underwear and the term ''underskirt'' was used to describe what showed under an open overskirt. === Stomacher === According to the ''O.E.D.'', a stomacher is "An ornamental covering for the chest (often covered with jewels) worn by women under the lacing of the bodice,"<ref>“stomacher, n.¹, sense 3.a”. ''Oxford English Dictionary'', Oxford University Press, September 2023, <https://doi.org/10.1093/OED/1169498955></ref> although by the end of the 19th century, the bodice did not often have visible laces. Some stomachers were so decorated that they were thought of as part of the jewelry. === Train === A train is The Length of the Train '''For the monarch [or a royal?]''' According to Debrett's,<blockquote>A peeress's coronation robe is a long-trained crimson velvet mantle, edged with miniver pure, with a miniver pure cape. The length of the train varies with the rank of the wearer: * Duchess: for rows of ermine; train to be six feet * Marchioness: three and a half rows of ermine; train to be three and three-quarters feet * Countess: three rows of ermine; train to be three and a half feet * Viscountess: two and a half rows of ermine; train to be three and a quarter feet * Baroness: two rows of ermine; train to be three feet<ref name=":2">{{Cite web|url=https://debretts.com/royal-family/dress-codes/|title=Dress Codes|website=debretts.com|language=en-US|access-date=2023-07-27}} https://debretts.com/royal-family/dress-codes/.</ref> </blockquote>The pattern on the coronet worn was also quite specific, similar but not exactly the same for peers and peeresses. Debrett's also distinguishes between coronets and tiaras, which were classified more like jewelry, which was regulated only in very general terms. Peeresses put on their coronets after the Queen or Queen Consort has been crowned. ['''peers?'''] === Undergarments === Victorian women's undergarments created the distinctive silhouette. The corset was an important element of this understructure, which also included hoops, bustles, petticoats and so on, but it has never been the only important element. ==== Corset ==== [[File:Corset - MET 1972.209.49a, b.jpg|thumb|alt=Photograph of an old silk corset on a mannequin, showing the closure down the front, similar to a button, and channels in the fabric for the boning. It is wider at the top and bottom, creating smooth curves from the bust to the compressed waist to the hips, with a long point below the waist in front.|French 1890s corset, now in the Metropolitan Museum of Art, NYC]] The understructure of Victorian women's clothing is what makes the costumes worn by the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] so distinctly Victorian in appearance. An example of a corset that has the kind of structure often worn by fashionably dressed women in 1897 is the one at right. This corset exaggerated the shape of the women's bodies and made possible a bodice that looked and was fitted in the way that is so distinctive of the time — very controlled and smooth. And, as a structural element, this foundation garment carried the weight of all those layers and all that fabric and decoration on the gowns, trains and mantles. (The trains and mantles could be attached directly to the corset itself.) * This foundation emphasizes the waist and the bust in particular, in part because of the contrast between the very small waist and the rounded fullness of the bust and hips. * The idealized waist is defined by its small span and the sexualizing point at the center-bottom of the bodice, which directs the eye downwards. Interestingly, the pointed waistline worn by Elizabethan men has become level in the Victorian age. Highly fashionable Victorian women wearing the traditional style, however, had extremely pointed waists. * The busk (a kind of boning in the front of a corset that is less flexible than the rest) smoothed the bodice, flattened the abdomen and prevented the point on the bodice from curling up. * The sharp definition of the waist was caused by ** length of the corset (especially on the sides) ** the stiffness of the boning ** the layers of fabric ** the lacing (especially if the woman used tightlacing) ** the over-all shape, which was so much wider at the top and the bottom ** the contrast between the waist and the wider top and bottom * The late-19th-century corset was long, ending below the waist even on the sides and back. * The boning and the top edge of the late 19th-century fashion corset pushed up the bust, rounding (rather than flattening, as in earlier styles) the breasts, drawing attention to their exposed curves and creating cleavage. * The exaggerated bust was larger than the hips, whenever possible, an impression reinforced by the A-line of the skirt and the inverted Vs in the decorative trim near the waist and on the skirt. * This corset made the bodice very smooth with a very precise fit, that had no wrinkles, folds or loose drapery. The bodice was also trimmed or decorated, but the base was always a smooth bodice. More formal gowns would still have the fitted bodice and more elaborate trim made from lace, embroidery, appliqué, beading and possibly even jewels. The advantages and disadvantages of corseting and especially tight lacing were the subject of thousands of articles and opinions in the periodical press for a great part of the century, but the fetishistic and politicized tight lacing was practiced by very few women. And no single approach to corsetry was practiced by all women all the time. Most of the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 ball]] were not tightly laced, but the progressive style does not dominate either, even though all the costumes are technically historical dress. Part of what gives most of the costumes their distinctive 19th-century "look" is the more traditional corset beneath them. Even though this highly fashionable look was widely present in the historical costumes at the ball, some women's waists were obviously very small and others were hardly '''emphasized''' at all. Women's waists are never mentioned in the newspaper coverage of the ball — or, indeed, of any of the social events attended by the network at the ball — so it is only in photographs that we can see the effects of how they used their corsets. ==== '''Farthingale or Vertugadin''' ==== ''Vertugadin'' is a French term for ''farthingale'', a cage made of hoops supporting a skirt — "un élément essentiel de la mode Tudor en Angleterre [an essential element of Tudor fashion in England]."<ref name=":0">{{Cite journal|date=2022-03-12|title=Vertugadin|url=https://fr.wikipedia.org/w/index.php?title=Vertugadin&oldid=191825729|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Vertugadin.</ref> In fact, "La princesse espagnole Catherine d'Aragon amena la mode en Angleterre pour son mariage avec le prince Arthur, fils aîné d'Henri VII en 1501 [The Spanish princess Catherine of Aragon brought the fashion to England for her marriage to Prince Arthur, eldest son of Henry VII in 1501]."<ref name=":0" /> Catherine of Aragon, of course, married Henry VIII after Arthur's death. The French and Spanish farthingales were not identical by the end of the 16th century. The Spanish farthingale shaped the skirt into an A-line with a graduated series of hoops sewn to an undergarment. The French farthingale was a flattish "cartwheel" or platter of hoops worn below the waist and above the hips held the skirt out more or less horizontally. Once past the vertugadin, the skirt then fell straight to the floor, shaping the skirt into a kind of drum. The shoes show in the portraits of women wearing the French farthingale. == '''Traditional vs Progressive Style''' == === Progressive Style === The terms ''artistic dress'' and ''aesthetic dress'' are not synonymous and were in use at different times to refer to different groups of people in different contexts, but we recognize them as referring to a similar kind of personal style in clothing, a style we call progressive dress or the progressive style. Used in a very precise way, ''artistic dress'' is associated with the Pre-Raphaelite artists and the women in their circle beginning in the 1860s. Similarly, ''aesthetic dress'' is associated with the 1880s and 1890s and dress reform movements. In general, the progressive style is characterized by its resistance to the highly structured fashion of its day, especially corseting, aniline dyes and an extremely close fit. === Traditional Style === By the end of the century designs from the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]] (or Maison Worth) define what we think of as the traditional Victorian look, which was very stylish and expensive. Blanche Payne describes an example of the 1895 "high style" in a gown by Worth with "the idiosyncrasies of the [1890s] full blown":<blockquote>The dress is white silk with wine-red stripes. Sleeves, collars, bows, bag, hat, and hem border match the stripes. The sleeve has reached its maximum volume; the bosom full and emphasized with added lace; the waistline is elongated, pointed, and laced to the point of distress; the skirt is smooth over the hips, gradually swinging out to sweep the floor. This is the much vaunted hourglass figure.<ref>Payne, Blanche. ''History of Costume from the Ancient Egyptians to the Twentieth Century''. Harper & Row, 1965.</ref>{{rp|530}}</blockquote> The Victorian-looking gowns at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] are stylish in a way that recalls the designs of the House of Worth. The elements that make their look so Victorian are anachronisms on the costumes representing fashion of earlier eras. The women wearing these gowns preferred the standards of beauty from their own day to a more-or-less historically accurate look. The style competing at the very end of the century with the Worth look was not the historical, however, but a progressive style called at the time ''artistic'' or ''aesthetic''. William Powell Frith's 1883 painting ''A Private View at the Royal Academy, 1881'' (discussion below) pits this kind of traditional style against the progressive or artistic style. === The Styles === [[File:Frith A Private View.jpg|thumb|William Powell Frith, ''A Private View at the Royal Academy, 1881'']] We typically think of the late-Victorian silhouette as universal but, in the periods in which corsets dominated women's dress, not all women wore corsets and not all corsets were the same, as William Powell Frith's 1883 ''A Private View at the Royal Academy, 1881'' (right) illustrates. Frith is clear in his memoir that this painting — "recording for posterity the aesthetic craze as regards dress" — deliberately contrasts what he calls the "folly" of the Artistic Dress movement and the look of the traditional corseted waist.<ref>Frith, William Powell. ''My Autobiography and Reminiscences''. 1887.</ref> Frith considered the Artistic Movement and Artistic Dress "ephemeral," but its rejection of corsetry looks far more consequential to us in hindsight than it did in the 19th century. As Frith sees it, his painting critiques the "craze" associated with the women in this set of identifiable portraits who are not corseted, but his commitment to realism shows us a spectrum, a range, of conservatism and if not political then at least stylistic progressivism among the women. The progressives, oddly, are the women wearing artistic (that is, somewhat historical) dress, because they’re not corseted. It is a misreading to see the presentation of the women’s fashion as a simple opposition. Constance, Countess of Lonsdale — situated at the center of this painting with Frederick Leighton, president of the Royal Academy of Art — is the most conservatively dressed of the women depicted, with her narrow sleeves, tight waist and almost perfectly smooth bodice, which tells us that her corset has eyelets so that it can be laced precisely and tightly, and it has stays (or "bones") to prevent wrinkles or natural folds in the overclothing. Lillie Langtry, in the white dress, with her stylish narrow sleeves, does not have such a tightly bound waist or smooth bodice, suggesting she may not be corseted at all, as we know she sometimes was not.['''citation'''] Jenny Trip, a painter’s model, is the woman in the green dress in the aesthetic group being inspected by Anthony Trollope, who may be taking notes. She looks like she is not wearing a corset. Both Langtry and Trip are toward the middle of this spectrum: neither is dressed in the more extreme artistic dress of, say, the two figures between Trip and Trollope. A lot has been written about the late-Victorian attraction to historical dress, especially in the context of fancy-dress balls and the Gothic revival in social events as well as art and music. Part of the appeal has to have been the way those costumes could just be beautiful clothing beautifully made. Historical dress provided an opportunity for some elite women to wear less-structured but still beautiful and influential clothing. ['''Calvert'''<ref>Calvert, Robyne Erica. ''Fashioning the Artist: Artistic Dress in Victorian Britain 1848-1900''. Ph.D. thesis, University of Glasgow, 2012. <nowiki>https://theses.gla.ac.uk/3279/</nowiki></ref>] The standards for beauty, then, with historical dress were Victorian, with the added benefit of possibly less structure. So, at the Duchess of Devonshire's ball, "while some attendees tried to hew closely to historical precedent, many rendered their historical or mythological personage in the sartorial vocabulary they knew best. The [photographs of people in their costumes at the ball offer] a glimpse into how Victorians understood history, not a glimpse into the costume of an authentic historical past."<ref>Mitchell, Rebecca N. "The Victorian Fancy Dress Ball, 1870–1900." ''Fashion Theory'' 2017 (21: 3): 291–315. DOI: 10.1080/1362704X.2016.1172817.</ref> (294) * historical dress: beautiful clothing. * the range at the ball, from Minnie Paget to Gwladys * "In light of such efforts, the ball remains to this day one of the best documented outings of the period, and a quick glance at the album shows that ..." Women had more choices about their waists than the simple opposition between no corset and tightlacing can accommodate. The range of choices is illustrated in Frith's painting, with a woman locating herself on it at a particular moment for particular reasons. Much analysis of 19th-century corsetry focuses on its sexualizing effects — corsets dominated Victorian photographic pornography ['''citations'''] and at the same time, the absence of a corset was sexual because it suggested nudity.['''citations'''] A great deal of analysis of 19th-century corsetry, on the other hand, assumes that women wore corsets for the male gaze ['''citations'''] or that they tightened their waists to compete with other women.['''citations'''] But as we can see in Frith's painting, the sexualizing effect was not universal or sweeping, and these analyses do not account for the choices women had in which corset to wear or how tightly to lace it. Especially given the way that some photographic portraits were mechanically altered to make the waist appear smaller, the size of a woman's waist had to do with how she was presenting herself to the world. That is, the fact that women made choices about the size of or emphasis on their waists suggests that they had agency that needs to be taken into account. As they navigated the complex social world, women's fashion choices had meaning. Society or political hostesses had agency not only in their clothing but generally in that complex social world. They had roles managing social events of the upper classes, especially of the upper aristocracy and oligarchy, like the Duchess of Devonshire's ball. Their class and rank, then, were essential to their agency, including to some degree their freedom to choose what kind of corset to wear and how to wear it. Also, by the end of the century lots of different kinds of corsets were available for lots of different purposes. Special corsets existed for pregnancy, sports (like tennis, bicycling, horseback riding, golf, fencing, archery, stalking and hunting), theatre and dance and, of course, for these women corsets could be made to support the special dress worn over it. Women's choices in how they presented themselves to the world included more than just their foundation garments, of course. "Every cap, bow, streamer, ruffle, fringe, bustle, glove," that is, the trim and decorations on their garments, their jewelry and accessories — which Davidoff calls "elaborations"<ref name=":1">Davidoff, Leonore. ''The Best Circles: Society Etiquette and the Season''. Intro., Victoria Glendinning. The Cressett Library (Century Hutchinson), 1986 (orig 1973).</ref>{{rp|93}} — pointed to a host of status categories, like class, rank, wealth, age, marital status, engagement with the empire, how sexual they wanted to seem, political alignment and purpose at the social event. For example, when women were being presented to the monarch, they were expected to wear three ostrich plumes, often called the [[Social Victorians/Terminology#Prince of Wales's Feathers or White Plumes|Prince of Wales's feathers]]. Like all fashions, the corset, which was quite long-lasting in all its various forms, eventually went out of style. Of the many factors that might have influenced its demise, perhaps most important was the women's movement, in which women's rights, freedom, employment and access to their own money and children were less slogan-worthy but at least as essential as votes for women. The activities of the animal-rights movements drew attention not only to the profligate use of the bodies and feathers of birds but also to the looming extinction of the baleen whale, which made whale bone scarce and expensive. Perhaps the century's debates over corseting and especially tightlacing were relevant to some decisions not to be corseted. And, of course, perhaps no other reason is required than that the nature of fashion is to change. == Cinque Cento == According to the ''Oxford English Dictionary'', ''Cinque Cento'' is a shortening of ''mil cinque cento'', or 1500.<ref>"cinquecento, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/33143. Accessed 7 February 2023.</ref> The term, then would refer, perhaps informally, to the sixteenth century. == Crevé == ''Creve'', without the accent, is an old word in English (c. 1450) for burst or split.<ref>"creve, v." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44339. Accessed 8 February 2023.</ref> ['''With the acute accent, it looks like a past participle in French.'''] == Elastic == Elastic had been invented and was in use by the end of the 19th century. For the sense of "Elastic cord or string, usually woven with india-rubber,"<ref name=":6">“elastic, adj. & n.”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, <https://doi.org/10.1093/OED/1199670313>.</ref> the ''Oxford English Dictionary'' has usage examples beginning in 1847. The example for 1886 is vivid: "The thorough-going prim man will always place a circle of elastic round his hair previous to putting on his college cap."<ref name=":6" /> == Elaborations == In her 1973 ''The Best Circles: Society, Etiquette and the Season'', Leonore Davidoff notes that women’s status was indicated by dress and especially ornament: “Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration,” she says, “symbolised some status category for the female wearer.”<ref name=":1" />{{rp|93}} Looking at these elaborations as meaningful rather than dismissing them as failed attempts at "historical accuracy" reveals a great deal about the individual women who wore or carried them — and about the society women and political hostesses in their roles as managers of the social world. In her review of ''The House of Worth: Portrait of an Archive'', Mary Frances Gormally says,<blockquote>In a socially regulated year, garments custom made with a Worth label provided women with total reassurance, whatever the season, time of day or occasion, setting them apart as members of the “Best Circles” dressed in luxurious, fashionable and always appropriate attire (Davidoff 1973). The woman with a Worth wardrobe was a woman of elegance, lineage, status, extreme wealth and faultless taste.<ref>Gormally, Mary Frances. Review essay of ''The House of Worth: Portrait of an Archive'', by Amy de la Haye and Valerie D. Mendes (V&A Publishing, 2014). ''Fashion Theory'' 2017 (21, 1): 109–126. DOI: 10.1080/1362704X.2016.1179400.</ref> (117)</blockquote> === Aglet, Aiglet === Historically, an aglet is a "point or metal piece that capped a string [or ribbon] used to attach two pieces of the garment together, i.e., sleeve and bodice."<ref name=":7" /> (4) Although they were decorative, they were not always visible on the outside of the clothing. They were often stuffed inside the layers at the waist (for example, attaching the bodice to a skirt or breeches). === Frou-frou === In French, ''frou-frou'' or, spelled as ''froufrou'', is the sound of the rustling of silk or sometimes of fabrics in general.<ref>{{Cite journal|date=2023-07-25|title=frou-frou|url=https://fr.wiktionary.org/w/index.php?title=frou-frou&oldid=32508509|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/frou-frou.</ref> The first use the French ''Wiktionnaire'' lists is Honoré Balzac, ''La Cousine Bette'', 1846.<ref>{{Cite journal|date=2023-06-03|title=froufrou|url=https://fr.wiktionary.org/w/index.php?title=froufrou&oldid=32330124|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/froufrou.</ref> ''Frou-frou'' is a term clothing historians use to describe decorative additions to an article of clothing; often the term has a slight negative connotation, suggesting that the additions are superficial. === Pouf, Puff, Poof === According to the French ''Wikipédia'', a pouf was, beginning in 1744, a "kind of women's hairstyle":<blockquote>The hairstyle in question, known as the “pouf”, had launched the reputation of the enterprising Rose Bertin, owner of the Grand Mogol, a very prominent fashion accessories boutique on Rue Saint-Honoré in Paris in 1774. Created in collaboration with the famous hairdresser, Monsieur Léonard, the pouf was built on a scaffolding of wire, fabric, gauze, horsehair, fake hair, and the client's own hair held up in an almost vertical position. — (Marie-Antoinette, ''Queen of Fashion'', translated from the American by Sylvie Lévy, in ''The Rules of the Game'', n° 40, 2009)</blockquote>''Puff'' and ''poof'' are used to describe clothing. === Shirring === ''Shirring'' is the gathering of fabric to make poufs or puffs. The 19th century is known for its use of this decorative technique. Even men's clothing had shirring: at the shoulder seam. === Sequins === Sequins, paillettes, spangles Sequins — or paillettes — are "small, scalelike glittering disks."<ref name=":7" />(216) The French ''Wiktionnaire'' defines ''paillette'' as "Lamelle de métal, brillante, mince, percée au milieu, ordinairement ronde, et qu’on applique sur une étoffe pour l’orner [A strip of metal, shiny, thin, pierced in the middle, usually round, and which is applied to a fabric in order to decorate it.]"<ref name=":8">{{Cite journal|date=2024-03-18|title=paillette|url=https://fr.wiktionary.org/w/index.php?title=paillette&oldid=33809572|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/paillette.</ref> According to the ''OED'', the use of ''sequin'' as a decorative device for clothing (as opposed to gold coins minted and used for international trade) goes back to the 1850s.<ref>“Sequin, N.” ''Oxford English Dictionary'', Oxford UP, September 2023, https://doi.org/10.1093/OED/4074851670.</ref> The first instance of ''spangle'' as "A small round thin piece of glittering metal (usually brass) with a hole in the centre to pass a thread through, used for the decoration of textile fabrics and other materials of various sorts" is from c. 1420.<ref>“Spangle, N. (1).” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/4727197141.</ref> The first use of ''paillette'' listed in the French ''Wiktionnaire'' is in Jules Verne in 1873 to describe colored spots on icy walls.<ref name=":8" /> Currently many distinguish between sequins (which are smaller) and paillettes (which are larger). Before the 20th century, sequins were metal discs or foil leaves, and so of course if they were silver or copper, they tarnished. It is not until well into the 20th century that plastics were invented and used for sequins. === Trim and Lace === ''A History of Feminine Fashion'', published sometime before 1927 and probably commissioned by [[Social Victorians/People/Dressmakers and Costumiers#Worth, of Paris|the Maison Worth]], describes Charles Frederick Worth's contributions to the development of embroidery and [[Social Victorians/Terminology#Passementerie|passementerie]] (trim) from about the middle of the 19th century:<blockquote>For it must be remembered that one of M. Worth's most important and lasting contributions to the prosperity of those who cater for women's needs, as well as to the variety and elegance of his clients' garments, was his insistence on new fabrics, new trimmings, new materials of every description. In his endeavours to restore in Paris the splendours of the days of La Pompadour, and of Marie Antoinette, he found himself confronted at the outset with a grave difficulty, which would have proved unsurmountable to a man of less energy, resource and initiative. The magnificent materials of those days were no longer to be had! The Revolution had destroyed the market for beautiful materials of this, type, and the Restoration and regime of Louis Philippe had left a dour aspect in the City of Light. ... On parallel lines [to his development of better [[Social Victorians/Terminology#Satin|satin]]], [Worth] stimulated also the manufacture of embroidery and ''passementerie''. It was he who first started the manufacture of laces copied from the designs of the real old laces. He was the / first dressmaker to use fur in the trimming of light materials — but he employed only the richer furs, such as sable and ermine, and had no use whatever for the inferior varieties of skins.<ref name=":9" />{{rp|6–7}}</blockquote> ==== Gold and Silver Fabric and Lace ==== The ''Encyclopaedia Britannica'' (9th edition) has an article on gold and silver fabric, threads and lace attached to the article on gold. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)<blockquote>GOLD AND SILVER LACE. Under this heading a general account may be given of the use of the precious metals in textiles of all descriptions into which they enter. That these metals were used largely in the sumptuous textiles of the earliest periods of civilization there is abundant testimony; and to this day, in the Oriental centres whence a knowledge and the use of fabrics inwoven, ornamented, and embroidered with gold and silver first spread, the passion for such brilliant and costly textiles is still most strongly and generally prevalent. The earliest mention of the use of gold in a woven fabric occurs in the description of the ephod made for Aaron (Exod. xxxix. 2, 3) — "And he made the ephod of gold, blue, and purple, and scarlet, and fine twined linen. And they did beat the gold into thin plates, and cut it into wires (strips), to work it in the blue, and in the purple, and in the scarlet, and in the fine linen, with cunning work." In both the ''Iliad'' and the ''Odyssey'' distinct allusion is frequently made to inwoven and embroidered golden textiles. Many circumstances point to the conclusion that the art of weaving and embroidering with gold and silver originated in India, where it is still principally prosecuted, and that from one great city to another the practice travelled westward, — Babylon, Tarsus, Baghdad, Damascus, the islands of Cyprus and Sicily, Con- / stantinople and Venice, all in the process of time becoming famous centres of these much prized manufactures. Alexander the Great found Indian kings and princes arrayed in robes of gold and purple; and the Persian monarch Darius, we are told, wore a war mantle of cloth of gold, on which were figured two golden hawks as if pecking at each other. There is reason, according to Josephus, to believe that the “royal apparel" worn by Herod on the day of his death (Acts xii. 21) was a tissue of silver. Agrippina, the wife of the emperor Claudius, had a robe woven entirely of gold, and from that period downwards royal personages and high ecclesiastical dignitaries used cloth and tissues of gold and silver for their state and ceremonial robes, as well as for costly hangings and decorations. In England, at different periods, various names were applied to cloths of gold, as ciclatoun, tartarium, naques or nac, baudekiu or baldachin, Cyprus damask, and twssewys or tissue. The thin flimsy paper known as tissue paper, is so called because it originally was placed between the folds of gold "tissue" to prevent the contiguous surfaces from fraying each other. At what time the drawing of gold wire for the preparation of these textiles was first practised is not accurately known. The art was probably introduced and applied in different localities at widely different dates, but down till mediaeval times the method graphically described in the Pentateuch continued to be practised with both gold and silver. Fabrics woven with gold and silver continue to be used on the largest scale to this day in India; and there the preparation of the varieties of wire, and the working of the various forms of lace, brocade, and embroidery, is at once an important and peculiar art. The basis of all modern fabrics of this kind is wire, the "gold wire" of the manufacturer being in all cases silver gilt wire, and silver wire being, of course, composed of pure silver. In India the wire is drawn by means of simple draw-plates, with rude and simple appliances, from rounded bars of silver, or gold-plated silver, as the case may be. The wire is flattened into the strip or ribbon-like form it generally assumes by passing it, fourteen or fifteen strands simultaneously, over a fine, smooth, round-topped anvil, and beating it as it passes with a heavy hammer having a slightly convex surface. From wire so flattened there is made in India soniri, a tissue or cloth of gold, the web or warp being composed entirely of golden strips, and ruperi, a similar tissue of silver. Gold lace is also made on a warp of thick yellow silk with a weft of flat wire, and in the case of ribbons the warp or web is composed of the metal. The flattened wires are twisted around orange (in the case of silver, white) coloured silk thread, so as completely to cover the thread and present the appearance of a continuous wire; and in this form it is chiefly employed for weaving into the rich brocades known as kincobs or kinkhábs. Wires flattened, or partially flattened, are also twisted into exceedingly fine spirals, and in this form they are the basis of numerous ornamental applications. Such spirals drawn out till they present a waved appearance, and in that state flattened, are much used for rich heavy embroideries termed karchobs. Spangles for embroideries, &c., are made from spirals of comparatively stout wire, by cutting them down ring by ring, laying each C-like ring on an anvil, and by a smart blow with a hammer flattening it out into a thin round disk with a slit extending from the centre to one edge. Fine spirals are also used for general embroidery purposes. The demand for various kinds of loom-woven and embroidered gold and silver work in India is immense; and the variety of textiles so ornamented is also very great. "Gold and silver," says Dr Birdwood in his ''Handbook to the British-Indian Section, Paris Exhibition'', 1878, "are worked into the decoration of all the more costly loom-made garments and Indian piece goods, either on the borders only, or in stripes throughout, or in diapered figures. The gold-bordered loom embroideries are made chiefly at Sattara, and the gold or silver striped at Tanjore; the gold figured ''mashrus'' at Tanjore, Trichinopoly, and Hyderabad in the Deccau; and the highly ornamented gold-figured silks and gold and silver tissues principally at Ahmedabad, Benares, Murshedabad, and Trichinopoly." Among the Western communities the demand for gold and silver lace and embroideries arises chiefly in connexion with naval and military uniforms, court costumes, public and private liveries, ecclesiastical robes and draperies, theatrical dresses, and the badges and insignia of various orders. To a limited extent there is a trade in gold wire and lace to India and China. The metallic basis of the various fabrics is wire round and flattened, the wire being of three kinds — 1st, gold wire, which is invariably silver gilt wire; 2d, copper gilt wire, used for common liveries and theatrical purposes; and 3d, silver wire. These wires are drawn by the ordinary processes, and the flattening, when done, is accomplished by passing the wire between a pair of revolving rollers of fine polished steel. The various qualities of wire are prepared and used in precisely the same way as in India, — round wire, flat wire, thread made of flat gold wire twisted round orange-coloured silk or cotton, known in the trade as "orris," fine spirals and spangles, all being in use in the West as in the East. The lace is woven in the same manner as ribbons, and there are very numerous varieties in richness, pattern, and quality. Cloth of gold, and brocades rich in gold and silver, are woven for ecclesiastical vestments and draperies. The proportions of gold and silver in the gold thread for the lace trade varies, but in all cases the proportion of gold is exceedingly small. An ordinary gold lace wire is drawn from a bar containing 90 parts of silver and 7 of copper, coated with 3 parts of gold. On an average each ounce troy of a bar so plated is drawn into 1500 yards of wire; and therefore about 16 grains of gold cover a mile of wire. It is estimated that about 250,000 ounces of gold wire are made annually in Great Britain, of which about 20 per cent, is used for the headings of calico, muslin, &c., and the remainder is worked up in the gold lace trade.<ref>William Chandler Roberts-Austen and H. Bauerman [W.C.R. — H.B.]. "Gold and Silver Lace." In "Gold." ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. 10 (X). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%2010%20%28G-GOT%29%20193592738.23/page/753/mode/1up (accessed January 2023): 753, Col. 2c – 754, Cols. 1a–b – 2a–b.</ref></blockquote> ==== Honiton Lace ==== Kate Stradsin says,<blockquote>Honiton lace was the finest English equivalent of Brussels bobbin lace and was constructed in small ‘sprigs, in the cottages of lacemakers[.'] These sprigs were then joined together and bleached to form the large white flounces that were so sought after in the mid-nineteenth century.<ref>Strasdin, Kate. "Rediscovering Queen Alexandra’s Wardrobe: The Challenges and Rewards of Object-Based Research." ''The Court Historian'' 24.2 (2019): 181-196. Rpt http://repository.falmouth.ac.uk/3762/15/Rediscovering%20Queen%20Alexandra%27s%20Wardrobe.pdf: 13, and (for the little quotation) n. 37, which reads "Margaret Tomlinson, ''Three Generations in the Honiton Lace Trade: A Family History'', self-published, 1983."</ref></blockquote> [[File:Strook in Alençon naaldkant, 1750-1775.jpg|thumb|alt=A long piece of complex white lace with garlands, flowers and bows|Point d'Alençon lace, 1750-1775]] ==== Passementerie ==== ''Passementerie'' is the French term for trim on clothing or furniture. The 19th century (especially during the First and Second Empire) was a time of great "''exubérance''" in passementerie in French design, including the development and widespread use of the Jacquard loom.<ref>{{Cite journal|date=2023-06-10|title=Passementerie|url=https://fr.wikipedia.org/w/index.php?title=Passementerie&oldid=205068926|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Passementerie.</ref> ==== Point d'Alençon Lace ==== A lace made by hand using a number of complex steps and layers. The lacemakers build the point d'Alençon design on some kind of mesh and sometimes leave some of the mesh in as part of the lace and perhaps to provide structure. Elizabeth Lewandowski defines point d'Alençon lace and Alençon lace separately. Point lace is needlepoint lace,<ref name=":7">Lewandowski, Elizabeth J. ''The Complete Costume Dictionary''. Scarecrow Press, 2011.</ref>{{rp|233}} so Alençon point is "a two thread [needlepoint] lace."<ref name=":7" />{{rp|7}} Alençon lace has a "floral design on [a] fine net ground [and is] referred to as [the] queen of French handmade needlepoint laces. The original handmade Alençon was a fine needlepoint lace made of linen thread."<ref name=":7" />{{rp|7}} The sample of point d'Alençon lace (right), from 1750–1775, shows the linen mesh that the lace was constructed on.<ref>{{Cite web|url=http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689|title=MoMu - Open Fashion|website=openfashion.momu.be|access-date=2024-02-26}} ModeMuseum Antwerpen. http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689.</ref> The consistency in this sample suggests it may have been made by machine. == Fabric == === Brocatelle === Brocatelle is a kind of brocade, more simple than most brocades because it uses fewer warp and weft threads and fewer colors to form the design. The article in the French ''Wikipédia'' defines it like this:<blockquote>La '''brocatelle''' est un type de tissu datant du <abbr>xvi<sup>e</sup></abbr> siècle qui comporte deux chaînes et deux trames, au minimum. Il est composé pour que le dessin ressorte avec un relief prononcé, grâce à la chaîne sur un fond en sergé. Les brocatelles les plus anciennes sont toujours fabriquées avec une des trames en lin.<ref>{{Cite journal|date=2023-06-01|title=Brocatelle|url=https://fr.wikipedia.org/w/index.php?title=Brocatelle&oldid=204796410|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Brocatelle.</ref></blockquote>Which translates to this:<blockquote>Brocatelle is a type of fabric dating from the 16th century that has two warps and two wefts, at a minimum. It is composed so that the design stands out with a pronounced relief, thanks to the weft threads on a twill background. The oldest brocades were always made with one of the wefts being linen.</blockquote>The ''Oxford English Dictionary'' says, brocatelle is an "imitation of brocade, usually made of silk or wool, used for tapestry, upholstery, etc., now also for dresses. Both the nature and the use of the stuff have changed" between the late 17th century and 1888, the last time this definition was revised.<ref>"brocatelle, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/23550. Accessed 4 July 2023.</ref> === Broché === === Ciselé === === Crépe de Chine === The ''Oxford English Dictionary'' distinguishes the use of ''crêpe'' (using a circumflex rather than an acute accent over the first ''e'') from ''crape'' in textiles, saying ''crêpe'' is "often borrowed [from the French] as a term for all crapy fabrics other than ordinary black mourning crape,"<ref>"crêpe, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44242. Accessed 10 February 2023.</ref> with usage examples ranging from 1797 to the mid 20th century. Crêpe de chine, it says is "a white or other coloured crape made of raw silk." === Épinglé Velvet === Often spelled ''épingle'' rather than ''épinglé'', this term appears to have been used for a fabric made of wool, or at least wool along with linen or cotton, that was heavier and stiffer than silk velvet. It was associated with outer garments and men's clothing. Nowadays, épinglé velvet is an upholstery fabric in which the pile is cut into designs and patterns, and the portrait of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Duchess of Hamilton]] shows a mantle described as épinglé velvet that does seem to be a velvet with a woven pattern perhaps cut into the pile. === Lace === While lace also functioned sometimes as fabric — at the décolletage, for example, on the stomacher or as a veil — here we organize it as a [[Social Victorians/Terminology#Trim and Lace|part of the elaboration of clothing]]. === Liberty Fabrics === === Lisse === According to the ''Oxford English Dictionary'', the term ''lisse'' as a "kind of silk gauze" was used in the 19th-century UK and US.<ref>"lisse, n.1." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/108978. Accessed 4 July 2023.</ref> === Satin === The pre-1927 ''History of Feminine Fashion'', probably commissioned by Charles Frederick Worth's sons, describes Worth's "insistence on new fabrics, new trimmings, new materials of every description" at the beginning of his career in the mid 19th century:<blockquote>When Worth first entered the business of dressmaking, the only materials of the richer sort used for woman's dress were velvet, faille, and watered silk. Satin, for example, was never used. M. Worth desired to use satin very extensively in the gowns he designed, but he was not satisfied with what could be had at the time; he wanted something very much richer than was produced by the mills at Lyons. That his requirements entailed the reconstruction of mills mattered little — the mills were reconstructed under his directions, and the Lyons looms turned out a richer satin than ever, and the manufacturers prospered accordingly.<ref name=":9">[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]</ref>{{rp|6 in printed, 26 in digital book}}</blockquote> === Selesia === According to the ''Oxford English Dictionary'', ''silesia'' is "A fine linen or cotton fabric originally manufactured in Silesia in what is now Germany (''Schlesien'').<ref>"Silesia, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/179664. Accessed 9 February 2023.</ref> It may have been used as a lining — for pockets, for example — in garments made of more luxurious or more expensive cloth. The word ''sleazy'' — "Of textile fabrics or materials: Thin or flimsy in texture; having little substance or body."<ref>"sleazy, adj." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/181563. Accessed 9 February 2023.</ref> — may be related. === Shot Fabric === According to the ''Oxford English Dictionary'', "Of a textile fabric: Woven with warp-threads of one colour and weft-threads of another, so that the fabric (usually silk) changes in tint when viewed from different points."<ref>“Shot, ''Adj.''”  ''Oxford English Dictionary'', Oxford UP,  July 2023, https://doi.org/10.1093/OED/2977164390.</ref> A shot fabric might also be made of silk and cotton fibers. === Tissue === A lightly woven fabric like gauze or chiffon. The light weave can make the fabric translucent and make pleating and gathering flatter and less bulky. Tissue can be woven to be shot, sheer, stiff or soft. Historically, the term in English was used for a "rich kind of cloth, often interwoven with gold or silver" or "various rich or fine fabrics of delicate or gauzy texture."<ref>“Tissue, N.” ''Oxford English Dictionary'', Oxford UP, March 2024, https://doi.org/10.1093/OED/5896731814.</ref> == Fan == The ''Encyclopaedia Britannica'' (9th edition) has an article on the fan. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)<blockquote>FAN (Latin, ''vannus''; French, ''éventail''), a light implement used for giving motion to the air. ''Ventilabrum'' and ''flabellum'' are names under which ecclesiastical fans are mentioned in old inventories. Fans for cooling the face have been in use in hot climates from remote ages. A bas-relief in the British Museum represents Sennacherib with female figures carrying feather fans. They were attributes of royalty along with horse-hair fly-flappers and umbrellas. Examples may be seen in plates of the Egyptian sculptures at Thebes and other places, and also in the ruins of Persepolis. In the museum of Boulak, near Cairo, a wooden fan handle showing holes for feathers is still preserved. It is from the tomb of Amen-hotep, of the 18th dynasty, 17th century <small>B</small>.<small>C</small>. In India fans were also attributes of men in authority, and sometimes sacred emblems. A heartshaped fan, with an ivory handle, of unknown age, and held in great veneration by the Hindus, was given to the prince of Wales. Large punkahs or screens, moved by a servant who does nothing else, are in common use by Europeans in India at this day. Fans were used in the early Middle Ages to keep flies from the sacred elements during the celebrations of the Christian mysteries. Sometimes they were round, with bells attached — of silver, or silver gilt. Notices of such fans in the ancient records of St Paul’s, London, Salisbury cathedral, and many other churches, exist still. For these purposes they are no longer used in the Western church, though they are retained in some Oriental rites. The large feather fans, however, are still carried in the state processions of the supreme pontiff in Rome, though not used during the celebration of the mass. The fan of Queen Theodolinda (7th century) is still preserved in the treasury of the cathedral of Monza. Fans made part of the bridal outfit, or ''mundus muliebris'', of ancient Roman ladies. Folding fans had their origin in Japan, and were imported thence to China. They were in the shape still used—a segment of a circle of paper pasted on a light radiating frame-work of bamboo, and variously decorated, some in colours, others of white paper on which verses or sentences are written. It is a compliment in China to invite a friend or distinguished guest to write some sentiment on your fan as a memento of any special occasion, and this practice has continued. A fan that has some celebrity in France was presented by the Chinese ambassador to the Comtesse de Clauzel at the coronation of Napoleon I. in 1804. When a site was given in 1635, on an artificial island, for the settlement of Portuguese merchants in Nippo in Japan, the space was laid out in the form of a fan as emblematic of an object agreeable for general use. Men and women of every rank both in China and Japan carry fans, even artisans using them with one hand while working with the other. In China they are often made of carved ivory, the sticks being plates very thin and sometimes carved on both sides, the intervals between the carved parts pierced with astonishing delicacy, and the plates held together by a ribbon. The Japanese make the two outer guards of the stick, which cover the others, occasionally of beaten iron, extremely thin and light, damascened with gold and other metals. Fans were used by Portuguese ladies in the 14th century, and were well known in England before the close of the reign of Richard II. In France the inventory of Charles V. at the end of the 14th century mentions a folding ivory fan. They were brought into general use in that country by Catherine de’ Medici, probably from Italy, then in advance of other countries in all matters of personal luxury. The court ladies of Henry VIII.’s reign in England were used to handling fans, A lady in the Dance of Death by Holbein holds a fan. Queen Elizabeth is painted with a round leather fan in her portrait at Gorhambury; and as many as twenty-seven are enumerated in her inventory (1606). Coryat, an English traveller, in 1608 describes them as common in Italy. They also became of general use from that time in Spain. In Italy, France, and Spain fans had special conventional uses, and various actions in handling them grew into a code of signals, by which ladies were supposed to convey hints or signals to admirers or to rivals in society. A paper in the ''Spectator'' humorously proposes to establish a regular drill for these purposes. The chief seat of the European manufacture of fans during the 17th century was Paris, where the sticks or frames, whether of wood or ivory, were made, and the decorations painted on mounts of very carefully prepared vellum (called latterly ''chicken skin'', but not correctly), — a material stronger and tougher than paper, which breaks at the folds. Paris makers exported fans unpainted to Madrid and other Spanish cities, where they were decorated by native artists. Many were exported complete; of old fans called Spanish a great number were in fact made in France. Louis XIV. issued edicts at various times to regulate the manufacture. Besides fans mounted with parchment, Dutch fans of ivory were imported into Paris, and decorated by the heraldic painters in the process called “Vernis Martin,” after a famous carriage painter and inventor of colourless lac varnish. Fans of this kind belonging to the Queen and to the late baroness de Rothschild were exhibited in 1870 at Kensington. A fan of the date of 1660, representing sacred subjects, is attributed to Philippe de Champagne, another to Peter Oliver in England in the / 17th century. Cano de Arevalo, a Spanish painter of the 17th century devoted himself to fan painting. Some harsh expressions of Queen Christina to the young ladies of the French court are said to have caused an increased ostentation in the splendour of their fans, which were set with jewels and mounted in gold. Rosalba Carriera was the name of a fan painter of celebrity in the 17th century. Lebrun and Romanelli were much employed during the same period. Klingstet, a Dutch artist, enjoyed a considerable reputation for his fans from the latter part of the 17th and the first thirty years of the 18th century. The revocation of the edict of Nantes drove many fan-makers out of France to Holland and England. The trade in England was well established under the Stuart sovereigns. Petitions were addressed by the fan-makers to Charles II. against the importation of fans from India, and a duty was levied upon such fans in consequence. This importation of Indian fans, according to Savary, extended also to France. During the reign of Louis XV. carved Indian and China fans displaced to some extent those formerly imported from Italy, which had been painted on swanskin parchment prepared with various perfumes. During the 18th century all the luxurious ornamentation of the day was bestowed on fans as far as they could display it. The sticks were made of mother-of-pearl or ivory, carved with extraordinary skill in France, Italy, England, and other countries. They were painted from designs of Boucher, Watteau, Lancret, and other "genre" painters, Hébert, Rau, Chevalier, Jean Boquet, Mad. Verité, are known as fan painters. These fashions were followed in most countries of Europe, with certain national differences. Taffeta and silk, as well as fine parchment, were used for the mounts. Little circles of glass were let into the stick to be looked through, and small telescopic glasses were sometimes contrived at the pivot of the stick. They were occasionally mounted with the finest point lace. An interesting fan (belonging to Madame de Thiac in France), the work of Le Flamand, was presented by the municipality of Dieppe to Marie Antoinette on the birth of her son the dauphin. From the time of the Revolution the old luxury expended on fans died out. Fine examples ceased to be exported to England and other countries. The painting on them represented scenes or personages connected with political events. At a later period fan mounts were often prints coloured by hand. The events of the day mark the date of many examples found in modern collections. Amongst the fanmakers of the present time the names of Alexandre, Duvelleroy, Fayet, Vanier, may be mentioned as well known in Paris. The sticks are chiefly made in the department of Oise, at Le Déluge, Crèvecœur, Méry, Ste Geneviève, and other villages, where whole families are engaged in preparing them; ivory sticks are carved at Dieppe. Water-colour painters of distinction often design and paint the mounts, the best designs being figure subjects. A great impulse has been given to the manufacture and painting of fans in England since the exhibition which took place at South Kensington in 1870. Other exhibitions have since been held, and competitive prizes offered, one of which was gained by the Princess Louise. Modern collections of fans take their date from the emigration of many noble families from France at the time of the Revolution. Such objects were given as souvenirs and occasionally sold by families in straitened circumstances. A large number of fans of all sorts, principally those of the 18th century, French, English, German, Italian Spanish, &c., have been lately bequeathed to the South Kensington Museum. Regarding the different parts of folding fans it may be well to state that the sticks are called in French ''brins'', the two outer guards ''panaches'', and the mount ''feuille''.<ref>J. H. Pollen [J.H.P.]. "Fan." ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. '''10''' ('''X'''). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%209%20%28FAL-FYZ%29%20193323016.23/page/26/mode/2up (accessed January 2023): 27, Col. 1b – 28, Col. 1c.</ref></blockquote> == Fancy-dress Ball == Fancy-dress (or costume) balls were popular and frequent in the U.K. and France as well as the rest of Europe during the 19th century. The themes and styles of the fancy-dress balls influenced those that followed. At the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the guests came dressed in costume from times before 1820, as instructed on '''the invitation''', but their clothing was much more about late-Victorian standards of beauty and fashion than the standards of whatever time period the portraits they were copying or basing their costumes on. ''The Queen'' published dress and fashion information and advice under the byline of Ardern Holt, who regularly answered questions from readers about fashion as well as about fancy dress. (More about Ardern Holt, which is almost certainly a pseudonym, can be found on the [[Social Victorians/People/Working in Publishing#Journalists|People Working in Publishing]] page.) Holt also ran wrote entire articles with suggestions for what might make an appealing fancy-dress costume as well as pointing readers away from costumes that had been worn too frequently. The suggestions for costumes are based on familiar types or portraits available to readers, similar to Holt's books on fancy dress, which ran through a number of editions in the 1880s and 1890s. Fancy-dress questions sometimes asked for details about costumes worn in theatrical or operatic productions, which Holt provides. In November 1897, Holt refers to the Duchess of Devonshire's 2 July ball: "Since the famous fancy ball, given at Devonshire House during this year, historical fancy dresses have assumed a prominence that they had not hitherto known."<ref>Holt, Ardern. "Fancy Dress a la Mode." The ''Queen'' 27 November 1897, Saturday: 94 [of 145 in BNA; print p. 1026], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18971127/459/0094.</ref> Holt goes on to provide a number of ideas for costumes for historical fancy dress, as always with a strong leaning toward Victorian standards of beauty and style and away from any concern for historical accuracy. Ardern Holt published books on fancy dress as well as writing for the ''Queen'' and other periodicals, but not all of them were about fancy dress. # ''Gentlemen's Fancy Dress: How to Choose It''. Wyman & Sons, 1882. (''Google Books'' has this: https://books.google.com/books/about/Gentlemen_s_Fancy_Dress.html?id=ED8CAAAAQAAJ.) Later editions: 1898 (HathiTrust) # ''Fancy Dresses Described; Or, What to Wear at Fancy Balls''. Debenham & Freebody, 1882. Illustr., Lillian Young. (HathiTrust has this.) Later editions: 4th ed — 1884; 1887 (HathiTrust); 6th ed. — 1896 (HathiTrust) As Leonore Davidoff says, "Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration symbolised some status category for the female wearer."<ref name=":1" />{{rp|93}} [handled under Elaborations] === Historical Accuracy === Many of the costumes at the ball were based on portraits, especially when the guest was dressed as a historical figure. If possible, we have found the portraits likely to have been the originals, or we have found, if possible, portraits that show the subjects from the two time periods at similar ages. The way clothing was cut changed quite a bit between the 18th and 19th centuries. We think of Victorian clothing — particularly women's clothing, and particularly at the end of the century — as inflexible and restrictive, especially compared to 20th- and 21st-century customs permitting freedom of movement. The difference is generally evolutionary rather than absolute — that is, as time has passed since the 18th century, clothing has allowed an increasingly greater range of movement, especially for people who did not do manual labor. By the end of the 19th century, garments like women's bodices and men's coats were made fitted and smooth by attention to the grain of the fabric and by the use of darts (rather than techniques that assembled many small, individual pieces of fabric). * clothing construction and flat-pattern techniques * Generally, the further back in time we go, the more 2-dimensional the clothing itself was. ==== Women's Versions of Historical Accuracy at the Ball ==== As always with this ball, whatever historical accuracy might be present in a woman's costume is altered so that the wearer is still a fashionable Victorian lady. What makes the costumes look "Victorian" to our eyes is the line of the silhouette caused by the foundation undergarments as well as the many "elaborations"<ref name=":1" />{{rp|93}}, mostly in the decorations, trim and accessories. Also, the clothing hangs and drapes differently because the fabric was cut on grain and the shoulders were freed by the way the sleeves were set in. ==== Men's Versions of Historical Accuracy at the Ball ==== Because men were not wearing a Victorian foundation garment at the end of the century, the men's costumes at the ball are more historically accurate in some ways. * Trim * Mixing neck treatments * Hair * Breeches * Shoes and boots * Military uniforms, arms, gloves, boots == Feathers and Plumes == === Aigrette === Elizabeth Lewandowski defines ''aigrette'' as "France. Feather or plume from an egret or heron."<ref name=":7" />(5) Sometimes the newspapers use the term to refer to an accessory (like a fan or ornament on a hat) that includes such a feather or plume. The straight and tapered feathers in an aigrette are in a bundle. === Prince of Wales's Feathers or White Plumes === The feathers in an aigrette came from egrets and herons; Prince of Wales's feathers came from ostriches. A fuller discussion of Prince of Wales's feathers and the white ostrich plumes worn at court appears on [[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|Victorian Things]]. For much of the late 18th and 19th centuries, white ostrich plumes were central to fashion at court, and at a certain point in the late 18th century they became required for women being presented to the monarch and for their sponsors. Our purpose here is to understand why women were wearing plumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] as part of their costumes. First published in 1893, [[Social Victorians/People/Lady Colin Campbell|Lady Colin Campbell]]'s ''Manners and Rules of Good Society'' (1911 edition) says that<blockquote>It was compulsory for both Married and Unmarried Ladies to Wear Plumes. The married lady’s Court plume consisted of three white feathers. An unmarried lady’s of two white feathers. The three white feathers should be mounted as a Prince of Wales plume and worn towards the left hand side of the head. Colored feathers may not be worn. In deep mourning, white feathers must be worn, black feathers are inadmissible.<p> White veils or lace lappets must be worn with the feathers. The veils should not be longer than 45 inches.<ref>{{Cite web|url=https://www.edwardianpromenade.com/etiquette/the-court-presentation/|title=The Court Presentation|last=Holl|first=Evangeline|date=2007-12-07|website=Edwardian Promenade|language=en-US|access-date=2022-12-18}} https://www.edwardianpromenade.com/etiquette/the-court-presentation/.</ref></blockquote>[[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|This fashion was imported from France]] in the mid 1770s.<ref>"Abstract" for Blackwell, Caitlin. "'<nowiki/>''The Feather'd Fair in a Fright''': The Emblem of the Feather in Graphic Satire of 1776." ''Journal for Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. ''Wiley Online'' DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x (accessed November 2022).</ref> Separately, a secondary heraldic emblem of the Prince of Wales has been a specific arrangement of 3 ostrich feathers in a gold coronet<ref>{{Cite journal|date=2022-11-07|title=Prince of Wales's feathers|url=https://en.wikipedia.org/w/index.php?title=Prince_of_Wales%27s_feathers&oldid=1120556015|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Prince_of_Wales's_feathers.</ref> since King Edward III (1312–1377<ref>{{Cite journal|date=2022-12-14|title=Edward III of England|url=https://en.wikipedia.org/w/index.php?title=Edward_III_of_England&oldid=1127343221|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Edward_III_of_England.</ref>). Some women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] wore white ostrich feathers in their hair, but most of them are not Prince of Wales's feathers. Most of the plumes in these portraits are arrangements of some kind of headdress to accompany the costume. A few, wearing what looks like the Princes of Wales's feathers, might be signaling that their character is royal or has royal ancestry. '''One of the women [which one?] was presented to the royals at this ball?''' Here is the list of women who are wearing white ostrich plumes in their portraits in the [[Social Victorians/1897 Fancy Dress Ball/Photographs|''Diamond Jubilee Fancy Dress Ball'' album of 286 photogravure portraits]]: # Kathleen Pelham-Clinton, the [[Social Victorians/People/Newcastle|Duchess of Newcastle]] # [[Social Victorians/People/Louisa Montagu Cavendish|Luise Cavendish]], the Duchess of Devonshire # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce|Marquisa de Santurce]] # Lady [[Social Victorians/People/Farquhar|Emilie Farquhar]] # Princess (Laura Williamina Seymour) Victor of  [[Social Victorians/People/Gleichen#Laura%20Williamina%20Seymour%20of%20Hohenlohe-Langenburg|Hohenlohe Langenburg]] # Louisa Acheson, [[Social Victorians/People/Gosford|Lady Gosford]] # Alice Emily White Coke, [[Social Victorians/People/Leicester|Viscountess Coke]] # Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry|Vane-Tempest-Stewart]] #[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill|Consuelo Vanderbilt Spencer-Churchill]], Duchess of [[Social Victorians/People/Marlborough|Marlborough]], dressed as the wife of the French Ambassador at the Court of Catherine of Russia (not white, but some color that reads dark in the black-and-white photograph) #Mrs. Mary [[Social Victorians/People/Chamberlain|Chamberlain]] (at 491), wearing white plumes, as Madame d'Epinay #Lady Clementine [[Social Victorians/People/Tweeddale|Hay]] (at 629), wearing white plumes, as St. Bris (''Les Huguenots'') #[[Social Victorians/People/Meysey-Thompson|Lady Meysey-Thompson]] (at 391), wearing white plumes, as Elizabeth, Queen of Bohemia #Mrs. [[Social Victorians/People/Grosvenor|Algernon (Catherine) Grosvenor]] (at 510), wearing white plumes, as Marie Louise #Lady [[Social Victorians/People/Ancaster|Evelyn Ewart]], at 401), wearing white plumes, as the Duchess of Ancaster, Mistress of the Robes to Queen Charlotte, 1757, after a picture by Hudson #[[Social Victorians/People/Lyttelton|Edith Sophy Balfour Lyttelton]] (at 580), wearing what might be white plumes on a large-brimmed white hat, after a picture by Romney #[[Social Victorians/People/Yznaga|Emilia Yznaga]] (at 360), wearing what might be white plumes, as Cydalise of the Comedie Italienne from the time of Louis XV #Lady [[Social Victorians/People/Ilchester|Muriel Fox Strangways]] (at 403), wearing what might be two smallish white plumes, as Lady Sarah Lennox, one of the bridesmaids of Queen Charlotte A.D. 1761 #Lady [[Social Victorians/People/Lucan|Violet Bingham]] (at 586), wearing perhaps one white plume in a headdress not related to the Prince of Wales's feathers #Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329), wearing a headdress that includes some white plumes, as Lady Burleigh #[[Social Victorians/People/Dupplin|Agnes Blanche Marie Hay-Drummond]] (at 682), in a big headdress topped with white plumes, as Mademoiselle Andrée de Taverney A.D. 1775 #Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336), wearing what looks like Prince of Wales's plumes #[[Social Victorians/People/Suffolk|Marguerite Hyde "Daisy" Leiter]] (at 684), wearing what looks like Prince of Wales's plumes #Lady [[Social Victorians/People/Spicer|Margaret Spicer]] (at 281), wearing one smallish white and one black plume, as Countess Zinotriff, Lady-in-Waiting to the Empress Catherine of Russia #Mrs. [[Social Victorians/People/Cavendish Bentinck|Arthur James]] (at 318), wearing what looks like Prince of Wales's plumes, as Elizabeth Cavendish, daughter of Bess of Hardwick #Nellie, [[Social Victorians/People/Kilmorey|Countess of Kilmorey]] (at 207), wearing three tall plumes, 2 white and one dark, as Comtesse du Barri #Daisy, [[Social Victorians/People/Warwick|Countess of Warwick]] (at 53), wearing at least 1 white plume, as Marie Antoinette More men than women were wearing plumes reminiscent of the Prince of Wales's feathers: * ==== Bibliography for Plumes and Prince of Wales's Feathers ==== * Blackwell, Caitlin. "'''The Feather'd Fair in a Fright'<nowiki/>'': The Emblem of the Feather in Graphic Satire of 1776." Journal for ''Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. Wiley Online DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x. * "Prince of Wales's feathers." ''Wikipedia'' https://en.wikipedia.org/wiki/Prince_of_Wales%27s_feathers (accessed November 2022). ['''Add women to this page'''] * Simpson, William. "On the Origin of the Prince of Wales' Feathers." ''Fraser's magazine'' 617 (1881): 637-649. Hathi Trust https://babel.hathitrust.org/cgi/pt?id=chi.79253140&view=1up&seq=643&q1=feathers (accessed December 2022). Deals mostly with use of feathers in other cultures and in antiquity; makes brief mention of feathers and plumes in signs and pub names that may not be associated with the Prince of Wales. No mention of the use of plumes in women's headdresses or court dress. == Honors == === The Bath === The Most Honourable Order of the Bath (GCB, Knight or Dame Grand Cross; KCB or DCB, Knight or Dame Commander; CB, Companion) === The Garter === The Most Noble Order of the Knights of the Garter (KG, Knight Companion; LG, Lady Companion) [[File:The Golden Fleece - collar exhibited at MET, NYC.jpg|thumb|The Golden Fleece collar and pendant for the 2019 "Last Knight" exhibition at the MET, NYC.|alt=Recent photograph of a gold necklace on a wide band, with a gold skin of a sheep hanging from it as a pendant]] === The Golden Fleece === To wear the golden fleece is to wear the insignia of the Order of the Golden Fleece, said to be "the most prestigious and historic order of chivalry in the world" because of its long history and strict limitations on membership.<ref name=":10">{{Cite journal|date=2020-09-25|title=Order of the Golden Fleece|url=https://en.wikipedia.org/w/index.php?title=Order_of_the_Golden_Fleece&oldid=980340875|journal=Wikipedia|language=en}}</ref> The monarchs of the U.K. were members of the originally Spanish order, as were others who could afford it, like the Duke of Wellington,<ref name=":12">Thompson, R[obert]. H[ugh]. "The Golden Fleece in Britain." Publication of the ''British Numismatic Society''. 2009 https://www.britnumsoc.org/publications/Digital%20BNJ/pdfs/2009_BNJ_79_8.pdf (accessed January 2023).</ref> the first Protestant to be admitted to the order.<ref name=":10" /> Founded in 1429/30 by Philip the Good, Duke of Burgundy, the order separated into two branches in 1714, one Spanish and the other Austrian, still led by the House of Habsburg.<ref name=":10" /> [[File:Prince Albert - Franz Xaver Winterhalter 1842.jpg|thumb|1842 Winterhalter portrait of Prince Albert wearing the insignia of the Order of the Golden Fleece, 1842|left|alt=1842 Portrait of Prince Albert by Winterhalter, wearing the insignia of the Golden Fleece]] The photograph (upper right) is of a Polish badge dating from the "turn of the XV and XVI centuries."<ref>{{Citation|title=Polski: Kolana orderowa orderu Złotego Runa, przełom XV i XVI wieku.|url=https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg|date=2019-11-10|accessdate=2023-01-10|last=Wulfstan}}. https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg.</ref> The collar to this Golden Fleece might be similar to the one the [[Social Victorians/People/Spencer Compton Cavendish#The Insignia of the Order of the Golden Fleece|Duke of Devonshire is wearing in the 1897 Lafayette portrait]]. The badges and collars that Knights of the Order actually wore vary quite a bit. The 1842 Franz Xaver Winterhalter portrait (left) of Prince Consort Albert, Victoria's husband and father of the Prince of Wales, shows him wearing the Golden Fleece on a red ribbon around his neck and the star of the Garter on the front of his coat.<ref>Winterhalter, Franz Xaver. ''Prince Albert''. {{Cite web|url=https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61|title=Explore the Royal Collection Online|website=www.rct.uk|access-date=2023-01-16}} https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61.</ref> === Royal Victorian Order === (GCVO, Knight or Dame Grand Cross; KCVO or DCVO, Knight or Dame Commander; CVO, Commander; LVO, Lieutenant; MVO, Member) === St. John === The Order of the Knights of St. John === Star of India === Most Exalted Order of the Star of India (GCSI, Knight Grand Commander; KCSI, Knight Commander; CSI, Companion) === Thistle === The Most Ancient and Most Noble Order of the Thistle == Jewelry and Stones == === Cabochon === This term describes both the treatment and shape of a precious or semiprecious stone. A cabochon treatment does not facet the stone but merely polishes it, removing "the rough parts" and the parts that are not the right stone.<ref>"cabochon, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/25778. Accessed 7 February 2023.</ref> A cabochon shape is often flat on one side and oval or round, forming a mound in the setting. === Jet === === ''Orfèvrerie'' === Sometimes misspelled in the newspapers as ''orvfèvrerie''. ''Orfèvrerie'' is the artistic work of a goldsmith, silversmith, or jeweler. === Turquoises === == Military == Several men from the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball at Devonshire House]] were dressed in military uniforms, some historical and some, possibly, not. === Baldric === According to the ''Oxford English Dictionary'', the primary sense of ''baldric'' is "A belt or girdle, usually of leather and richly ornamented, worn pendent from one shoulder across the breast and under the opposite arm, and used to support the wearer's sword, bugle, etc."<ref>"baldric, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/14849. Accessed 17 May 2023.</ref> This sense has been in existence since c. 1300. === Cuirass === According to the ''Oxford English Dictionary'', the primary sense of ''cuirass'' is "A piece of armour for the body (originally of leather); ''spec.'' a piece reaching down to the waist, and consisting of a breast-plate and a back-plate, buckled or otherwise fastened together ...."<ref>"cuirass, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/45604. Accessed 17 May 2023.</ref> [[File:Knötel IV, 04.jpg|thumb|alt=An Old drawing in color of British soldiers on horses brandishing swords in 1815.|1890 illustration of the Household Cavalry (Life Guard, left; Horse Guard, right) at the Battle of Waterloo, 1815]] === Household Cavalry === The Royal Household contains the Household Cavalry, a corps of British Army units assigned to the monarch. It is made up of 2 regiments, the Life Guards and what is now called The Blues and Royals, which were formed around the time of "the Restoration of the Monarchy in 1660."<ref name=":3">Joll, Christopher. "Tales of the Household Cavalry, No. 1. Roles." The Household Cavalry Museum, https://householdcavalry.co.uk/app/uploads/sites/2/2021/06/Household-Cavalry-Museum-video-series-large-print-text-Tales-episode-01.pdf.</ref>{{rp|1}} Regimental Historian Christopher Joll says, "the original Life Guards were formed as a mounted bodyguard for the exiled King Charles II, The Blues were raised as Cromwellian cavalry and The Royals were established to defend Tangier."<ref name=":3" />{{rp|1–2}} The 1st and 2nd Life Guards were formed from "the Troops of Horse and Horse Grenadier Guards ... in 1788."<ref name=":3" />{{rp|3}} The Life Guards were and are still official bodyguards of the queen or king, but through history they have been required to do quite a bit more than serve as bodyguards for the monarch. The Household Cavalry fought in the Battle of Waterloo on Sunday, 18 June 1815 as heavy cavalry.<ref name=":3" />{{rp|3}} Besides arresting the Cato Steet conspirators in 1820 "and guarding their subsequent execution," the Household Cavalry contributed to the "the expedition to rescue General Gordon, who was trapped in Khartoum by The Mahdi and his army of insurgents" in 1884.<ref name=":3" />{{rp|3}} In 1887 they "were involved ... in the suppression of rioters in Trafalgar Square on Bloody Sunday."<ref name=":3" />{{rp|3}} ==== Grenadier Guards ==== Three men — [[Social Victorians/People/Gordon-Lennox#Lord Algernon Gordon Lennox|Lord Algernon Gordon-Lennox]], [[Social Victorians/People/Stanley#Edward George Villiers Stanley, Lord Stanley|Lord Stanley]], and [[Social Victorians/People/Stanley#Hon. Ferdinand Charles Stanley|Hon. F. C. Stanley]] — attended the ball as officers of the Grenadier Guards, wearing "scarlet tunics, ... full blue breeches, scarlet hose and shoes, lappet wigs" as well as items associated with weapons and armor.<ref name=":14">“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|p. 34, Col. 2a}} Founded in England in 1656 as Foot Guards, this infantry regiment "was granted the 'Grenadier' designation by a Royal Proclamation" at the end of the Napoleonic Wars.<ref>{{Cite journal|date=2023-04-22|title=Grenadier Guards|url=https://en.wikipedia.org/w/index.php?title=Grenadier_Guards&oldid=1151238350|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Grenadier_Guards.</ref> They were not called Grenadier Guards, then, before about 1815. In 1660, the Stuart Restoration, they were called Lord Wentworth's Regiment, because they were under the command of Thomas Wentworth, 5th Baron Wentworth.<ref>{{Cite journal|date=2022-07-24|title=Lord Wentworth's Regiment|url=https://en.wikipedia.org/w/index.php?title=Lord_Wentworth%27s_Regiment&oldid=1100069077|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Lord_Wentworth%27s_Regiment.</ref> At the time of Lord Wentworth's Regiment, the style of the French cavalier had begun to influence wealthy British royalists. In the British military, a Cavalier was a wealthy follower of Charles I and Charles II — a commander, perhaps, or a field officer, but probably not a soldier.<ref>{{Cite journal|date=2023-04-22|title=Cavalier|url=https://en.wikipedia.org/w/index.php?title=Cavalier&oldid=1151166569|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier.</ref> The Guards were busy as infantry in the 17th century, engaging in a number of armed conflicts for Great Britain, but they also served the sovereign. According to the Guards Museum,<blockquote>In 1678 the Guards were ordered to form Grenadier Companies, these men were the strongest and tallest of the regiment, they carried axes, hatches and grenades, they were the shock troops of their day. Instead of wearing tri-corn hats they wore a mitre shaped cap.<ref>{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/|title=Service to the Crown|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/.</ref></blockquote>The name comes from ''grenades'', then, and we are accustomed to seeing them in front of Buckingham Palace, with their tall mitre hats. The Guard fought in the American Revolution, and in the 19th century, the Grenadier Guards fought in the Crimean War, Sudan and the Boer War. They have roles as front-line troops and as ceremonial for the sovereign, which makes them elite:<blockquote>Queen Victoria decreed that she did not want to see a single chevron soldier within her Guards. Other then [sic] the two senior Warrant Officers of the British Army, the senior Warrant Officers of the Foot Guards wear a large Sovereigns personal coat of arms badge on their upper arm. No other regiments of the British Army are allowed to do so; all the others wear a small coat of arms of their lower arms. Up until 1871 all officers in the Foot Guards had the privilege of having double rankings. An Ensign was ranked as an Ensign and Lieutenant, a Lieutenant as Lieutenant and Captain and a Captain as Captain and Lieutenant Colonel. This was because at the time officers purchased their own ranks and it cost more to purchase a commission in the Foot Guards than any other regiments in the British Army. For example if it cost an officer in the Foot Guards £1,000 for his first rank, in the rest of the Army it would be £500 so if he transferred to another regiment he would loose [sic] £500, hence the higher rank, if he was an Ensign in the Guards and he transferred to a Line Regiment he went in at the higher rank of Lieutenant.<ref>{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/|title=Formation and role of the Regiments|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/.</ref></blockquote> ==== Life Guards ==== [[Social Victorians/People/Shrewsbury#Reginald Talbot's Costume|General the Hon. Reginald Talbot]], a member of the 1st Life Guards, attended the Duchess of Devonshire's ball dressed in the uniform of his regiment during the Battle of Waterloo.<ref name=":14" />{{rp|p. 36, Col. 3b}} At the Battle of Waterloo the 1st Life Guards were part of the 1st Brigade — the Household Brigade — and were commanded by Major-General Lord Edward Somerset.<ref name=":4">{{Cite journal|date=2023-09-30|title=Battle of Waterloo|url=https://en.wikipedia.org/w/index.php?title=Battle_of_Waterloo&oldid=1177893566|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Battle_of_Waterloo.</ref> The 1st Life Guards were on "the extreme right" of a French countercharge and "kept their cohesion and consequently suffered significantly fewer casualties."<ref name=":4" /> == Photography == == Footnotes == {{reflist}} svoa9uquxjsnshkvkswce9lc6s3m0dr 2683491 2683488 2024-11-11T15:30:27Z Scogdill 1331941 /* Aglet, Aiglet */ 2683491 wikitext text/x-wiki Especially with respect to fashion, the newspapers at the end of the 19th century in the UK often used specialized terminology. The definitions on this page are to provide a sense of what someone in the late 19th century might have meant by the term rather than a definition of what we might mean by it today. In the absence of a specialized glossary from the end of the 19th century in the U.K., we use the ''Oxford English Dictionary'' because the senses of a word are illustrated with examples that have dates so we can be sure that the senses we pick are appropriate for when they are used in the quotations we have. We also sometimes use the French ''Wikipédia'' to define a word because many technical terms of fashion were borrowings from the French. Also, often the French ''Wikipédia'' provides historical context for the uses of a word similar to the way the OED does. == Articles or Parts of Clothing: Non-gender-specific == === Mantle, Cloak, Cape === In 19th-century newspaper accounts, these terms are sometimes used without precision as synonyms. These are all outer garments. '''Mantle''' A mantle — often a long outer garment — might have elements like a train, sleeves, collars, revers, fur, and a cape. A late-19th-century writer making a distinction between a mantle and a cloak might use ''mantle'' if the garment is more voluminous. '''Cloak''' '''Cape''' === Peplum === According to the French ''Wiktionnaire'', a peplum is a "Short skirt or flared flounce layered at the waist of a jacket, blouse or dress" [translation by Google Translate].<ref>{{Cite journal|date=2021-07-02|title=péplum|url=https://fr.wiktionary.org/w/index.php?title=p%C3%A9plum&oldid=29547727|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/p%C3%A9plum.</ref> The ''Oxford English Dictionary'' has a fuller definition, although, it focuses on women's clothing because the sense is written for the present day:<blockquote>''Fashion''. ... a kind of overskirt resembling the ancient peplos (''obsolete''). Hence (now usually) in modern use: a short flared, gathered, or pleated strip of fabric attached at the waist of a woman's jacket, dress, or blouse to create a hanging frill or flounce.<ref name=":5">“peplum, n.”. ''Oxford English Dictionary'', Oxford University Press, September 2023, <https://doi.org/10.1093/OED/1832614702>.</ref></blockquote>Men haven't worn peplums since the 18th century, except when wearing costumes based on historical portraits. The ''Daily News'' reported in 1896 that peplums had been revived as a fashion item for women.<ref name=":5" /> === Revers === According to the ''Oxford English Dictionary'', ''revers'' are the "edge[s] of a garment turned back to reveal the undersurface (often at the lapel or cuff) (chiefly in ''plural''); the material covering such an edge."<ref>"revers, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/164777. Accessed 17 April 2023.</ref> The term is French and was used this way in the 19th century (according to the ''Wiktionnaire'').<ref>{{Cite journal|date=2023-03-07|title=revers|url=https://fr.wiktionary.org/w/index.php?title=revers&oldid=31706560|journal=Wiktionnaire|language=fr}} https://fr.wiktionary.org/wiki/revers.</ref> == Articles or Parts of Clothing: Men's == [[Social Victorians/Terminology#Military|Men's military uniforms]] are discussed below. === À la Romaine === [[File:Johann Baptist Straub - Mars um 1772-1.jpg|thumb|left|alt=Old and damaged marble statue of a Roman god of war with flowing cloak, big helmet with a plume on top, and armor|Johann Baptist Straub's 1772 ''à la romaine'' ''Mars'']] A few people who attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's fancy-dress ball in 1897]] personated Roman gods or people. They were dressed not as Romans, however, but ''à la romaine'', which was a standardized style of depicting Roman figures that was used in paintings, sculpture and the theatre for historical dress from the 17th until the 20th century. The codification of the style was developed in France in the 17th century for theatre and ballet, when it became popular for masked balls. Women as well as men could be dressed ''à la romaine'', but much sculpture, portraiture and theatre offered opportunities for men to dress in Roman style — with armor and helmets — and so it was most common for men. In large part because of the codification of the style as well as the painting and sculpture, the style persisted and remained influential into the 20th century and can be found in museums and galleries and on monuments. For example, Johann Baptist Straub's 1772 statue of Mars (left), now in the Bayerisches Nationalmuseum, Munich, missing part of an arm, shows Mars ''à la romaine''. In London, an early 17th-century example of a figure of Mars ''à la romaine'', with a helmet, '''was''' "at the foot of the Buckingham tomb in Henry VII's Chapel at Westminster Abbey."<ref>Webb, Geoffrey. “Notes on Hubert Le Sueur-II.” ''The Burlington Magazine for Connoisseurs'' 52, no. 299 (1928): 81–89. http://www.jstor.org/stable/863535.</ref>{{rp|81, Col. 2c}} === Cavalier === [[File:Sir-Anthony-van-Dyck-Lord-John-Stuart-and-His-Brother-Lord-Bernard-Stuart.jpg|thumb|alt=Old painting of 2 men flamboyantly and stylishly dressed in colorful silk, with white lace, high-heeled boots and long hair|Van Dyck's c. 1638 painting of cavaliers Lord John Stuart and his brother Lord Bernard Stuart]] As a signifier in the form of clothing of a royalist political and social ideology begun in France in the early 17th century, the cavalier established France as the leader in fashion and taste. Adopted by [[Social Victorians/Terminology#Military|wealthy royalist British military officers]] during the time of the Restoration, the style signified a political and social position, both because of the loyalty to Charles I and II as well the wealth required to achieve the cavalier look. The style spread beyond the political, however, to become associated generally with dress as well as a style of poetry.<ref>{{Cite journal|date=2023-04-25|title=Cavalier poet|url=https://en.wikipedia.org/w/index.php?title=Cavalier_poet&oldid=1151690299|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier_poet.</ref> Van Dyck's 1638 painting of two brothers (right) emphasizes the cavalier style of dress. === Coats === ==== Doublet ==== * In the 19th-century newspaper accounts we have seen that use this word, doublet seems always to refer to a garment worn by a man, but historically women may have worn doublets. In fact, a doublet worn by Queen Elizabeth I exists and '''is somewhere'''. * Technically doublets were long sleeved, although we cannot be certain what this or that Victorian tailor would have done for a costume. For example, the [[Social Victorians/People/Spencer Compton Cavendish#Costume at the Duchess of Devonshire's 2 July 1897 Fancy-dress Ball|Duke of Devonshire's costume as Charles V]] shows long sleeves that may be part of the surcoat but should be the long sleeves of the doublet. ==== Pourpoint ==== A padded doublet worn under armor to protect the warrior from the metal chafing. A pourpoint could also be worn without the armor. ==== Surcoat ==== Sometimes just called ''coat''. [[File:Oscar Wilde by Sarony 1882 18.jpg|thumb|alt=Old photograph of a young man wearing a velvet jacket, knee breeches, silk hose and shiny pointed shoes with bows, seated on a sofa and leaning on his left hand and holding a book in his right| Oscar Wilde, 1882, by Napoleon Sarony]] === Hose, Stockings and Tights === Newspaper accounts from the late 19th century of men's clothing use the term ''hose'' for what we might call stockings or tights. In fact, the terminology is specific. ''Stockings'' is the more general term and could refer to hose or tights. With knee breeches men wore hose, which ended above the knee, and women wore hose under their dresses. The ''Oxford English Dictionary'' defines tights as "Tight-fitting breeches, worn by men in the 18th and early 19th centuries, and still forming part of court-dress."<ref>“Tights, N.” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/2693287467.</ref> By 1897, the term was in use for women's stockings, which may have come up only to the knee. Tights were also worn by dancers and acrobats. This general sense of ''tights'' does not assume that they were knitted. ''Clocking'' is decorative embroidery on hose, usually, at the ankles on either the inside or the outside of the leg. It started at the ankle and went up the leg, sometimes as far as the knee. On women's hose, the clocking could be quite colorful and elaborate, while the clocking on men's hose was more inconspicuous. In many photographs men's hose are wrinkled, especially at the ankles and the knees, because they were shaped from woven fabric. Silk hose were knitted instead of woven, which gave them elasticity and reduced the wrinkling. The famous Sarony carte de visite photograph of Oscar Wilde (right) shows him in 1882 wearing knee breeches and silk hose, which are shiny and quite smoothly fitted although they show a few wrinkles at the ankles and knees. In the portraits of people in costume at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the men's hose are sometimes quite smooth, which means they were made of knitted silk and may have been smoothed for the portrait. In painted portraits the hose are almost always depicted as smooth, part of the artist's improvement of the appearance of the subject. === Shoes and Boots === == Articles or Parts of Clothing: Women's == === '''Chérusque''' === According to the French ''Wikipedia'', ''chérusque'' is a 19th-century term for the kind of standing collar like the ones worn by ladies in the Renaissance.<ref>{{Cite journal|date=2021-06-26|title=Collerette (costume)|url=https://fr.wikipedia.org/w/index.php?title=Collerette_(costume)&oldid=184136746|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Collerette_(costume)#Au+xixe+siècle+:+la+Chérusque.</ref> === Corsage === According to the ''Oxford English Dictionary'', the corsage is the "'body' of a woman's dress; a bodice."<ref>"corsage, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/42056. Accessed 7 February 2023.</ref> This sense is well documented in the ''OED'' for the mid and late 19th-century, used this way in fiction as well as in a publication like ''Godey's Lady's Book'', which would be expected to use appropriate terminology associated with fashion and dress making. The sense of "a bouquet worn on the bodice" is, according to the ''OED'', American. === Décolletage === === Girdle === === Mancheron === According to the ''Oxford English Dictionary'', a ''mancheron'' is a "historical" word for "A piece of trimming on the upper part of a sleeve on a woman's dress."<ref>"mancheron, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/113251. Accessed 17 April 2023.</ref> At the present, in French, a ''mancheron'' is a cap sleeve "cut directly on the bodice."<ref>{{Cite journal|date=2022-11-28|title=Manche (vêtement)|url=https://fr.wikipedia.org/w/index.php?title=Manche_(v%C3%AAtement)&oldid=199054843|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Manche_(v%C3%AAtement).</ref> === Petticoat === According to the ''O.E.D.'', a petticoat is a <blockquote>skirt, as distinguished from a bodice, worn either externally or showing beneath a dress as part of the costume (often trimmed or ornamented); an outer skirt; a decorative underskirt. Frequently in ''plural'': a woman's or girl's upper skirts and underskirts collectively. Now ''archaic'' or ''historical''.<ref>“petticoat, n., sense 2.b”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, <https://doi.org/10.1093/OED/1021034245></ref> </blockquote>This sense is, according to the ''O.E.D.'', "The usual sense between the 17th and 19th centuries." However, while petticoats belong in both outer- and undergarments — that is, meant to be seen or hidden, like underwear — they were always under another garment, for example, underneath an open overskirt. The primary sense seems to have shifted through the 19th century so that, by the end, petticoats were underwear and the term ''underskirt'' was used to describe what showed under an open overskirt. === Stomacher === According to the ''O.E.D.'', a stomacher is "An ornamental covering for the chest (often covered with jewels) worn by women under the lacing of the bodice,"<ref>“stomacher, n.¹, sense 3.a”. ''Oxford English Dictionary'', Oxford University Press, September 2023, <https://doi.org/10.1093/OED/1169498955></ref> although by the end of the 19th century, the bodice did not often have visible laces. Some stomachers were so decorated that they were thought of as part of the jewelry. === Train === A train is The Length of the Train '''For the monarch [or a royal?]''' According to Debrett's,<blockquote>A peeress's coronation robe is a long-trained crimson velvet mantle, edged with miniver pure, with a miniver pure cape. The length of the train varies with the rank of the wearer: * Duchess: for rows of ermine; train to be six feet * Marchioness: three and a half rows of ermine; train to be three and three-quarters feet * Countess: three rows of ermine; train to be three and a half feet * Viscountess: two and a half rows of ermine; train to be three and a quarter feet * Baroness: two rows of ermine; train to be three feet<ref name=":2">{{Cite web|url=https://debretts.com/royal-family/dress-codes/|title=Dress Codes|website=debretts.com|language=en-US|access-date=2023-07-27}} https://debretts.com/royal-family/dress-codes/.</ref> </blockquote>The pattern on the coronet worn was also quite specific, similar but not exactly the same for peers and peeresses. Debrett's also distinguishes between coronets and tiaras, which were classified more like jewelry, which was regulated only in very general terms. Peeresses put on their coronets after the Queen or Queen Consort has been crowned. ['''peers?'''] === Undergarments === Victorian women's undergarments created the distinctive silhouette. The corset was an important element of this understructure, which also included hoops, bustles, petticoats and so on, but it has never been the only important element. ==== Corset ==== [[File:Corset - MET 1972.209.49a, b.jpg|thumb|alt=Photograph of an old silk corset on a mannequin, showing the closure down the front, similar to a button, and channels in the fabric for the boning. It is wider at the top and bottom, creating smooth curves from the bust to the compressed waist to the hips, with a long point below the waist in front.|French 1890s corset, now in the Metropolitan Museum of Art, NYC]] The understructure of Victorian women's clothing is what makes the costumes worn by the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] so distinctly Victorian in appearance. An example of a corset that has the kind of structure often worn by fashionably dressed women in 1897 is the one at right. This corset exaggerated the shape of the women's bodies and made possible a bodice that looked and was fitted in the way that is so distinctive of the time — very controlled and smooth. And, as a structural element, this foundation garment carried the weight of all those layers and all that fabric and decoration on the gowns, trains and mantles. (The trains and mantles could be attached directly to the corset itself.) * This foundation emphasizes the waist and the bust in particular, in part because of the contrast between the very small waist and the rounded fullness of the bust and hips. * The idealized waist is defined by its small span and the sexualizing point at the center-bottom of the bodice, which directs the eye downwards. Interestingly, the pointed waistline worn by Elizabethan men has become level in the Victorian age. Highly fashionable Victorian women wearing the traditional style, however, had extremely pointed waists. * The busk (a kind of boning in the front of a corset that is less flexible than the rest) smoothed the bodice, flattened the abdomen and prevented the point on the bodice from curling up. * The sharp definition of the waist was caused by ** length of the corset (especially on the sides) ** the stiffness of the boning ** the layers of fabric ** the lacing (especially if the woman used tightlacing) ** the over-all shape, which was so much wider at the top and the bottom ** the contrast between the waist and the wider top and bottom * The late-19th-century corset was long, ending below the waist even on the sides and back. * The boning and the top edge of the late 19th-century fashion corset pushed up the bust, rounding (rather than flattening, as in earlier styles) the breasts, drawing attention to their exposed curves and creating cleavage. * The exaggerated bust was larger than the hips, whenever possible, an impression reinforced by the A-line of the skirt and the inverted Vs in the decorative trim near the waist and on the skirt. * This corset made the bodice very smooth with a very precise fit, that had no wrinkles, folds or loose drapery. The bodice was also trimmed or decorated, but the base was always a smooth bodice. More formal gowns would still have the fitted bodice and more elaborate trim made from lace, embroidery, appliqué, beading and possibly even jewels. The advantages and disadvantages of corseting and especially tight lacing were the subject of thousands of articles and opinions in the periodical press for a great part of the century, but the fetishistic and politicized tight lacing was practiced by very few women. And no single approach to corsetry was practiced by all women all the time. Most of the women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 ball]] were not tightly laced, but the progressive style does not dominate either, even though all the costumes are technically historical dress. Part of what gives most of the costumes their distinctive 19th-century "look" is the more traditional corset beneath them. Even though this highly fashionable look was widely present in the historical costumes at the ball, some women's waists were obviously very small and others were hardly '''emphasized''' at all. Women's waists are never mentioned in the newspaper coverage of the ball — or, indeed, of any of the social events attended by the network at the ball — so it is only in photographs that we can see the effects of how they used their corsets. ==== '''Farthingale or Vertugadin''' ==== ''Vertugadin'' is a French term for ''farthingale'', a cage made of hoops supporting a skirt — "un élément essentiel de la mode Tudor en Angleterre [an essential element of Tudor fashion in England]."<ref name=":0">{{Cite journal|date=2022-03-12|title=Vertugadin|url=https://fr.wikipedia.org/w/index.php?title=Vertugadin&oldid=191825729|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Vertugadin.</ref> In fact, "La princesse espagnole Catherine d'Aragon amena la mode en Angleterre pour son mariage avec le prince Arthur, fils aîné d'Henri VII en 1501 [The Spanish princess Catherine of Aragon brought the fashion to England for her marriage to Prince Arthur, eldest son of Henry VII in 1501]."<ref name=":0" /> Catherine of Aragon, of course, married Henry VIII after Arthur's death. The French and Spanish farthingales were not identical by the end of the 16th century. The Spanish farthingale shaped the skirt into an A-line with a graduated series of hoops sewn to an undergarment. The French farthingale was a flattish "cartwheel" or platter of hoops worn below the waist and above the hips held the skirt out more or less horizontally. Once past the vertugadin, the skirt then fell straight to the floor, shaping the skirt into a kind of drum. The shoes show in the portraits of women wearing the French farthingale. == '''Traditional vs Progressive Style''' == === Progressive Style === The terms ''artistic dress'' and ''aesthetic dress'' are not synonymous and were in use at different times to refer to different groups of people in different contexts, but we recognize them as referring to a similar kind of personal style in clothing, a style we call progressive dress or the progressive style. Used in a very precise way, ''artistic dress'' is associated with the Pre-Raphaelite artists and the women in their circle beginning in the 1860s. Similarly, ''aesthetic dress'' is associated with the 1880s and 1890s and dress reform movements. In general, the progressive style is characterized by its resistance to the highly structured fashion of its day, especially corseting, aniline dyes and an extremely close fit. === Traditional Style === By the end of the century designs from the [[Social Victorians/People/Dressmakers and Costumiers#The House of Worth|House of Worth]] (or Maison Worth) define what we think of as the traditional Victorian look, which was very stylish and expensive. Blanche Payne describes an example of the 1895 "high style" in a gown by Worth with "the idiosyncrasies of the [1890s] full blown":<blockquote>The dress is white silk with wine-red stripes. Sleeves, collars, bows, bag, hat, and hem border match the stripes. The sleeve has reached its maximum volume; the bosom full and emphasized with added lace; the waistline is elongated, pointed, and laced to the point of distress; the skirt is smooth over the hips, gradually swinging out to sweep the floor. This is the much vaunted hourglass figure.<ref>Payne, Blanche. ''History of Costume from the Ancient Egyptians to the Twentieth Century''. Harper & Row, 1965.</ref>{{rp|530}}</blockquote> The Victorian-looking gowns at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] are stylish in a way that recalls the designs of the House of Worth. The elements that make their look so Victorian are anachronisms on the costumes representing fashion of earlier eras. The women wearing these gowns preferred the standards of beauty from their own day to a more-or-less historically accurate look. The style competing at the very end of the century with the Worth look was not the historical, however, but a progressive style called at the time ''artistic'' or ''aesthetic''. William Powell Frith's 1883 painting ''A Private View at the Royal Academy, 1881'' (discussion below) pits this kind of traditional style against the progressive or artistic style. === The Styles === [[File:Frith A Private View.jpg|thumb|William Powell Frith, ''A Private View at the Royal Academy, 1881'']] We typically think of the late-Victorian silhouette as universal but, in the periods in which corsets dominated women's dress, not all women wore corsets and not all corsets were the same, as William Powell Frith's 1883 ''A Private View at the Royal Academy, 1881'' (right) illustrates. Frith is clear in his memoir that this painting — "recording for posterity the aesthetic craze as regards dress" — deliberately contrasts what he calls the "folly" of the Artistic Dress movement and the look of the traditional corseted waist.<ref>Frith, William Powell. ''My Autobiography and Reminiscences''. 1887.</ref> Frith considered the Artistic Movement and Artistic Dress "ephemeral," but its rejection of corsetry looks far more consequential to us in hindsight than it did in the 19th century. As Frith sees it, his painting critiques the "craze" associated with the women in this set of identifiable portraits who are not corseted, but his commitment to realism shows us a spectrum, a range, of conservatism and if not political then at least stylistic progressivism among the women. The progressives, oddly, are the women wearing artistic (that is, somewhat historical) dress, because they’re not corseted. It is a misreading to see the presentation of the women’s fashion as a simple opposition. Constance, Countess of Lonsdale — situated at the center of this painting with Frederick Leighton, president of the Royal Academy of Art — is the most conservatively dressed of the women depicted, with her narrow sleeves, tight waist and almost perfectly smooth bodice, which tells us that her corset has eyelets so that it can be laced precisely and tightly, and it has stays (or "bones") to prevent wrinkles or natural folds in the overclothing. Lillie Langtry, in the white dress, with her stylish narrow sleeves, does not have such a tightly bound waist or smooth bodice, suggesting she may not be corseted at all, as we know she sometimes was not.['''citation'''] Jenny Trip, a painter’s model, is the woman in the green dress in the aesthetic group being inspected by Anthony Trollope, who may be taking notes. She looks like she is not wearing a corset. Both Langtry and Trip are toward the middle of this spectrum: neither is dressed in the more extreme artistic dress of, say, the two figures between Trip and Trollope. A lot has been written about the late-Victorian attraction to historical dress, especially in the context of fancy-dress balls and the Gothic revival in social events as well as art and music. Part of the appeal has to have been the way those costumes could just be beautiful clothing beautifully made. Historical dress provided an opportunity for some elite women to wear less-structured but still beautiful and influential clothing. ['''Calvert'''<ref>Calvert, Robyne Erica. ''Fashioning the Artist: Artistic Dress in Victorian Britain 1848-1900''. Ph.D. thesis, University of Glasgow, 2012. <nowiki>https://theses.gla.ac.uk/3279/</nowiki></ref>] The standards for beauty, then, with historical dress were Victorian, with the added benefit of possibly less structure. So, at the Duchess of Devonshire's ball, "while some attendees tried to hew closely to historical precedent, many rendered their historical or mythological personage in the sartorial vocabulary they knew best. The [photographs of people in their costumes at the ball offer] a glimpse into how Victorians understood history, not a glimpse into the costume of an authentic historical past."<ref>Mitchell, Rebecca N. "The Victorian Fancy Dress Ball, 1870–1900." ''Fashion Theory'' 2017 (21: 3): 291–315. DOI: 10.1080/1362704X.2016.1172817.</ref> (294) * historical dress: beautiful clothing. * the range at the ball, from Minnie Paget to Gwladys * "In light of such efforts, the ball remains to this day one of the best documented outings of the period, and a quick glance at the album shows that ..." Women had more choices about their waists than the simple opposition between no corset and tightlacing can accommodate. The range of choices is illustrated in Frith's painting, with a woman locating herself on it at a particular moment for particular reasons. Much analysis of 19th-century corsetry focuses on its sexualizing effects — corsets dominated Victorian photographic pornography ['''citations'''] and at the same time, the absence of a corset was sexual because it suggested nudity.['''citations'''] A great deal of analysis of 19th-century corsetry, on the other hand, assumes that women wore corsets for the male gaze ['''citations'''] or that they tightened their waists to compete with other women.['''citations'''] But as we can see in Frith's painting, the sexualizing effect was not universal or sweeping, and these analyses do not account for the choices women had in which corset to wear or how tightly to lace it. Especially given the way that some photographic portraits were mechanically altered to make the waist appear smaller, the size of a woman's waist had to do with how she was presenting herself to the world. That is, the fact that women made choices about the size of or emphasis on their waists suggests that they had agency that needs to be taken into account. As they navigated the complex social world, women's fashion choices had meaning. Society or political hostesses had agency not only in their clothing but generally in that complex social world. They had roles managing social events of the upper classes, especially of the upper aristocracy and oligarchy, like the Duchess of Devonshire's ball. Their class and rank, then, were essential to their agency, including to some degree their freedom to choose what kind of corset to wear and how to wear it. Also, by the end of the century lots of different kinds of corsets were available for lots of different purposes. Special corsets existed for pregnancy, sports (like tennis, bicycling, horseback riding, golf, fencing, archery, stalking and hunting), theatre and dance and, of course, for these women corsets could be made to support the special dress worn over it. Women's choices in how they presented themselves to the world included more than just their foundation garments, of course. "Every cap, bow, streamer, ruffle, fringe, bustle, glove," that is, the trim and decorations on their garments, their jewelry and accessories — which Davidoff calls "elaborations"<ref name=":1">Davidoff, Leonore. ''The Best Circles: Society Etiquette and the Season''. Intro., Victoria Glendinning. The Cressett Library (Century Hutchinson), 1986 (orig 1973).</ref>{{rp|93}} — pointed to a host of status categories, like class, rank, wealth, age, marital status, engagement with the empire, how sexual they wanted to seem, political alignment and purpose at the social event. For example, when women were being presented to the monarch, they were expected to wear three ostrich plumes, often called the [[Social Victorians/Terminology#Prince of Wales's Feathers or White Plumes|Prince of Wales's feathers]]. Like all fashions, the corset, which was quite long-lasting in all its various forms, eventually went out of style. Of the many factors that might have influenced its demise, perhaps most important was the women's movement, in which women's rights, freedom, employment and access to their own money and children were less slogan-worthy but at least as essential as votes for women. The activities of the animal-rights movements drew attention not only to the profligate use of the bodies and feathers of birds but also to the looming extinction of the baleen whale, which made whale bone scarce and expensive. Perhaps the century's debates over corseting and especially tightlacing were relevant to some decisions not to be corseted. And, of course, perhaps no other reason is required than that the nature of fashion is to change. == Cinque Cento == According to the ''Oxford English Dictionary'', ''Cinque Cento'' is a shortening of ''mil cinque cento'', or 1500.<ref>"cinquecento, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/33143. Accessed 7 February 2023.</ref> The term, then would refer, perhaps informally, to the sixteenth century. == Crevé == ''Creve'', without the accent, is an old word in English (c. 1450) for burst or split.<ref>"creve, v." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44339. Accessed 8 February 2023.</ref> ['''With the acute accent, it looks like a past participle in French.'''] == Elastic == Elastic had been invented and was in use by the end of the 19th century. For the sense of "Elastic cord or string, usually woven with india-rubber,"<ref name=":6">“elastic, adj. & n.”.  ''Oxford English Dictionary'', Oxford University Press,  September 2023, <https://doi.org/10.1093/OED/1199670313>.</ref> the ''Oxford English Dictionary'' has usage examples beginning in 1847. The example for 1886 is vivid: "The thorough-going prim man will always place a circle of elastic round his hair previous to putting on his college cap."<ref name=":6" /> == Elaborations == In her 1973 ''The Best Circles: Society, Etiquette and the Season'', Leonore Davidoff notes that women’s status was indicated by dress and especially ornament: “Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration,” she says, “symbolised some status category for the female wearer.”<ref name=":1" />{{rp|93}} Looking at these elaborations as meaningful rather than dismissing them as failed attempts at "historical accuracy" reveals a great deal about the individual women who wore or carried them — and about the society women and political hostesses in their roles as managers of the social world. In her review of ''The House of Worth: Portrait of an Archive'', Mary Frances Gormally says,<blockquote>In a socially regulated year, garments custom made with a Worth label provided women with total reassurance, whatever the season, time of day or occasion, setting them apart as members of the “Best Circles” dressed in luxurious, fashionable and always appropriate attire (Davidoff 1973). The woman with a Worth wardrobe was a woman of elegance, lineage, status, extreme wealth and faultless taste.<ref>Gormally, Mary Frances. Review essay of ''The House of Worth: Portrait of an Archive'', by Amy de la Haye and Valerie D. Mendes (V&A Publishing, 2014). ''Fashion Theory'' 2017 (21, 1): 109–126. DOI: 10.1080/1362704X.2016.1179400.</ref> (117)</blockquote> === Aglet, Aiglet === Historically, an aglet is a "point or metal piece that capped a string [or ribbon] used to attach two pieces of the garment together, i.e., sleeve and bodice."<ref name=":7" />{{rp|4}} Although they were decorative, they were not always visible on the outside of the clothing. They were often stuffed inside the layers at the waist (for example, attaching the bodice to a skirt or breeches). === Frou-frou === In French, ''frou-frou'' or, spelled as ''froufrou'', is the sound of the rustling of silk or sometimes of fabrics in general.<ref>{{Cite journal|date=2023-07-25|title=frou-frou|url=https://fr.wiktionary.org/w/index.php?title=frou-frou&oldid=32508509|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/frou-frou.</ref> The first use the French ''Wiktionnaire'' lists is Honoré Balzac, ''La Cousine Bette'', 1846.<ref>{{Cite journal|date=2023-06-03|title=froufrou|url=https://fr.wiktionary.org/w/index.php?title=froufrou&oldid=32330124|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/froufrou.</ref> ''Frou-frou'' is a term clothing historians use to describe decorative additions to an article of clothing; often the term has a slight negative connotation, suggesting that the additions are superficial. === Pouf, Puff, Poof === According to the French ''Wikipédia'', a pouf was, beginning in 1744, a "kind of women's hairstyle":<blockquote>The hairstyle in question, known as the “pouf”, had launched the reputation of the enterprising Rose Bertin, owner of the Grand Mogol, a very prominent fashion accessories boutique on Rue Saint-Honoré in Paris in 1774. Created in collaboration with the famous hairdresser, Monsieur Léonard, the pouf was built on a scaffolding of wire, fabric, gauze, horsehair, fake hair, and the client's own hair held up in an almost vertical position. — (Marie-Antoinette, ''Queen of Fashion'', translated from the American by Sylvie Lévy, in ''The Rules of the Game'', n° 40, 2009)</blockquote>''Puff'' and ''poof'' are used to describe clothing. === Shirring === ''Shirring'' is the gathering of fabric to make poufs or puffs. The 19th century is known for its use of this decorative technique. Even men's clothing had shirring: at the shoulder seam. === Sequins === Sequins, paillettes, spangles Sequins — or paillettes — are "small, scalelike glittering disks."<ref name=":7" />(216) The French ''Wiktionnaire'' defines ''paillette'' as "Lamelle de métal, brillante, mince, percée au milieu, ordinairement ronde, et qu’on applique sur une étoffe pour l’orner [A strip of metal, shiny, thin, pierced in the middle, usually round, and which is applied to a fabric in order to decorate it.]"<ref name=":8">{{Cite journal|date=2024-03-18|title=paillette|url=https://fr.wiktionary.org/w/index.php?title=paillette&oldid=33809572|journal=Wiktionnaire, le dictionnaire libre|language=fr}} https://fr.wiktionary.org/wiki/paillette.</ref> According to the ''OED'', the use of ''sequin'' as a decorative device for clothing (as opposed to gold coins minted and used for international trade) goes back to the 1850s.<ref>“Sequin, N.” ''Oxford English Dictionary'', Oxford UP, September 2023, https://doi.org/10.1093/OED/4074851670.</ref> The first instance of ''spangle'' as "A small round thin piece of glittering metal (usually brass) with a hole in the centre to pass a thread through, used for the decoration of textile fabrics and other materials of various sorts" is from c. 1420.<ref>“Spangle, N. (1).” ''Oxford English Dictionary'', Oxford UP, July 2023, https://doi.org/10.1093/OED/4727197141.</ref> The first use of ''paillette'' listed in the French ''Wiktionnaire'' is in Jules Verne in 1873 to describe colored spots on icy walls.<ref name=":8" /> Currently many distinguish between sequins (which are smaller) and paillettes (which are larger). Before the 20th century, sequins were metal discs or foil leaves, and so of course if they were silver or copper, they tarnished. It is not until well into the 20th century that plastics were invented and used for sequins. === Trim and Lace === ''A History of Feminine Fashion'', published sometime before 1927 and probably commissioned by [[Social Victorians/People/Dressmakers and Costumiers#Worth, of Paris|the Maison Worth]], describes Charles Frederick Worth's contributions to the development of embroidery and [[Social Victorians/Terminology#Passementerie|passementerie]] (trim) from about the middle of the 19th century:<blockquote>For it must be remembered that one of M. Worth's most important and lasting contributions to the prosperity of those who cater for women's needs, as well as to the variety and elegance of his clients' garments, was his insistence on new fabrics, new trimmings, new materials of every description. In his endeavours to restore in Paris the splendours of the days of La Pompadour, and of Marie Antoinette, he found himself confronted at the outset with a grave difficulty, which would have proved unsurmountable to a man of less energy, resource and initiative. The magnificent materials of those days were no longer to be had! The Revolution had destroyed the market for beautiful materials of this, type, and the Restoration and regime of Louis Philippe had left a dour aspect in the City of Light. ... On parallel lines [to his development of better [[Social Victorians/Terminology#Satin|satin]]], [Worth] stimulated also the manufacture of embroidery and ''passementerie''. It was he who first started the manufacture of laces copied from the designs of the real old laces. He was the / first dressmaker to use fur in the trimming of light materials — but he employed only the richer furs, such as sable and ermine, and had no use whatever for the inferior varieties of skins.<ref name=":9" />{{rp|6–7}}</blockquote> ==== Gold and Silver Fabric and Lace ==== The ''Encyclopaedia Britannica'' (9th edition) has an article on gold and silver fabric, threads and lace attached to the article on gold. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)<blockquote>GOLD AND SILVER LACE. Under this heading a general account may be given of the use of the precious metals in textiles of all descriptions into which they enter. That these metals were used largely in the sumptuous textiles of the earliest periods of civilization there is abundant testimony; and to this day, in the Oriental centres whence a knowledge and the use of fabrics inwoven, ornamented, and embroidered with gold and silver first spread, the passion for such brilliant and costly textiles is still most strongly and generally prevalent. The earliest mention of the use of gold in a woven fabric occurs in the description of the ephod made for Aaron (Exod. xxxix. 2, 3) — "And he made the ephod of gold, blue, and purple, and scarlet, and fine twined linen. And they did beat the gold into thin plates, and cut it into wires (strips), to work it in the blue, and in the purple, and in the scarlet, and in the fine linen, with cunning work." In both the ''Iliad'' and the ''Odyssey'' distinct allusion is frequently made to inwoven and embroidered golden textiles. Many circumstances point to the conclusion that the art of weaving and embroidering with gold and silver originated in India, where it is still principally prosecuted, and that from one great city to another the practice travelled westward, — Babylon, Tarsus, Baghdad, Damascus, the islands of Cyprus and Sicily, Con- / stantinople and Venice, all in the process of time becoming famous centres of these much prized manufactures. Alexander the Great found Indian kings and princes arrayed in robes of gold and purple; and the Persian monarch Darius, we are told, wore a war mantle of cloth of gold, on which were figured two golden hawks as if pecking at each other. There is reason, according to Josephus, to believe that the “royal apparel" worn by Herod on the day of his death (Acts xii. 21) was a tissue of silver. Agrippina, the wife of the emperor Claudius, had a robe woven entirely of gold, and from that period downwards royal personages and high ecclesiastical dignitaries used cloth and tissues of gold and silver for their state and ceremonial robes, as well as for costly hangings and decorations. In England, at different periods, various names were applied to cloths of gold, as ciclatoun, tartarium, naques or nac, baudekiu or baldachin, Cyprus damask, and twssewys or tissue. The thin flimsy paper known as tissue paper, is so called because it originally was placed between the folds of gold "tissue" to prevent the contiguous surfaces from fraying each other. At what time the drawing of gold wire for the preparation of these textiles was first practised is not accurately known. The art was probably introduced and applied in different localities at widely different dates, but down till mediaeval times the method graphically described in the Pentateuch continued to be practised with both gold and silver. Fabrics woven with gold and silver continue to be used on the largest scale to this day in India; and there the preparation of the varieties of wire, and the working of the various forms of lace, brocade, and embroidery, is at once an important and peculiar art. The basis of all modern fabrics of this kind is wire, the "gold wire" of the manufacturer being in all cases silver gilt wire, and silver wire being, of course, composed of pure silver. In India the wire is drawn by means of simple draw-plates, with rude and simple appliances, from rounded bars of silver, or gold-plated silver, as the case may be. The wire is flattened into the strip or ribbon-like form it generally assumes by passing it, fourteen or fifteen strands simultaneously, over a fine, smooth, round-topped anvil, and beating it as it passes with a heavy hammer having a slightly convex surface. From wire so flattened there is made in India soniri, a tissue or cloth of gold, the web or warp being composed entirely of golden strips, and ruperi, a similar tissue of silver. Gold lace is also made on a warp of thick yellow silk with a weft of flat wire, and in the case of ribbons the warp or web is composed of the metal. The flattened wires are twisted around orange (in the case of silver, white) coloured silk thread, so as completely to cover the thread and present the appearance of a continuous wire; and in this form it is chiefly employed for weaving into the rich brocades known as kincobs or kinkhábs. Wires flattened, or partially flattened, are also twisted into exceedingly fine spirals, and in this form they are the basis of numerous ornamental applications. Such spirals drawn out till they present a waved appearance, and in that state flattened, are much used for rich heavy embroideries termed karchobs. Spangles for embroideries, &c., are made from spirals of comparatively stout wire, by cutting them down ring by ring, laying each C-like ring on an anvil, and by a smart blow with a hammer flattening it out into a thin round disk with a slit extending from the centre to one edge. Fine spirals are also used for general embroidery purposes. The demand for various kinds of loom-woven and embroidered gold and silver work in India is immense; and the variety of textiles so ornamented is also very great. "Gold and silver," says Dr Birdwood in his ''Handbook to the British-Indian Section, Paris Exhibition'', 1878, "are worked into the decoration of all the more costly loom-made garments and Indian piece goods, either on the borders only, or in stripes throughout, or in diapered figures. The gold-bordered loom embroideries are made chiefly at Sattara, and the gold or silver striped at Tanjore; the gold figured ''mashrus'' at Tanjore, Trichinopoly, and Hyderabad in the Deccau; and the highly ornamented gold-figured silks and gold and silver tissues principally at Ahmedabad, Benares, Murshedabad, and Trichinopoly." Among the Western communities the demand for gold and silver lace and embroideries arises chiefly in connexion with naval and military uniforms, court costumes, public and private liveries, ecclesiastical robes and draperies, theatrical dresses, and the badges and insignia of various orders. To a limited extent there is a trade in gold wire and lace to India and China. The metallic basis of the various fabrics is wire round and flattened, the wire being of three kinds — 1st, gold wire, which is invariably silver gilt wire; 2d, copper gilt wire, used for common liveries and theatrical purposes; and 3d, silver wire. These wires are drawn by the ordinary processes, and the flattening, when done, is accomplished by passing the wire between a pair of revolving rollers of fine polished steel. The various qualities of wire are prepared and used in precisely the same way as in India, — round wire, flat wire, thread made of flat gold wire twisted round orange-coloured silk or cotton, known in the trade as "orris," fine spirals and spangles, all being in use in the West as in the East. The lace is woven in the same manner as ribbons, and there are very numerous varieties in richness, pattern, and quality. Cloth of gold, and brocades rich in gold and silver, are woven for ecclesiastical vestments and draperies. The proportions of gold and silver in the gold thread for the lace trade varies, but in all cases the proportion of gold is exceedingly small. An ordinary gold lace wire is drawn from a bar containing 90 parts of silver and 7 of copper, coated with 3 parts of gold. On an average each ounce troy of a bar so plated is drawn into 1500 yards of wire; and therefore about 16 grains of gold cover a mile of wire. It is estimated that about 250,000 ounces of gold wire are made annually in Great Britain, of which about 20 per cent, is used for the headings of calico, muslin, &c., and the remainder is worked up in the gold lace trade.<ref>William Chandler Roberts-Austen and H. Bauerman [W.C.R. — H.B.]. "Gold and Silver Lace." In "Gold." ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. 10 (X). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%2010%20%28G-GOT%29%20193592738.23/page/753/mode/1up (accessed January 2023): 753, Col. 2c – 754, Cols. 1a–b – 2a–b.</ref></blockquote> ==== Honiton Lace ==== Kate Stradsin says,<blockquote>Honiton lace was the finest English equivalent of Brussels bobbin lace and was constructed in small ‘sprigs, in the cottages of lacemakers[.'] These sprigs were then joined together and bleached to form the large white flounces that were so sought after in the mid-nineteenth century.<ref>Strasdin, Kate. "Rediscovering Queen Alexandra’s Wardrobe: The Challenges and Rewards of Object-Based Research." ''The Court Historian'' 24.2 (2019): 181-196. Rpt http://repository.falmouth.ac.uk/3762/15/Rediscovering%20Queen%20Alexandra%27s%20Wardrobe.pdf: 13, and (for the little quotation) n. 37, which reads "Margaret Tomlinson, ''Three Generations in the Honiton Lace Trade: A Family History'', self-published, 1983."</ref></blockquote> [[File:Strook in Alençon naaldkant, 1750-1775.jpg|thumb|alt=A long piece of complex white lace with garlands, flowers and bows|Point d'Alençon lace, 1750-1775]] ==== Passementerie ==== ''Passementerie'' is the French term for trim on clothing or furniture. The 19th century (especially during the First and Second Empire) was a time of great "''exubérance''" in passementerie in French design, including the development and widespread use of the Jacquard loom.<ref>{{Cite journal|date=2023-06-10|title=Passementerie|url=https://fr.wikipedia.org/w/index.php?title=Passementerie&oldid=205068926|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Passementerie.</ref> ==== Point d'Alençon Lace ==== A lace made by hand using a number of complex steps and layers. The lacemakers build the point d'Alençon design on some kind of mesh and sometimes leave some of the mesh in as part of the lace and perhaps to provide structure. Elizabeth Lewandowski defines point d'Alençon lace and Alençon lace separately. Point lace is needlepoint lace,<ref name=":7">Lewandowski, Elizabeth J. ''The Complete Costume Dictionary''. Scarecrow Press, 2011.</ref>{{rp|233}} so Alençon point is "a two thread [needlepoint] lace."<ref name=":7" />{{rp|7}} Alençon lace has a "floral design on [a] fine net ground [and is] referred to as [the] queen of French handmade needlepoint laces. The original handmade Alençon was a fine needlepoint lace made of linen thread."<ref name=":7" />{{rp|7}} The sample of point d'Alençon lace (right), from 1750–1775, shows the linen mesh that the lace was constructed on.<ref>{{Cite web|url=http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689|title=MoMu - Open Fashion|website=openfashion.momu.be|access-date=2024-02-26}} ModeMuseum Antwerpen. http://openfashion.momu.be/#9ce5f00e-8a06-4dab-a833-05c3371f3689.</ref> The consistency in this sample suggests it may have been made by machine. == Fabric == === Brocatelle === Brocatelle is a kind of brocade, more simple than most brocades because it uses fewer warp and weft threads and fewer colors to form the design. The article in the French ''Wikipédia'' defines it like this:<blockquote>La '''brocatelle''' est un type de tissu datant du <abbr>xvi<sup>e</sup></abbr> siècle qui comporte deux chaînes et deux trames, au minimum. Il est composé pour que le dessin ressorte avec un relief prononcé, grâce à la chaîne sur un fond en sergé. Les brocatelles les plus anciennes sont toujours fabriquées avec une des trames en lin.<ref>{{Cite journal|date=2023-06-01|title=Brocatelle|url=https://fr.wikipedia.org/w/index.php?title=Brocatelle&oldid=204796410|journal=Wikipédia|language=fr}} https://fr.wikipedia.org/wiki/Brocatelle.</ref></blockquote>Which translates to this:<blockquote>Brocatelle is a type of fabric dating from the 16th century that has two warps and two wefts, at a minimum. It is composed so that the design stands out with a pronounced relief, thanks to the weft threads on a twill background. The oldest brocades were always made with one of the wefts being linen.</blockquote>The ''Oxford English Dictionary'' says, brocatelle is an "imitation of brocade, usually made of silk or wool, used for tapestry, upholstery, etc., now also for dresses. Both the nature and the use of the stuff have changed" between the late 17th century and 1888, the last time this definition was revised.<ref>"brocatelle, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/23550. Accessed 4 July 2023.</ref> === Broché === === Ciselé === === Crépe de Chine === The ''Oxford English Dictionary'' distinguishes the use of ''crêpe'' (using a circumflex rather than an acute accent over the first ''e'') from ''crape'' in textiles, saying ''crêpe'' is "often borrowed [from the French] as a term for all crapy fabrics other than ordinary black mourning crape,"<ref>"crêpe, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/44242. Accessed 10 February 2023.</ref> with usage examples ranging from 1797 to the mid 20th century. Crêpe de chine, it says is "a white or other coloured crape made of raw silk." === Épinglé Velvet === Often spelled ''épingle'' rather than ''épinglé'', this term appears to have been used for a fabric made of wool, or at least wool along with linen or cotton, that was heavier and stiffer than silk velvet. It was associated with outer garments and men's clothing. Nowadays, épinglé velvet is an upholstery fabric in which the pile is cut into designs and patterns, and the portrait of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Mary, Duchess of Hamilton]] shows a mantle described as épinglé velvet that does seem to be a velvet with a woven pattern perhaps cut into the pile. === Lace === While lace also functioned sometimes as fabric — at the décolletage, for example, on the stomacher or as a veil — here we organize it as a [[Social Victorians/Terminology#Trim and Lace|part of the elaboration of clothing]]. === Liberty Fabrics === === Lisse === According to the ''Oxford English Dictionary'', the term ''lisse'' as a "kind of silk gauze" was used in the 19th-century UK and US.<ref>"lisse, n.1." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/108978. Accessed 4 July 2023.</ref> === Satin === The pre-1927 ''History of Feminine Fashion'', probably commissioned by Charles Frederick Worth's sons, describes Worth's "insistence on new fabrics, new trimmings, new materials of every description" at the beginning of his career in the mid 19th century:<blockquote>When Worth first entered the business of dressmaking, the only materials of the richer sort used for woman's dress were velvet, faille, and watered silk. Satin, for example, was never used. M. Worth desired to use satin very extensively in the gowns he designed, but he was not satisfied with what could be had at the time; he wanted something very much richer than was produced by the mills at Lyons. That his requirements entailed the reconstruction of mills mattered little — the mills were reconstructed under his directions, and the Lyons looms turned out a richer satin than ever, and the manufacturers prospered accordingly.<ref name=":9">[Worth, House of.] {{Cite book|url=http://archive.org/details/AHistoryOfFeminineFashion|title=A History Of Feminine Fashion (1800s to 1920s)}} Before 1927. [Likely commissioned by Worth. Link is to Archive.org; info from Wikimedia Commons: https://commons.wikimedia.org/wiki/File:Worth_Biarritz_salon.jpg.]</ref>{{rp|6 in printed, 26 in digital book}}</blockquote> === Selesia === According to the ''Oxford English Dictionary'', ''silesia'' is "A fine linen or cotton fabric originally manufactured in Silesia in what is now Germany (''Schlesien'').<ref>"Silesia, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/179664. Accessed 9 February 2023.</ref> It may have been used as a lining — for pockets, for example — in garments made of more luxurious or more expensive cloth. The word ''sleazy'' — "Of textile fabrics or materials: Thin or flimsy in texture; having little substance or body."<ref>"sleazy, adj." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/181563. Accessed 9 February 2023.</ref> — may be related. === Shot Fabric === According to the ''Oxford English Dictionary'', "Of a textile fabric: Woven with warp-threads of one colour and weft-threads of another, so that the fabric (usually silk) changes in tint when viewed from different points."<ref>“Shot, ''Adj.''”  ''Oxford English Dictionary'', Oxford UP,  July 2023, https://doi.org/10.1093/OED/2977164390.</ref> A shot fabric might also be made of silk and cotton fibers. === Tissue === A lightly woven fabric like gauze or chiffon. The light weave can make the fabric translucent and make pleating and gathering flatter and less bulky. Tissue can be woven to be shot, sheer, stiff or soft. Historically, the term in English was used for a "rich kind of cloth, often interwoven with gold or silver" or "various rich or fine fabrics of delicate or gauzy texture."<ref>“Tissue, N.” ''Oxford English Dictionary'', Oxford UP, March 2024, https://doi.org/10.1093/OED/5896731814.</ref> == Fan == The ''Encyclopaedia Britannica'' (9th edition) has an article on the fan. (This article is based on knowledge that would have been available toward the end of the 19th century and does not, obviously, reflect current knowledge or ways of talking.)<blockquote>FAN (Latin, ''vannus''; French, ''éventail''), a light implement used for giving motion to the air. ''Ventilabrum'' and ''flabellum'' are names under which ecclesiastical fans are mentioned in old inventories. Fans for cooling the face have been in use in hot climates from remote ages. A bas-relief in the British Museum represents Sennacherib with female figures carrying feather fans. They were attributes of royalty along with horse-hair fly-flappers and umbrellas. Examples may be seen in plates of the Egyptian sculptures at Thebes and other places, and also in the ruins of Persepolis. In the museum of Boulak, near Cairo, a wooden fan handle showing holes for feathers is still preserved. It is from the tomb of Amen-hotep, of the 18th dynasty, 17th century <small>B</small>.<small>C</small>. In India fans were also attributes of men in authority, and sometimes sacred emblems. A heartshaped fan, with an ivory handle, of unknown age, and held in great veneration by the Hindus, was given to the prince of Wales. Large punkahs or screens, moved by a servant who does nothing else, are in common use by Europeans in India at this day. Fans were used in the early Middle Ages to keep flies from the sacred elements during the celebrations of the Christian mysteries. Sometimes they were round, with bells attached — of silver, or silver gilt. Notices of such fans in the ancient records of St Paul’s, London, Salisbury cathedral, and many other churches, exist still. For these purposes they are no longer used in the Western church, though they are retained in some Oriental rites. The large feather fans, however, are still carried in the state processions of the supreme pontiff in Rome, though not used during the celebration of the mass. The fan of Queen Theodolinda (7th century) is still preserved in the treasury of the cathedral of Monza. Fans made part of the bridal outfit, or ''mundus muliebris'', of ancient Roman ladies. Folding fans had their origin in Japan, and were imported thence to China. They were in the shape still used—a segment of a circle of paper pasted on a light radiating frame-work of bamboo, and variously decorated, some in colours, others of white paper on which verses or sentences are written. It is a compliment in China to invite a friend or distinguished guest to write some sentiment on your fan as a memento of any special occasion, and this practice has continued. A fan that has some celebrity in France was presented by the Chinese ambassador to the Comtesse de Clauzel at the coronation of Napoleon I. in 1804. When a site was given in 1635, on an artificial island, for the settlement of Portuguese merchants in Nippo in Japan, the space was laid out in the form of a fan as emblematic of an object agreeable for general use. Men and women of every rank both in China and Japan carry fans, even artisans using them with one hand while working with the other. In China they are often made of carved ivory, the sticks being plates very thin and sometimes carved on both sides, the intervals between the carved parts pierced with astonishing delicacy, and the plates held together by a ribbon. The Japanese make the two outer guards of the stick, which cover the others, occasionally of beaten iron, extremely thin and light, damascened with gold and other metals. Fans were used by Portuguese ladies in the 14th century, and were well known in England before the close of the reign of Richard II. In France the inventory of Charles V. at the end of the 14th century mentions a folding ivory fan. They were brought into general use in that country by Catherine de’ Medici, probably from Italy, then in advance of other countries in all matters of personal luxury. The court ladies of Henry VIII.’s reign in England were used to handling fans, A lady in the Dance of Death by Holbein holds a fan. Queen Elizabeth is painted with a round leather fan in her portrait at Gorhambury; and as many as twenty-seven are enumerated in her inventory (1606). Coryat, an English traveller, in 1608 describes them as common in Italy. They also became of general use from that time in Spain. In Italy, France, and Spain fans had special conventional uses, and various actions in handling them grew into a code of signals, by which ladies were supposed to convey hints or signals to admirers or to rivals in society. A paper in the ''Spectator'' humorously proposes to establish a regular drill for these purposes. The chief seat of the European manufacture of fans during the 17th century was Paris, where the sticks or frames, whether of wood or ivory, were made, and the decorations painted on mounts of very carefully prepared vellum (called latterly ''chicken skin'', but not correctly), — a material stronger and tougher than paper, which breaks at the folds. Paris makers exported fans unpainted to Madrid and other Spanish cities, where they were decorated by native artists. Many were exported complete; of old fans called Spanish a great number were in fact made in France. Louis XIV. issued edicts at various times to regulate the manufacture. Besides fans mounted with parchment, Dutch fans of ivory were imported into Paris, and decorated by the heraldic painters in the process called “Vernis Martin,” after a famous carriage painter and inventor of colourless lac varnish. Fans of this kind belonging to the Queen and to the late baroness de Rothschild were exhibited in 1870 at Kensington. A fan of the date of 1660, representing sacred subjects, is attributed to Philippe de Champagne, another to Peter Oliver in England in the / 17th century. Cano de Arevalo, a Spanish painter of the 17th century devoted himself to fan painting. Some harsh expressions of Queen Christina to the young ladies of the French court are said to have caused an increased ostentation in the splendour of their fans, which were set with jewels and mounted in gold. Rosalba Carriera was the name of a fan painter of celebrity in the 17th century. Lebrun and Romanelli were much employed during the same period. Klingstet, a Dutch artist, enjoyed a considerable reputation for his fans from the latter part of the 17th and the first thirty years of the 18th century. The revocation of the edict of Nantes drove many fan-makers out of France to Holland and England. The trade in England was well established under the Stuart sovereigns. Petitions were addressed by the fan-makers to Charles II. against the importation of fans from India, and a duty was levied upon such fans in consequence. This importation of Indian fans, according to Savary, extended also to France. During the reign of Louis XV. carved Indian and China fans displaced to some extent those formerly imported from Italy, which had been painted on swanskin parchment prepared with various perfumes. During the 18th century all the luxurious ornamentation of the day was bestowed on fans as far as they could display it. The sticks were made of mother-of-pearl or ivory, carved with extraordinary skill in France, Italy, England, and other countries. They were painted from designs of Boucher, Watteau, Lancret, and other "genre" painters, Hébert, Rau, Chevalier, Jean Boquet, Mad. Verité, are known as fan painters. These fashions were followed in most countries of Europe, with certain national differences. Taffeta and silk, as well as fine parchment, were used for the mounts. Little circles of glass were let into the stick to be looked through, and small telescopic glasses were sometimes contrived at the pivot of the stick. They were occasionally mounted with the finest point lace. An interesting fan (belonging to Madame de Thiac in France), the work of Le Flamand, was presented by the municipality of Dieppe to Marie Antoinette on the birth of her son the dauphin. From the time of the Revolution the old luxury expended on fans died out. Fine examples ceased to be exported to England and other countries. The painting on them represented scenes or personages connected with political events. At a later period fan mounts were often prints coloured by hand. The events of the day mark the date of many examples found in modern collections. Amongst the fanmakers of the present time the names of Alexandre, Duvelleroy, Fayet, Vanier, may be mentioned as well known in Paris. The sticks are chiefly made in the department of Oise, at Le Déluge, Crèvecœur, Méry, Ste Geneviève, and other villages, where whole families are engaged in preparing them; ivory sticks are carved at Dieppe. Water-colour painters of distinction often design and paint the mounts, the best designs being figure subjects. A great impulse has been given to the manufacture and painting of fans in England since the exhibition which took place at South Kensington in 1870. Other exhibitions have since been held, and competitive prizes offered, one of which was gained by the Princess Louise. Modern collections of fans take their date from the emigration of many noble families from France at the time of the Revolution. Such objects were given as souvenirs and occasionally sold by families in straitened circumstances. A large number of fans of all sorts, principally those of the 18th century, French, English, German, Italian Spanish, &c., have been lately bequeathed to the South Kensington Museum. Regarding the different parts of folding fans it may be well to state that the sticks are called in French ''brins'', the two outer guards ''panaches'', and the mount ''feuille''.<ref>J. H. Pollen [J.H.P.]. "Fan." ''Encyclopaedia Britannica'', 9th Edition (1875–1889). Vol. '''10''' ('''X'''). Adam and Charles Black (Publisher). https://archive.org/details/encyclopaedia-britannica-9ed-1875/Vol%209%20%28FAL-FYZ%29%20193323016.23/page/26/mode/2up (accessed January 2023): 27, Col. 1b – 28, Col. 1c.</ref></blockquote> == Fancy-dress Ball == Fancy-dress (or costume) balls were popular and frequent in the U.K. and France as well as the rest of Europe during the 19th century. The themes and styles of the fancy-dress balls influenced those that followed. At the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]], the guests came dressed in costume from times before 1820, as instructed on '''the invitation''', but their clothing was much more about late-Victorian standards of beauty and fashion than the standards of whatever time period the portraits they were copying or basing their costumes on. ''The Queen'' published dress and fashion information and advice under the byline of Ardern Holt, who regularly answered questions from readers about fashion as well as about fancy dress. (More about Ardern Holt, which is almost certainly a pseudonym, can be found on the [[Social Victorians/People/Working in Publishing#Journalists|People Working in Publishing]] page.) Holt also ran wrote entire articles with suggestions for what might make an appealing fancy-dress costume as well as pointing readers away from costumes that had been worn too frequently. The suggestions for costumes are based on familiar types or portraits available to readers, similar to Holt's books on fancy dress, which ran through a number of editions in the 1880s and 1890s. Fancy-dress questions sometimes asked for details about costumes worn in theatrical or operatic productions, which Holt provides. In November 1897, Holt refers to the Duchess of Devonshire's 2 July ball: "Since the famous fancy ball, given at Devonshire House during this year, historical fancy dresses have assumed a prominence that they had not hitherto known."<ref>Holt, Ardern. "Fancy Dress a la Mode." The ''Queen'' 27 November 1897, Saturday: 94 [of 145 in BNA; print p. 1026], Col. 1a [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002627/18971127/459/0094.</ref> Holt goes on to provide a number of ideas for costumes for historical fancy dress, as always with a strong leaning toward Victorian standards of beauty and style and away from any concern for historical accuracy. Ardern Holt published books on fancy dress as well as writing for the ''Queen'' and other periodicals, but not all of them were about fancy dress. # ''Gentlemen's Fancy Dress: How to Choose It''. Wyman & Sons, 1882. (''Google Books'' has this: https://books.google.com/books/about/Gentlemen_s_Fancy_Dress.html?id=ED8CAAAAQAAJ.) Later editions: 1898 (HathiTrust) # ''Fancy Dresses Described; Or, What to Wear at Fancy Balls''. Debenham & Freebody, 1882. Illustr., Lillian Young. (HathiTrust has this.) Later editions: 4th ed — 1884; 1887 (HathiTrust); 6th ed. — 1896 (HathiTrust) As Leonore Davidoff says, "Every cap, bow, streamer, ruffle, fringe, bustle, glove and other elaboration symbolised some status category for the female wearer."<ref name=":1" />{{rp|93}} [handled under Elaborations] === Historical Accuracy === Many of the costumes at the ball were based on portraits, especially when the guest was dressed as a historical figure. If possible, we have found the portraits likely to have been the originals, or we have found, if possible, portraits that show the subjects from the two time periods at similar ages. The way clothing was cut changed quite a bit between the 18th and 19th centuries. We think of Victorian clothing — particularly women's clothing, and particularly at the end of the century — as inflexible and restrictive, especially compared to 20th- and 21st-century customs permitting freedom of movement. The difference is generally evolutionary rather than absolute — that is, as time has passed since the 18th century, clothing has allowed an increasingly greater range of movement, especially for people who did not do manual labor. By the end of the 19th century, garments like women's bodices and men's coats were made fitted and smooth by attention to the grain of the fabric and by the use of darts (rather than techniques that assembled many small, individual pieces of fabric). * clothing construction and flat-pattern techniques * Generally, the further back in time we go, the more 2-dimensional the clothing itself was. ==== Women's Versions of Historical Accuracy at the Ball ==== As always with this ball, whatever historical accuracy might be present in a woman's costume is altered so that the wearer is still a fashionable Victorian lady. What makes the costumes look "Victorian" to our eyes is the line of the silhouette caused by the foundation undergarments as well as the many "elaborations"<ref name=":1" />{{rp|93}}, mostly in the decorations, trim and accessories. Also, the clothing hangs and drapes differently because the fabric was cut on grain and the shoulders were freed by the way the sleeves were set in. ==== Men's Versions of Historical Accuracy at the Ball ==== Because men were not wearing a Victorian foundation garment at the end of the century, the men's costumes at the ball are more historically accurate in some ways. * Trim * Mixing neck treatments * Hair * Breeches * Shoes and boots * Military uniforms, arms, gloves, boots == Feathers and Plumes == === Aigrette === Elizabeth Lewandowski defines ''aigrette'' as "France. Feather or plume from an egret or heron."<ref name=":7" />(5) Sometimes the newspapers use the term to refer to an accessory (like a fan or ornament on a hat) that includes such a feather or plume. The straight and tapered feathers in an aigrette are in a bundle. === Prince of Wales's Feathers or White Plumes === The feathers in an aigrette came from egrets and herons; Prince of Wales's feathers came from ostriches. A fuller discussion of Prince of Wales's feathers and the white ostrich plumes worn at court appears on [[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|Victorian Things]]. For much of the late 18th and 19th centuries, white ostrich plumes were central to fashion at court, and at a certain point in the late 18th century they became required for women being presented to the monarch and for their sponsors. Our purpose here is to understand why women were wearing plumes at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] as part of their costumes. First published in 1893, [[Social Victorians/People/Lady Colin Campbell|Lady Colin Campbell]]'s ''Manners and Rules of Good Society'' (1911 edition) says that<blockquote>It was compulsory for both Married and Unmarried Ladies to Wear Plumes. The married lady’s Court plume consisted of three white feathers. An unmarried lady’s of two white feathers. The three white feathers should be mounted as a Prince of Wales plume and worn towards the left hand side of the head. Colored feathers may not be worn. In deep mourning, white feathers must be worn, black feathers are inadmissible.<p> White veils or lace lappets must be worn with the feathers. The veils should not be longer than 45 inches.<ref>{{Cite web|url=https://www.edwardianpromenade.com/etiquette/the-court-presentation/|title=The Court Presentation|last=Holl|first=Evangeline|date=2007-12-07|website=Edwardian Promenade|language=en-US|access-date=2022-12-18}} https://www.edwardianpromenade.com/etiquette/the-court-presentation/.</ref></blockquote>[[Social Victorians/Victorian Things#Ostrich Feathers and Prince of Wales's Feathers|This fashion was imported from France]] in the mid 1770s.<ref>"Abstract" for Blackwell, Caitlin. "'<nowiki/>''The Feather'd Fair in a Fright''': The Emblem of the Feather in Graphic Satire of 1776." ''Journal for Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. ''Wiley Online'' DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x (accessed November 2022).</ref> Separately, a secondary heraldic emblem of the Prince of Wales has been a specific arrangement of 3 ostrich feathers in a gold coronet<ref>{{Cite journal|date=2022-11-07|title=Prince of Wales's feathers|url=https://en.wikipedia.org/w/index.php?title=Prince_of_Wales%27s_feathers&oldid=1120556015|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Prince_of_Wales's_feathers.</ref> since King Edward III (1312–1377<ref>{{Cite journal|date=2022-12-14|title=Edward III of England|url=https://en.wikipedia.org/w/index.php?title=Edward_III_of_England&oldid=1127343221|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Edward_III_of_England.</ref>). Some women at the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball]] wore white ostrich feathers in their hair, but most of them are not Prince of Wales's feathers. Most of the plumes in these portraits are arrangements of some kind of headdress to accompany the costume. A few, wearing what looks like the Princes of Wales's feathers, might be signaling that their character is royal or has royal ancestry. '''One of the women [which one?] was presented to the royals at this ball?''' Here is the list of women who are wearing white ostrich plumes in their portraits in the [[Social Victorians/1897 Fancy Dress Ball/Photographs|''Diamond Jubilee Fancy Dress Ball'' album of 286 photogravure portraits]]: # Kathleen Pelham-Clinton, the [[Social Victorians/People/Newcastle|Duchess of Newcastle]] # [[Social Victorians/People/Louisa Montagu Cavendish|Luise Cavendish]], the Duchess of Devonshire # Jesusa Murrieta del Campo Mello y Urritio (née Bellido), [[Social Victorians/People/Santurce|Marquisa de Santurce]] # Lady [[Social Victorians/People/Farquhar|Emilie Farquhar]] # Princess (Laura Williamina Seymour) Victor of  [[Social Victorians/People/Gleichen#Laura%20Williamina%20Seymour%20of%20Hohenlohe-Langenburg|Hohenlohe Langenburg]] # Louisa Acheson, [[Social Victorians/People/Gosford|Lady Gosford]] # Alice Emily White Coke, [[Social Victorians/People/Leicester|Viscountess Coke]] # Lady Mary Stewart, Helen Mary Theresa [[Social Victorians/People/Londonderry|Vane-Tempest-Stewart]] #[[Social Victorians/People/Consuelo Vanderbilt Spencer-Churchill|Consuelo Vanderbilt Spencer-Churchill]], Duchess of [[Social Victorians/People/Marlborough|Marlborough]], dressed as the wife of the French Ambassador at the Court of Catherine of Russia (not white, but some color that reads dark in the black-and-white photograph) #Mrs. Mary [[Social Victorians/People/Chamberlain|Chamberlain]] (at 491), wearing white plumes, as Madame d'Epinay #Lady Clementine [[Social Victorians/People/Tweeddale|Hay]] (at 629), wearing white plumes, as St. Bris (''Les Huguenots'') #[[Social Victorians/People/Meysey-Thompson|Lady Meysey-Thompson]] (at 391), wearing white plumes, as Elizabeth, Queen of Bohemia #Mrs. [[Social Victorians/People/Grosvenor|Algernon (Catherine) Grosvenor]] (at 510), wearing white plumes, as Marie Louise #Lady [[Social Victorians/People/Ancaster|Evelyn Ewart]], at 401), wearing white plumes, as the Duchess of Ancaster, Mistress of the Robes to Queen Charlotte, 1757, after a picture by Hudson #[[Social Victorians/People/Lyttelton|Edith Sophy Balfour Lyttelton]] (at 580), wearing what might be white plumes on a large-brimmed white hat, after a picture by Romney #[[Social Victorians/People/Yznaga|Emilia Yznaga]] (at 360), wearing what might be white plumes, as Cydalise of the Comedie Italienne from the time of Louis XV #Lady [[Social Victorians/People/Ilchester|Muriel Fox Strangways]] (at 403), wearing what might be two smallish white plumes, as Lady Sarah Lennox, one of the bridesmaids of Queen Charlotte A.D. 1761 #Lady [[Social Victorians/People/Lucan|Violet Bingham]] (at 586), wearing perhaps one white plume in a headdress not related to the Prince of Wales's feathers #Rosamond Fellowes, [[Social Victorians/People/de Ramsey|Lady de Ramsey]] (at 329), wearing a headdress that includes some white plumes, as Lady Burleigh #[[Social Victorians/People/Dupplin|Agnes Blanche Marie Hay-Drummond]] (at 682), in a big headdress topped with white plumes, as Mademoiselle Andrée de Taverney A.D. 1775 #Florence Canning, [[Social Victorians/People/Garvagh|Lady Garvagh]] (at 336), wearing what looks like Prince of Wales's plumes #[[Social Victorians/People/Suffolk|Marguerite Hyde "Daisy" Leiter]] (at 684), wearing what looks like Prince of Wales's plumes #Lady [[Social Victorians/People/Spicer|Margaret Spicer]] (at 281), wearing one smallish white and one black plume, as Countess Zinotriff, Lady-in-Waiting to the Empress Catherine of Russia #Mrs. [[Social Victorians/People/Cavendish Bentinck|Arthur James]] (at 318), wearing what looks like Prince of Wales's plumes, as Elizabeth Cavendish, daughter of Bess of Hardwick #Nellie, [[Social Victorians/People/Kilmorey|Countess of Kilmorey]] (at 207), wearing three tall plumes, 2 white and one dark, as Comtesse du Barri #Daisy, [[Social Victorians/People/Warwick|Countess of Warwick]] (at 53), wearing at least 1 white plume, as Marie Antoinette More men than women were wearing plumes reminiscent of the Prince of Wales's feathers: * ==== Bibliography for Plumes and Prince of Wales's Feathers ==== * Blackwell, Caitlin. "'''The Feather'd Fair in a Fright'<nowiki/>'': The Emblem of the Feather in Graphic Satire of 1776." Journal for ''Eighteenth-Century Studies'' 20 January 2013 (Vol. 36, Issue 3): 353-376. Wiley Online DOI: https://doi.org/10.1111/j.1754-0208.2012.00550.x. * "Prince of Wales's feathers." ''Wikipedia'' https://en.wikipedia.org/wiki/Prince_of_Wales%27s_feathers (accessed November 2022). ['''Add women to this page'''] * Simpson, William. "On the Origin of the Prince of Wales' Feathers." ''Fraser's magazine'' 617 (1881): 637-649. Hathi Trust https://babel.hathitrust.org/cgi/pt?id=chi.79253140&view=1up&seq=643&q1=feathers (accessed December 2022). Deals mostly with use of feathers in other cultures and in antiquity; makes brief mention of feathers and plumes in signs and pub names that may not be associated with the Prince of Wales. No mention of the use of plumes in women's headdresses or court dress. == Honors == === The Bath === The Most Honourable Order of the Bath (GCB, Knight or Dame Grand Cross; KCB or DCB, Knight or Dame Commander; CB, Companion) === The Garter === The Most Noble Order of the Knights of the Garter (KG, Knight Companion; LG, Lady Companion) [[File:The Golden Fleece - collar exhibited at MET, NYC.jpg|thumb|The Golden Fleece collar and pendant for the 2019 "Last Knight" exhibition at the MET, NYC.|alt=Recent photograph of a gold necklace on a wide band, with a gold skin of a sheep hanging from it as a pendant]] === The Golden Fleece === To wear the golden fleece is to wear the insignia of the Order of the Golden Fleece, said to be "the most prestigious and historic order of chivalry in the world" because of its long history and strict limitations on membership.<ref name=":10">{{Cite journal|date=2020-09-25|title=Order of the Golden Fleece|url=https://en.wikipedia.org/w/index.php?title=Order_of_the_Golden_Fleece&oldid=980340875|journal=Wikipedia|language=en}}</ref> The monarchs of the U.K. were members of the originally Spanish order, as were others who could afford it, like the Duke of Wellington,<ref name=":12">Thompson, R[obert]. H[ugh]. "The Golden Fleece in Britain." Publication of the ''British Numismatic Society''. 2009 https://www.britnumsoc.org/publications/Digital%20BNJ/pdfs/2009_BNJ_79_8.pdf (accessed January 2023).</ref> the first Protestant to be admitted to the order.<ref name=":10" /> Founded in 1429/30 by Philip the Good, Duke of Burgundy, the order separated into two branches in 1714, one Spanish and the other Austrian, still led by the House of Habsburg.<ref name=":10" /> [[File:Prince Albert - Franz Xaver Winterhalter 1842.jpg|thumb|1842 Winterhalter portrait of Prince Albert wearing the insignia of the Order of the Golden Fleece, 1842|left|alt=1842 Portrait of Prince Albert by Winterhalter, wearing the insignia of the Golden Fleece]] The photograph (upper right) is of a Polish badge dating from the "turn of the XV and XVI centuries."<ref>{{Citation|title=Polski: Kolana orderowa orderu Złotego Runa, przełom XV i XVI wieku.|url=https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg|date=2019-11-10|accessdate=2023-01-10|last=Wulfstan}}. https://commons.wikimedia.org/wiki/File:The_Golden_Fleece_-_collar_exhibited_at_MET,_NYC.jpg.</ref> The collar to this Golden Fleece might be similar to the one the [[Social Victorians/People/Spencer Compton Cavendish#The Insignia of the Order of the Golden Fleece|Duke of Devonshire is wearing in the 1897 Lafayette portrait]]. The badges and collars that Knights of the Order actually wore vary quite a bit. The 1842 Franz Xaver Winterhalter portrait (left) of Prince Consort Albert, Victoria's husband and father of the Prince of Wales, shows him wearing the Golden Fleece on a red ribbon around his neck and the star of the Garter on the front of his coat.<ref>Winterhalter, Franz Xaver. ''Prince Albert''. {{Cite web|url=https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61|title=Explore the Royal Collection Online|website=www.rct.uk|access-date=2023-01-16}} https://www.rct.uk/collection/search#/16/collection/401412/prince-albert-1819-61.</ref> === Royal Victorian Order === (GCVO, Knight or Dame Grand Cross; KCVO or DCVO, Knight or Dame Commander; CVO, Commander; LVO, Lieutenant; MVO, Member) === St. John === The Order of the Knights of St. John === Star of India === Most Exalted Order of the Star of India (GCSI, Knight Grand Commander; KCSI, Knight Commander; CSI, Companion) === Thistle === The Most Ancient and Most Noble Order of the Thistle == Jewelry and Stones == === Cabochon === This term describes both the treatment and shape of a precious or semiprecious stone. A cabochon treatment does not facet the stone but merely polishes it, removing "the rough parts" and the parts that are not the right stone.<ref>"cabochon, n." ''OED Online'', Oxford University Press, December 2022, www.oed.com/view/Entry/25778. Accessed 7 February 2023.</ref> A cabochon shape is often flat on one side and oval or round, forming a mound in the setting. === Jet === === ''Orfèvrerie'' === Sometimes misspelled in the newspapers as ''orvfèvrerie''. ''Orfèvrerie'' is the artistic work of a goldsmith, silversmith, or jeweler. === Turquoises === == Military == Several men from the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 1897 fancy-dress ball at Devonshire House]] were dressed in military uniforms, some historical and some, possibly, not. === Baldric === According to the ''Oxford English Dictionary'', the primary sense of ''baldric'' is "A belt or girdle, usually of leather and richly ornamented, worn pendent from one shoulder across the breast and under the opposite arm, and used to support the wearer's sword, bugle, etc."<ref>"baldric, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/14849. Accessed 17 May 2023.</ref> This sense has been in existence since c. 1300. === Cuirass === According to the ''Oxford English Dictionary'', the primary sense of ''cuirass'' is "A piece of armour for the body (originally of leather); ''spec.'' a piece reaching down to the waist, and consisting of a breast-plate and a back-plate, buckled or otherwise fastened together ...."<ref>"cuirass, n." ''OED Online'', Oxford University Press, March 2023, www.oed.com/view/Entry/45604. Accessed 17 May 2023.</ref> [[File:Knötel IV, 04.jpg|thumb|alt=An Old drawing in color of British soldiers on horses brandishing swords in 1815.|1890 illustration of the Household Cavalry (Life Guard, left; Horse Guard, right) at the Battle of Waterloo, 1815]] === Household Cavalry === The Royal Household contains the Household Cavalry, a corps of British Army units assigned to the monarch. It is made up of 2 regiments, the Life Guards and what is now called The Blues and Royals, which were formed around the time of "the Restoration of the Monarchy in 1660."<ref name=":3">Joll, Christopher. "Tales of the Household Cavalry, No. 1. Roles." The Household Cavalry Museum, https://householdcavalry.co.uk/app/uploads/sites/2/2021/06/Household-Cavalry-Museum-video-series-large-print-text-Tales-episode-01.pdf.</ref>{{rp|1}} Regimental Historian Christopher Joll says, "the original Life Guards were formed as a mounted bodyguard for the exiled King Charles II, The Blues were raised as Cromwellian cavalry and The Royals were established to defend Tangier."<ref name=":3" />{{rp|1–2}} The 1st and 2nd Life Guards were formed from "the Troops of Horse and Horse Grenadier Guards ... in 1788."<ref name=":3" />{{rp|3}} The Life Guards were and are still official bodyguards of the queen or king, but through history they have been required to do quite a bit more than serve as bodyguards for the monarch. The Household Cavalry fought in the Battle of Waterloo on Sunday, 18 June 1815 as heavy cavalry.<ref name=":3" />{{rp|3}} Besides arresting the Cato Steet conspirators in 1820 "and guarding their subsequent execution," the Household Cavalry contributed to the "the expedition to rescue General Gordon, who was trapped in Khartoum by The Mahdi and his army of insurgents" in 1884.<ref name=":3" />{{rp|3}} In 1887 they "were involved ... in the suppression of rioters in Trafalgar Square on Bloody Sunday."<ref name=":3" />{{rp|3}} ==== Grenadier Guards ==== Three men — [[Social Victorians/People/Gordon-Lennox#Lord Algernon Gordon Lennox|Lord Algernon Gordon-Lennox]], [[Social Victorians/People/Stanley#Edward George Villiers Stanley, Lord Stanley|Lord Stanley]], and [[Social Victorians/People/Stanley#Hon. Ferdinand Charles Stanley|Hon. F. C. Stanley]] — attended the ball as officers of the Grenadier Guards, wearing "scarlet tunics, ... full blue breeches, scarlet hose and shoes, lappet wigs" as well as items associated with weapons and armor.<ref name=":14">“The Duchess of Devonshire’s Ball.” The ''Gentlewoman'' 10 July 1897 Saturday: 32–42 [of 76], Cols. 1a–3c [of 3]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0003340/18970710/155/0032.</ref>{{rp|p. 34, Col. 2a}} Founded in England in 1656 as Foot Guards, this infantry regiment "was granted the 'Grenadier' designation by a Royal Proclamation" at the end of the Napoleonic Wars.<ref>{{Cite journal|date=2023-04-22|title=Grenadier Guards|url=https://en.wikipedia.org/w/index.php?title=Grenadier_Guards&oldid=1151238350|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Grenadier_Guards.</ref> They were not called Grenadier Guards, then, before about 1815. In 1660, the Stuart Restoration, they were called Lord Wentworth's Regiment, because they were under the command of Thomas Wentworth, 5th Baron Wentworth.<ref>{{Cite journal|date=2022-07-24|title=Lord Wentworth's Regiment|url=https://en.wikipedia.org/w/index.php?title=Lord_Wentworth%27s_Regiment&oldid=1100069077|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Lord_Wentworth%27s_Regiment.</ref> At the time of Lord Wentworth's Regiment, the style of the French cavalier had begun to influence wealthy British royalists. In the British military, a Cavalier was a wealthy follower of Charles I and Charles II — a commander, perhaps, or a field officer, but probably not a soldier.<ref>{{Cite journal|date=2023-04-22|title=Cavalier|url=https://en.wikipedia.org/w/index.php?title=Cavalier&oldid=1151166569|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Cavalier.</ref> The Guards were busy as infantry in the 17th century, engaging in a number of armed conflicts for Great Britain, but they also served the sovereign. According to the Guards Museum,<blockquote>In 1678 the Guards were ordered to form Grenadier Companies, these men were the strongest and tallest of the regiment, they carried axes, hatches and grenades, they were the shock troops of their day. Instead of wearing tri-corn hats they wore a mitre shaped cap.<ref>{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/|title=Service to the Crown|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-2/.</ref></blockquote>The name comes from ''grenades'', then, and we are accustomed to seeing them in front of Buckingham Palace, with their tall mitre hats. The Guard fought in the American Revolution, and in the 19th century, the Grenadier Guards fought in the Crimean War, Sudan and the Boer War. They have roles as front-line troops and as ceremonial for the sovereign, which makes them elite:<blockquote>Queen Victoria decreed that she did not want to see a single chevron soldier within her Guards. Other then [sic] the two senior Warrant Officers of the British Army, the senior Warrant Officers of the Foot Guards wear a large Sovereigns personal coat of arms badge on their upper arm. No other regiments of the British Army are allowed to do so; all the others wear a small coat of arms of their lower arms. Up until 1871 all officers in the Foot Guards had the privilege of having double rankings. An Ensign was ranked as an Ensign and Lieutenant, a Lieutenant as Lieutenant and Captain and a Captain as Captain and Lieutenant Colonel. This was because at the time officers purchased their own ranks and it cost more to purchase a commission in the Foot Guards than any other regiments in the British Army. For example if it cost an officer in the Foot Guards £1,000 for his first rank, in the rest of the Army it would be £500 so if he transferred to another regiment he would loose [sic] £500, hence the higher rank, if he was an Ensign in the Guards and he transferred to a Line Regiment he went in at the higher rank of Lieutenant.<ref>{{Cite web|url=https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/|title=Formation and role of the Regiments|website=The Guards Museum|language=en-GB|access-date=2023-05-15}} https://theguardsmuseum.com/about-the-guards/history-of-the-foot-guards/history-page-1/.</ref></blockquote> ==== Life Guards ==== [[Social Victorians/People/Shrewsbury#Reginald Talbot's Costume|General the Hon. Reginald Talbot]], a member of the 1st Life Guards, attended the Duchess of Devonshire's ball dressed in the uniform of his regiment during the Battle of Waterloo.<ref name=":14" />{{rp|p. 36, Col. 3b}} At the Battle of Waterloo the 1st Life Guards were part of the 1st Brigade — the Household Brigade — and were commanded by Major-General Lord Edward Somerset.<ref name=":4">{{Cite journal|date=2023-09-30|title=Battle of Waterloo|url=https://en.wikipedia.org/w/index.php?title=Battle_of_Waterloo&oldid=1177893566|journal=Wikipedia|language=en}} https://en.wikipedia.org/wiki/Battle_of_Waterloo.</ref> The 1st Life Guards were on "the extreme right" of a French countercharge and "kept their cohesion and consequently suffered significantly fewer casualties."<ref name=":4" /> == Photography == == Footnotes == {{reflist}} 9jk5tz36wdj9v1h3aa9gwoumgz36npj Are axioms definitions in disguise? 0 290132 2684003 2602008 2024-11-11T22:06:50Z Jaredscribe 2906761 /* Con */ wikipedia link 2684003 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] k7vlc77e7v7zd2usf6fjhm2g7okiaid 2684007 2684003 2024-11-11T22:19:16Z Jaredscribe 2906761 /* Axioms are definitions in disguise */ 2684007 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. {{Objection|An axiom is αχιωμα, that which is considered worthy, held as self-evident.}} * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] gso2mp38s5w77l2oj8grgv9ti1fch3n 2684008 2684007 2024-11-11T22:19:55Z Jaredscribe 2906761 /* Axioms are definitions in disguise */ Add objection #DebateTools 2684008 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. ** {{Objection}} An axiom is αχιωμα, that which is considered worthy, held as self-evident. {{Objection|An axiom is αχιωμα, that which is considered worthy, held as self-evident.}} * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] 7gwioqsjxyvfskzd3kvqu7qqlwx5lfu 2684009 2684008 2024-11-11T22:23:16Z Jaredscribe 2906761 /* Axioms are definitions in disguise */ An axiom is αχιωμα, that which is considered worthy, held as self-evident by those who possess common sense and are capable of speaking a natural language. 2684009 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. ** {{Objection}} An axiom is αχιωμα, that which is considered worthy, held as self-evident by those who possess common sense and are capable of speaking a natural language. * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] byz5jqmzlwdesrttthlh3c0y4xaea7c 2684010 2684009 2024-11-11T22:29:41Z Jaredscribe 2906761 /* Axioms are definitions in disguise */ Add argument against #DebateTools 2684010 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. ** {{Objection}} An axiom is αχιωμα, that which is considered worthy, held as self-evident by those who possess common sense and are capable of speaking a natural language. * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. * {{Argument against}} The proposition commits the [[w:nominalist]] fallacy: assuming that the earth (geo) that we measure (meter), exists merely because the geometers said so. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] 19pb5rrcbvxh98skqdbzcyu682pqedw 2684050 2684010 2024-11-12T00:07:03Z Jaredscribe 2906761 {{Argument against}} The proposition commits the [[w:nominalist]] fallacy by assuming that the earth (geo) that we measure (meter), exists merely because the geometers said so. 2684050 wikitext text/x-wiki {{Wikidebate}} Some argue that axioms are definitions in disguise. Are they right? Henri Poincaré seems to have though so, but Karl Popper disagreed.<!-- to be traced to sources--> Search terms: definitions in disguise, axioms are definitions, implicit definitions. == Axioms are definitions in disguise == === Pro === * {{Argument for}} A theory providing axioms but no definitions has the axioms serve as definitions. The terms refer to that which meets the axioms. The axioms do not make any claims about anything so long as the terms they use have no definitions, and therefore, no meaning other than the one that axioms give them. Axioms are therefore neither true nor false: before they bind terms to their meaning, the axioms do not mean anything and thus have no truth value. ** {{Objection}} An axiom is αχιωμα, that which is considered worthy, held as self-evident by those who possess common sense and are capable of speaking a natural language. * {{Argument for}} Even if axioms do not unequivocally pick the referents of the terms, they point to canonical ones, as if located in the shared semantic context. Thus, if one mathematician gives Peano arithmetic to another one, does not tell him what it is supposed to do, does not use the mnemonic symbols 0, s, +, and *, and then asks, what do you think this is, the mathematician should be able to guess these are natural numbers. A guess not worth making is that the referents are the terms themselves since all consistent sets of axioms of first-order logic have such a model, and it has no priority or significance. And when a mathematician sees Peano arithmetic, he sees the natural numbers as he understands them and not the variant where the Gödel sentence is false. This bears witness to natural numbers having a priority in the list of candidate interpretations. Admittedly, this does not hold of all sets of axioms: if one has axioms of the notion of group from algebra, it is hard to guess which group is meant. This idea points to sentences about terms constraining their semantics, even if not completely. Thus, if one has two notions from biology, X and Y, and one says X is part of Y, then X and Y can be leaf and tree, but not the other way around. In this way, the semantic relations of hyponymy and meronymy are part of the definition process, and so is instance of. A set of constraints on a set of terms with unknown or unclear semantics that uses semantic relations and other well understood relations can thereby act as an effective definition helping clarity and precision that a genus-differentia definition often does not reach. Similarly, if one sees axioms of Euclidean geometry that do not use the mnemonic words "point" and "line", one should be able to guess that the referents are points and lines. Of course, one can, in the spirit of modern mathematics, think these are in fact pure sets since everything is pure set, but that is ontologically wrong: points are not sets but rather points. === Con === * {{Argument against}} There is another interpretation of axioms: the terms do have meaning, but are undefined. What the axioms do is not define the terms but rather provide true claims that are left without proof or derivation but rather serve as basis for proof or derivation. That axioms do not necessarily provide a definition for terms used by them is clear from [[w:Peano_arithmetic|Peano arithmetic]]: while natural numbers are one model (satisfying interpretation of) Peano arithmetic, terms of the arithmetic are another model. Thus, in one model, s(s(0)) is assigned to 2, while in another model, s(s(0)) is assigned to "s(s(0))". The axioms of Peano arithmetic do not pick between the two models, and thus, they do not define the terms "0", "s(0)", etc., (they do not state the genus, to say the least) merely expose their relational properties. Admittedly, once the proof system has axioms at its disposal, it does not need definitions, especially genus-differentia definitions. This gives the meaning to the claim that "mathematicians do not know what they are talking about": systems of axioms used for symbolic or algebraic manipulation do not need definitions and do not need to have any idea of what kind of entities are being referred to: all the entities have to do is have terms be bound to them behave in a way that meets the axioms. Elementary school geometry gets rather far with intuitive definitions by example of "point" and "line", perhaps stressing that the points are "infinitely thin" and that the lines are "straight", but not necessarily wondering about the genus of "point" and its distinguishing characteristics. The definitions rely on children knowing what "infinitely thin" and "straight" means. ** {{Objection}} The above interpretation makes sense for Euclidean geometry and natural numbers since they probably correspond to innate human intuitions. But it does not make sense for, say, hyperbolic geometry. If we start with the notion of a ''line'' as given but undefined, then we may ask whether it is Euclidean or a hyperbolic geometry that is true; both cannot be true. But if axioms are definitions in disguise, then there is ''Euclidean line'' and ''hyperbolic line'', two different notions. As a result, geometries are not true or false. Each geometry is a mathematical object of its own. Without hyperbolic axioms, we would not know what ''hyperbolic line'' means. (It seems to have been this problem of incompatible geometries that lead Poincaré to the idea that axioms are definitions in disguise.) See [[W:Hyperbolic geometry]]. *** {{Objection}} Good points. However, perhaps we could use some definition process that would explain what ''hyperbolic lines'' are without relying on axioms. It would be some kind of definition by pointing. Or we could embed hyperbolic geometry in Euclidean geometry, saying that hyperbolic line is a kind of Euclidean line segment or something of the sort. Axioms are probably not the only way to define ''hyperbolic line''. *** {{Objection}} As a nitpick, a geometry can still be true in some physical sense. Geometry was not originally some kind of abstract mathematical enterprise but rather an attempt to accurately describe the real physical space. **** {{Objection}} Fair point. However, our modern understanding is that mathematical objects live in their own world of abstract objects, and that they merely ''model'' the physical world. Thus, geometry is a better or worse model of the physical world. From the purely mathematical standpoint, whether a particular geometry actually models anything in the real world does not really matter. Mathematics can be interested in more geometries than are relevant to the empirical world, more numbers than are reflected in the empirical world, more modal logics than users in the empirical world find practically relevant, etc. **** {{Objection}} Right, it can be ''true'' in the sense that it ''accurately'' represents the real physical space. However, in that sense, Euclidean geometry seems ''false'' given modern physics, relativity and space curvature, but that is not what mathematicians think. The geometry is consistent, has a model (interpretation meeting the axioms), and that makes it fine. Of course, it is also fine for many practical applications. **** {{Objection}} It is possible that real physical space is so arcane that it will be hard to find a geometry that perfectly accurately represents it. After all, relativity theory is not a theory of everything and not necessarily the final version of physics. Mathematics is not advanced by mathematicians worrying about whether the geometries they are investigating are all ''false'' in that physical sense. Thus, the notion that geometries are neither true nor false but rather abstract objects existing in the dedicated abstract world is a good position for a mathematician to take. * {{Argument against}} The proposition commits the [[w:nominalist]] fallacy by assuming that the earth (geo) that we measure (meter), exists merely because the geometers said so. == Further reading == * [https://philarchive.org/archive/SHIPOT-6 Poincaré on the Foundation of Geometry in the Understanding] by Jeremy Shipley, philarchive.org * [https://philpapers.org/rec/SPICAT-2 Conventionalism and the Philosophy of Henri Poincare] by Peter Laurence Spirtes, philpapers.org * [https://lacl.fr/~lfontanella/papers/IHPST15.pdf On the definitional character of axioms] by Laura Fontanella, 2015 * [https://www.researchgate.net/publication/331176200_Axioms_as_Definitions_Revisiting_Poincare_and_Hilbert Axioms as Definitions: Revisiting Poincaré and Hilbert] by Laura Fontanella, 2019 * [http://users.uoa.gr/~psillos/PapersI/27%20A%20Priori.pdf THE A PRIORI: BETWEEN CONVENTIONSAND IMPLICIT DEFINITIONS] * [[Wikipedia:Peano arithmetic]] * [[Wikipedia:Gödel's incompleteness theorems]] [[Category:Philosophy]] 8ourjx6xpxo2ac2eyxktdseui80es9y Should Ukraine surrender to Russia in 2022? 0 290818 2684012 2638779 2024-11-11T23:07:01Z Jaredscribe 2906761 /* Ukraine should surrender to Russia in 2022 */ Related question for debate: /* Russia should surrender and recognize Ukrainian independence */ 2684012 wikitext text/x-wiki {{Wikidebate}} {{Politics}} Should Ukraine surrender to Russia in 2022? See [[W:2022 Russian invasion of Ukraine]]. Those who are arguing against sending arms to Ukraine seem to be supporting that position since fewer arms means shorter ability to resist, but they may have other reasons as well. Predicates and items: civilian lives, civilian infrastructure, disruption of Ukrainian economy, disruption of Ukrainian agricultural export, mineable resources in Donbas, nuclear weapons, nuclear power plants, appeasement, Munich agreement, national self-determination, 1968 invasion of Czechoslovakia, geographic defense features, Holodomor, Russian imperial ambitions beyond Ukraine. == Ukraine should surrender to Russia in 2022 == === Arguments for === * {{Argument for}} If Ukraine surrenders, it will save many Ukrainian lives and prevent of lot of damage to country infrastructure including civilian buildings. Given the amount of missiles that Russia can fire at Ukraine, it is very unclear whether Ukraine can defend itself. And if Russia is truly determined to take Ukraine, they may use tactical nuclear weapons as well. It all depends on how much sane or reckless those in Russia that are in power are. Fighting a nuclear superpower is a very uncertain prospect. The worst case outcome is that Ukraine will stand defeated with many lost lives and buildings in ruin. A rather bad case outcome is that Ukraine will defend itself but many lives will be lost, residential and industrial buildings and other structures badly damaged, facing winter, facing economic problems, facing possible hunger, etc. A risk is that the fighting will hit a nuclear power plant and a catastrophe will ensue, and given the Russians act like crazy, it is a real risk. ** {{Objection}} It may result in many Ukrainians losing their lives anyway, and maybe even more lives long-term. *** {{Objection}} Some lives yes, but it is not clear more lives would be lost. And Russia would have no interest to destroy infrastructure when it can instead take it over. If Russia is after territorial expansion and natural resources as it seems to be, it does not have a deep interest in killing civilians other than as a means of terror as part of a war. Hitler did not kill all that many Czechs in Bohemia and Moravia (part of today's Czechia) either, and he was a real monster. The countries that did not surrender in World War II suffered much worse. **** {{Objection}} less than 20 years after the Bolsheviks won in Ukraine, there was the Holodomor. Hitler controlled Czechoslovakia for less than 8 years. **** {{Objection}} That is defeatist and cowardly. If all democracies (or semi-democracies) did that in 1945, the Nazis would have gained and kept much of Europe, and Japan have much of China, in 1865, the southern states might still have slavery, in 1784, the US would still be a British colony. ***** {{Objection}} Nazi-occupied Europe might have been good for the people of Africa and Asia (e.g. the [[w:Bengal famine of 1943]] less severe), we aren't sure about the southern states maintaining slavery for over 135 years after 1855), and the US was bad for indigenous people. ***** {{Objection}} True: no one will earn respect by surrendering instead of fighting. The songs are sung about those who fight and never give up. But earning respect is not the only thing of value; civilian lives and buildings are also of value. ****** {{Objection}} The above kind of reasoning is what Putin is betting on. ******* {{Objection}} Of course he is since it is part of the logic of the situation. That alone does not make the logic bad. **** {{Objection}} That is not like Churchill. The world would have turned bad if Churchill gave up. ***** {{Objection}} If Churchill, the Soviet Union might have been weaker by 1945. Indeed, it might have ceased existing west of the Urals. ***** {{Objection}} Churchill was on an island, which provides significant defensive capability, he had a lot of resources of the Commonwealth/Empire. If the going got too tough, he could have also fled to Northern Ireland, Newfoundland, or even Jamaica, and still arguably be in UK, and to get to UK, Hitler had to go through France or a German amphibious invasion attempt would be a lot longer. Czechoslovakia was none of these. Poland even took a chunk out of Czechoslovakia around that time. Poland fought back but it was for nothing. Ukraine does not have good geographic features for defense, unlike the Great Britain. ****** {{Objection}} The situation is not analogous to Poland: Poland was attacked on two fronts by Hitler in the west and Stalin in the east. So far, Ukraine only has to defend against Russia.  ******* {{Objection}} The above does not detract from an island being much better defensible than a mostly landlocked country with no mountains separating it from the attacker, Russia. ******* {{Objection}} The situation is similar to the Polish one in some regards, and dissimilar in others. What 1939 Poland and 2022 Ukraine have in common is that they fought an apparently much more powerful enemy alone and that they were isolated from the enemy neither by mountains nor by ocean. ******** {{Objection}} The Nazi invasion of Poland took 35 days. ≥453 days after Russia's invasion (not counting the events of 2014), and 80% of Ukraine is still independent. ****** {{Objection}} The Soviet Union also did not have good geographic defense features, except perhaps for winter. They did not give up and instead lost very many lives. ******* {{Objection}} The Soviet Union had great industrial weapon production capacity and huge populace. ******** {{Objection}} Ukraine has weapon supplies from the West: as far as weapon supplies, Ukraine is fine. ********* {{Objection}} Ukraine will probably run out of Soviet SAMs by the time F16s arrive. ********* {{Objection}} But Russia outnumbers Ukrainians by population. ********** {{Objection}} Russians don't seem as motivated except for Russian "boomers" giving pro-Putin views on certain YouTube videos and rent-a-crowd rallies and celebrations. *********** {{Objection}} Putin is very very popular in Russia, to argue that it’s just boomers who support him is a bit ignorant. Russian cultural values are not identical to the west.  ************ {{Objection}} Russian polls are probably less reliable than Western polls, Russian boomers are far less likely to be conscripted than young Russian men, many young Russians have left Russia since early 2022, and Russian cultural values aren't (totally) different to the West.  ******* {{Objection}} Indeed, and Ukraine, which was part of the USSR, fared better under post-Holodomor USSR than it did under Hitler. **** {{Objection}} Surrendering could be seen as a form of collaboration with Russia. ***** {{Objection}} It is not clear how the countries that are not ready for active military intervention on the side of Ukraine could legitimately complain. If they showed willingness to deploy actual troops, that would be a whole different signal for Putin. Of course, that would also increase the risk of World War III, one reason for why they are unlikely to do it. Other countries should show empathy for the dire situation Ukraine is in. ** {{Objection}} Ukraine has defended itself against Russian missiles for over a year. At the same time Ukraine is reclaiming ground from Russia, and Russia is also being adversely affected by sanctions. Winning is not impossible. *** {{Objection}} The above statement does not contradict the first sentence of argument for, nor does it contradict multiple other sentences. (Should such an obviously invalid item be deleted from the debate?) *** {{Objection}} Getting Russian soldiers out of Donetsk and Sevastopol probably won't be as easy as Kyiv, or even Kherson. ** {{Objection}} If Putin used nukes, it'd be the 3rd time—and likely 4th and more times—in warfare, the first time in over 75 years, the first time this century, the first time in Europe, and the only living leader to have ordered it. Effects such as fallout might affect Russian soldiers and winds might blow it into Russia or Belarus. Ukrainian church buildings wanted by the Russian Orthodox church might be destroyed. Also, the effects might not be as bad. It's likely that most cities in Ukraine have a higher concrete-to-wood ratio than Hiroshima and Nagasaki, know better the effects of nuclear explosions—the flash (e.g. wear light clothing if nuclear war threatens), blast, and radiation (e.g. fall-out shelters, have potassium iodine, stay away for a few weeks). Also, it'd give more countries that border Russia—including Ukraine—reason to develop their own WMDs. ** {{Objection}} Vietnam successfully fought nuclear powers such as the US and in the late 1970s, the PRC. ** {{Objection}} If buildings are destroyed, Ukraine can rebuild them. However, If Ukraine ceases to exist, Ukrainians cannot easily regain their country, like how Poland ceased to exist for over 100 years after it was partitioned by neighboring countries. ** {{Objection}} If a nuclear power plant is hit, Belarus and Russia might be affected by the radiation (e.g. [[:File:Chernobyl radiation map 1996.svg]]). * {{Argument for}} Many Ukrainians self-identify as Christians. Christ preached pacifism. As part of the Sermon on the Mount in [[w:Matthew 5:39|Matthew 5:39]], Jesus says "But I tell you, don't resist him who is evil; but whoever strikes you on your right cheek, turn to him to the other also." In [[w:Matthew 26:52|Matthew 26:52]], after one of Jesus's disciples cut of the ear of the high priest's servants in response to Jesus being arrested, Jesus told him "Put your sword back into its place, for all those who take the sword will die by the sword". Ergo, surrendering, or at least refusing to fight, would be the Christian thing to do. ** {{Objection}} The Bible condemns vengeance but does not uniformly condemn self-defense. For example, in [[w:Nehemiah 4|Nehemiah 4]], the Israelites rebuilt the walls of Jerusalem to defend themselves against attacks.  *** {{Objection}} The actions of the Israelites is not a good basis for morality. In [[w:Numbers 31|Numbers 31]], the after defeating the Midianites, killed everyone except virgin women. We should focus instead on actions and life of Jesus, who preached radical pacifism. === Arguments against === * {{Argument against}} If Ukraine surrenders, it will lose its statehood and the nation will be suppressed. The Russian empire has a history of suppressing the Ukrainian language, and causing harm to Ukrainian people including Holodomor, sometimes recognized as act of genocide. It is hard to estimate what bad things Russians will do in Ukraine if it falls under their control, given the barbarism they are showing so far. ** {{Objection}} What's so precious about the Ukrainian language? What about other languages in the area such as Polish, or the language of the Tatars? Has Ukrainian been banned in Crimea or Russian-controlled Donbas? *** {{Objection}} The extermination, suppression, or altering of an existing culture, group, or language done in the name of hatred or expansion is an affront to life itself and infringes not only on basic human rights, but also removes valuable information, societies, and demographics from play, in some cases completely erasing them. It is ethically questionable to imply that because a language or culture isn't "precious" it shouldn't be protected as what it is. Additionally, yes, the Ukrainian language is actively being denied in its existence in Crimea<ref>{{Cite web|url=https://euromaidanpress.com/2014/09/06/german-mp-beck-luhansk-occupation-russian-troops-annexation/|title=Is Luhansk about to be annexed by Russia?|date=2014-09-06|website=Euromaidan Press|language=en-US|access-date=2023-12-07}}</ref> and you can find a greater list of infractions regarding it [[wikipedia:Chronology_of_Ukrainian_language_suppression|here,]] the most relevant and recent case being from 2022, wherein Russian officials are repeatedly denying the existence of the Ukrainian language as "part of incitement to genocide" and are even burning books.<ref>https://newlinesinstitute.org/wp-content/uploads/English-Report.pdf</ref><ref>{{Cite web|url=https://www.kyivpost.com/post/1282|title=Linguicide in the Occupied Territories|last=Luczkiw|first=Stash|website=Get the Latest Ukraine News Today - KyivPost|language=en|access-date=2023-12-07}}</ref> ** {{Objection}} The Ukrainian people were arguably their most prosperous during post-Stalin Soviet times, and the Russians are no more barbaric than the US—which is funding this war—did in Afghanistan, Iraq, or Vietnam—which was decades more recent than the 1930s. *** {{Objection}} What the US did to those countries is somewhat irrelevant to this conflict: the US is killing no Ukrainian civilians: Russia is. Also, Russia ≠ USSR. * {{Argument against}} If Ukraine surrenders, it will turn back on its citizens who want to live in Ukraine with the sort of freedoms that it has and do not want to be part of the Russian world with poor freedom of speech and poor treatment of homosexuals, transsexuals, etc., including those citizens who speak Russian as their primary language. ** {{Objection}} Ukraine isn't much more liberated/Russia isn't much more repressive. Ukraine has banned political parties. It conscripted its men and forbade most of them from leaving Russia. Its laws on abortions and drugs such as marijuana aren't much better. Ukrainian society is still somewhat homophobic and patriarchal. The Azov Battalion uses Nazi-like symbols and even flashed swastikas. Edward Snowden has become a Russian citizen. *** {{Objection}} Those parties might have been Russian fronts. *** {{Objection}} Ukraine is facing an existential threat: besides, most Ukrainian women chose/choose to stay in Ukraine with many who left returning. Also, some Ukrainian men could go to Russia, and from Russia, maybe other parts of the world. (There's also the issue of Ukrainian transmen, transwomen, and non-binaries.) *** {{Objection}} In Ukraine, laws and attitudes on issues such as abortion, drugs such as marijuana, homophobia, and gender equality seem to be getting better, whereas in Russia, they seem to be getting worse. * {{Argument against}} If Ukraine surrenders, Putin will not stop there and will attack other countries. ** {{Objection}} That is not so clear since other neighbor states are in NATO and if Russia attacks any of them, NATO will have to show its true colors and is likely to engage back in a conventional warfare or prove to be worthless. *** {{Objection}} Moldova and Georgia aren't NATO members. ** {{Objection}} That is a concern for other countries, but not for the Ukrainian citizens. The question is not whether other countries should encourage Ukraine to fight but rather whether Ukraine would do well to surrender. *** {{Objection}} The question is, "should Ukraine surrender?" The question is vague and could apply to a number of perspectives, including the value of Ukrainian statehood, civilian/military lives as well as the future outcomes of a Ukrainian surrender on the global scale. The worldwide implications of a Russian victory, especially from Ukrainian surrender are valid concerns. *** {{Objection}} If Russia annexes Ukraine, it might have Ukrainians fight other opponents of Russia, much like the USSR had Ukrainians fight in Afghanistan, and likely suppress protesters in Hungary in 1956 and Czechoslovakia in 1968. * {{Argument against}} The Hitler Munich experience confirmed that it is foolish to try to appease an aggressive dictator. ** {{Objection}} It would have seemed more foolish for Czechoslovakia to fight the dictator without anyone else's military help. It would end up like Poland or worse. (It was not Czechoslovakia's fault that no one came in its support.) Whether a coalition of military powers should have appeased Hitler is a whole different question. How good the chances are of victory, the feasibility of victory, makes a difference. *** {{Objection}} Czechoslovakia could have ignored the [[w:Munich Agreement]] and warn the Germans that agreement by France and UK for Germany, or no agreement, they'd fight any German soldier who set foot into their country (maybe also arrest Henlein and other SDP members). The results might not have been worse. **** {{Objection}} If Czechoslovakia ignored the Munich Agreement and fought Germany, the result is very likely to have been many more deaths of Czechoslovak citizens than actually took place, and Czechoslovak citizens are not to be blamed for the failure of the West to resist Hitler (Hitler had no nukes to threaten retaliation.) * {{Argument against}} It is not reasonable to expect Ukraine to simply surrender; imagine if it was your country that was being attacked. ** {{Objection}} The debate is structured and conceived in terms of person-free argument, and therefore, the part "imagine if it was your country that was being attacked" is out of scope of the debate. ** {{Objection}} One can imagine that one's country is being attacked, e.g. Czechoslovakia in 1938; and from that perspective, the statement "It is not reasonable to expect COUNTRY_C to simply surrender" has no force, especially since it is part of the substance of the argument-based debate to articulate "reasonableness" rather than simply assert it. ** {{Objection}} On a note similar to the above, one may ask whether Czechoslovakia should have fought Russians and the other invaders in 1968 (see also [[W:Warsaw Pact invasion of Czechoslovakia]]), since, "one must not appease an aggressor". The answer is not obvious; arguably, if Czechoslovakia fought, the result would still be subjugation, but with many more deaths. * {{Argument against}} Impossible, it's 2023, Ukraine didn't surrender. ** {{Objection}} That is irrelevant since one can rephrase the question as follows: From the perspective of the information known in the middle of year 2022, should Ukraine have surrenderred to Russia in 2022? ** {{Comment}} Even if one accepts this objection, one can create a new debate, Should Ukraine surrender to Russia in 2023? Some of the input into the debate is likely to be very similar, including, 1) what if the semi-crazed Russian leadership starts using tactical (mid-impact) nuclear weapons, and 2) what if the semi-crazed Russians cause a serious accident in the Russian-occupied nuclear power plant in Ukraine? Which can be linked to: 3) semi-crazed Russians already caused a serious accident in a large dam in Ukraine. == Russia should surrender and recognize Ukrainian independence == === Pro === === Con === == See also == * [[Is aggressive war of territorial expansion good?]] == Further reading == * [[W:2022 Russian invasion of Ukraine]] * [[W:Legality of the 2022 Russian invasion of Ukraine]] * [https://voxukraine.org/en/the-last-colonial-war-in-europe-or-why-ukraine-cannot-surrender/ The last colonial war in Europe or why Ukraine cannot surrender], voxukraine.org * [https://www.bbc.com/news/world-europe-63016675 Ukraine war: Putin not bluffing about nuclear weapons, EU says], bbc.com * [https://www.npr.org/2022/10/04/1126714896/elon-musk-ukraine-peace-plan-zelenskyy Elon Musk's peace plan for Ukraine draws condemnation from Zelenskyy], 2022, npr.org * [https://www.ghanaweb.com/GhanaHomePage/NewsArchive/Ukraine-must-surrender-for-the-good-of-the-world-Nana-Akomea-advises-1486829 Ukraine must surrender for the good of the world - Nana Akomea advises], ghanaweb.com * [https://dailynous.com/2022/03/02/philosophers-on-the-russian-attack-on-ukraine/ Philosophers On The Russian Attack On Ukraine], 2022, dailynous.com * [https://www.washingtonpost.com/world/2022/05/24/henry-kissinger-ukraine-russia-territory-davos/ Henry Kissinger says Ukraine should concede territory to Russia to end the war], 2022, washingtonpost.com * [https://www.aljazeera.com/news/2022/5/26/never-going-to-happen-ukraine-blasts-trading-land-for-peace ‘Never going to happen’: Ukraine blasts trading land for peace], 2022 May, aljazeera.com * [https://www.wsj.com/articles/in-new-poll-89-of-ukrainians-reject-ceding-land-to-reach-peace-with-russia-11656504002 In New Poll, 89% of Ukrainians Reject Ceding Land to Reach Peace With Russia], wsj.com * [https://edition.cnn.com/2022/06/28/politics/white-house-ukraine-projection/index.html Biden officials privately doubt that Ukraine can win back all of its territory], 2022, cnn.com [[Category:Ukraine]] [[Category:Russia]] [[Category:2020s in Europe]] [[Category:21st-century military history]] b5201lwpnkheed049951etuswpuyo73 File:Multiple Object Tracking.pdf 6 294892 2684136 2624669 2024-11-12T03:42:55Z OhanaUnited 18921 OhanaUnited uploaded a new version of [[File:Multiple Object Tracking.pdf]] 2624669 wikitext text/x-wiki == Summary == {{Information |Description= English: [[WikiJournal of Science/Multiple object tracking]] |Source= 10.15347/WJS/2023.003 |Date= 12/5/2023 |Author= Alex O. Holcombe |Permission= This file is licensed under the creative commons attribution share-alike 3.0 unported license. }} == Licensing == {{cc-by-sa-3.0}} [[Category:WikiJournal]] hip7z683cnpzywxs7351lshxalac0gr User:Jaredscribe 2 295750 2683985 2651553 2024-11-11T21:06:37Z Jaredscribe 2906761 2683985 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Book study guides in Incubation: Help Wanted== {{Research project}} * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] * [[User:Jaredscribe/2024 US Presidential Debate]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * [[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} 2xob0hc19bxkzdbdung990zksie7dix 2683988 2683985 2024-11-11T21:08:20Z Jaredscribe 2906761 2683988 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] * [[User:Jaredscribe/2024 US Presidential Debate]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} g7wes48tqr87qsnow0jmocniqab32mr 2683990 2683988 2024-11-11T21:12:41Z Jaredscribe 2906761 /* Research Projects, Study Notes and Draft Syllabi */ 2683990 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] [[US Foreign Policy]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} eayn5rassk9z4gxs8u3nqe47gu8cmoi 2683993 2683990 2024-11-11T21:15:05Z Jaredscribe 2906761 /* Notes for Someday/Maybe */ 2683993 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] [[Foreign policy from Obama to Trump]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} eenmv1cfm7e6cjom2p0om5eapzextzt 2684004 2683993 2024-11-11T22:08:25Z Jaredscribe 2906761 /* Notes for Someday/Maybe */ 2684004 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] [[Foreign policy from Obama to Trump]] [[Are axioms definitions in disguise?#Con|Are axioms definitions in disguise? Con]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} 6v96rhten7m7hx7vibvrxt4arc139vb 2684005 2684004 2024-11-11T22:10:32Z Jaredscribe 2906761 /* Notes for Someday/Maybe */ 2684005 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] [[Foreign policy from Obama to Trump]] [[Are axioms definitions in disguise?#Con|Are axioms definitions in disguise? Con]] [[Does Israel commit genocide in Israel–Hamas war?|Does_Israel_commit_genocide_in_Israel–Hamas_war%3F#Have_Hamas,_Palestinian_Islamic_Jihad,_and_their_allies_attempted_genocide_of_the_Jewish_people?]] == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} o77jz982zq7aj4gspda1ft3mn3idn3h 2684064 2684005 2024-11-12T00:26:38Z Jaredscribe 2906761 /* Notes for Someday/Maybe */ 2684064 wikitext text/x-wiki ''universitas magistrorum et scholarium'' = community of masters and scholars. [[m:User:Jaredscribe#Scholarly manifestos and project activity]] ==Study Companions to Published books: Help Wanted== {{Research project}} * * [[User:Jaredscribe/Biology of mental illness|User:Jaredscribe/Biology of mental illness, and Psychiatry's Troubled Search]] {{expand}} and continue *[[Draft:Aristotle for Everybody]] on [[Aristotle|Aristotelian]] and Newtonian physics (natural philosophy), metaphysics, and natural theology (ontology), ethics, politics, and poetics, as arranged and presented by [[w:Mortimer_Adler|Mortimer Adler]]. * [[User:Jaredscribe/Antijudaism: The Western Tradition]] as presented by [[w:David_Nirenberg|David Nirenberg]] ([[w:fr:David_Nirenberg|fr)]] ([[w:he:דייוויד_נירנברג|he]]) * [[s:User:Jaredscribe/The Israel-Palestine reader]]<ref>{{Cite book|title=The Israel/Palestine reader|date=2019|publisher=Polity|isbn=978-1-5095-2733-5|editor-last=Dowty|editor-first=Alan|location=Cambridge, UK ; Medford, MA}}</ref> * [[Draft:The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric]] by [[w:Miriam_Joseph|Miriam Joseph]] * [[User:Jaredscribe/Basic errors in modern thought]] ==Research Projects, Study Notes and Draft Syllabi== * [[User:Jaredscribe/Comparative law]] * [[w:User:Jaredscribe|en.wikipedia.org/wiki/User:Jaredscribe]] and subpages * [[User:Jaredscribe/Russia|User:Jaredscribe/Russia and its many Revolutions]] * [[User:Jaredscribe/The Virtues, Vices, and Systemic Differences of the Many Wikipedias|User:Jaredscribe/The Virtues, Vices, and Systemic Differences in Policy and Bias of the Many Wikipedias]] {{expand}} and continue == Liberal Arts Basic Curriculum == The [[w:Trivium]] of Liberal Arts: Grammar, Logic, and Rhetoric. * {{cite book|url=https://archive.org/details/triviumliberalar0000miri|title=The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric|last1=Joseph|first1=Sister Miriam|year=2002|isbn=978-0967967509|editor-last=McGlinn|editor-first=Marguerite|edition=3rd|author-link=w:Sister Miriam Joseph|orig-year=1948|url-access=registration}} * {{cite book|title=Aristotle for Everybody: Difficult Thought Made Easy|title-link=Aristotle for Everybody|author-link=w:Mortimer Adler|last=Adler|first=Mortimer|date=1997|publisher=Touchstone|ISBN=0-684-83823-0|location=New York|author-link=Mortimer J. Adler|orig-date=1978}} * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-Rules|Rules of Reasoning in Philosophy]], [[Philosophiæ Naturalis Principia Mathematica#Rules of Reasoning in Philosophy|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Isaac Newton|Isaac Newton]] (1726). [[wikisource:The_Mathematical_Principles_of_Natural_Philosophy_(1846)/BookIII-General_Scholium|General Scholium]], [[Philosophiæ Naturalis Principia Mathematica#General Scholium|Philosophiæ Naturalis Principia Mathematica]], 2nd edition (1713), ammended 3rd edition (1726) * [[w:Maimonides|Maimonides]], [[s:Guide for the Perplexed|Guide for the Perplexed]] * Euclid, [[s:Elements_of_Geometry_(Euclid)|Elements of Geometry]] * {{cite book|title=The Basic Works of Aristotle|author=Aristotle|date=1941|publisher=Random House|editor=Richard McKeon|editor-link=w:Richard McKeon|location=New York|author-link=s:Author:Aristotle}} * [[w:Koheleth|Koheleth]], Son of David, King of Jerusalem, [[wikisource:Ecclesiastes (Bible)|Ecclesiastes]] ==Course Curriculums in Progress and Reading Lists == * [[User:Jaredscribe/Weekly Learning Schedule for Natural Philosophy]], Science, and Mathematics * {{Note2|text=[[History of Topics in Special Relativity/Lorentz transformation (introduction)]] - an example of a good wikiversity course that evolved from the long version of wikipedia article that was redacted for brevity. This is how the two projects differentiate from and also support each other. Thanks to [[User:D.H.]]}} {{expand}} and continue == Critical Theory == == History of Human Error == * [[User:Jaredscribe/The Solution to Porphyry's problem of universals in a revised Isagoge to Aristotle's Categories]] * [[User:Jaredscribe/The Magical Polytheistic Fantasy of CS Lewis|User:Jaredscribe/The Reality Check to CS Lewis's Magical Polytheistic Fantasy]] {{expand}} ==Ontology and Metaphysics on Wikidata== Planning to model topics in natural philosophy, analytics, science, and math, with the collected works of [[wikisource:Aristotle|Aristotle]] and his commentators and critics, correlated to wikiquotes drawn from wikisource. Notes are at [[d:User:Jaredscribe]], where I've also sketched out a future presentation on the metaphysics of ontology. (However unfortunately, matters of diplomacy, war, and current events may be preoccupations in the near term future.) == Student and Adjunct Faculty Union== Announcing the formation of a local [[User:Jaredscribe/Teachers unions|Substitute Teachers and High School Students and Adjunct Faculty Union]] and inviting students to go on strike for learn-ins, study-ins, and teach-ins at the school and public libraries, on wikiprojects, and on social and traditional media, for [[User:Jaredscribe/Armistice of WWI Remembrance and Veterans Day|Armistice of WWI Remembrance]] this and every future 11th November (Veterans Day). == Notes for Someday/Maybe == *[[User:Jaredscribe/Heculaneum papyri]] [[Palestinian campus occupations of 2024]] [[Foreign policy from Obama to Trump]] [[Are axioms definitions in disguise?#Con|Are axioms definitions in disguise? Con]] [[Does Israel commit genocide in Israel–Hamas war?|Does Israel commit genocide in Israel–Hamas war? Have Hamas, Palestinian Islamic Jihad, and their allies attempted genocide of the Jewish_people?]] [[Should Ukraine surrender to Russia in 2022?#Russia should surrender and recognize Ukrainian independence|Should Ukraine surrender to Russia in 2022? Should Russia surrender and recognize Ukrainian independence]]? == Scholarly Ethics and Wiki Politics== [[w:he:משתמש:Jaredscribe/דרך_ארץ_ויקי#וק:שבע_דברים_בויקיגולם_ושבע_בויקיחכם]] [[:meta:User:Jaredscribe/UCoC]] {{Template:Scholarly_ethics}} {{Template:Free culture}} {{using Wikiversity}} gysnb6bzks9h6ggw1p5mj6bvw4167sc User:Jaredscribe/Russia 2 295999 2684011 2625813 2024-11-11T22:51:29Z Jaredscribe 2906761 /* Welcome Competent Contributors */ 2684011 wikitext text/x-wiki ''Migrating from [[w:en:User:Jaredscribe/Russia]]. TODO convert wikilinks'' [[Boris Savinkov|Бори́с Ви́кторович Са́винков]] writes 1921, ''"The Russian people do not want Lenin, Trotsky and Dzerzhinsky, not merely because the Bolsheviks mobilize them, shoot them, take their grain and are ruining Russia. The Russian people do not want them for the simple reason that .... nobody elected them."''{{sfn|Volkogonov|1994|p=72}} [[Dmitry Volkogonov|Дми́трий Анто́нович Волкого́нов]] writes "It never occured to us", he wrote, "that the [[October revolution|'breakthrough' of October 1917]] might be a counter-revolution, when compared to the [[February Revolution|events of February of that year]]."{{sfn|Volkogonov|1994|p=478}} * [[Draft:De-Leninization]] * {{slink|Talk:Russian_Revolution#Major Ommissions and Leninist-Bolshevik POV}} ** {{slink|Wikipedia_talk:WikiProject_Russia#Neutral_rewrite_of_Russian_Revolution_lede_is_needed}} * {{slink|Talk:Enlargement_of_NATO#WP%3AWEIGHT_%22What_Gorbachev_heard%22%2C_and_what_did_the_Allied_negotiators_actually_say%3F}} == Post-Soviet Analysis== === On Ukraine and Crimea === [[Volodymyr Zelenskyy|Володимир Олександрович Зеленський]] lead actor [[Kvartal TV]] produced [[Servant_of_the_People_(TV_series)]], formed [[Servant_of_the_People_(political_party)]], 2019 elected Ukrainian president. [[Richard Lourie]] states that "the [[Orange Revolution|2004 Orange Revolution]] in [[Ukraine]] might have been seen by Putin as only an internal question if [[NATO]] had not at the same time conferred membership on seven former [[Eastern Bloc]] countries, three of them former Soviet republics, moving the alliance right up to Russia's western border."{{Sfn|Lourie|2017|p=224}} He predicts (2017) that Russia "will be satisfied with some low level of continued turmoil in [[eastern Ukraine]], because NATO will not offer membership to countries with frozen conflicts and border disputes."{{Sfn|Lourie|2017|p=148}} See also: [[War in Donbas]], part of the broader [[Russo-Ukrainian War]], in the aftermath of the [[2014 Ukrainian revolution]] and the [[Euromaidan]] movement. He suspects that Putin's other goal is to create a land bridge to [[Crimea]].{{Sfn|Lourie|2017|p=148}}{{Expand section|date=February 2022}} === On Putin and post-Communist Russia === Lourie's assesses that despite his status as the richest man in Russia and all Europe, the "failure at the core of Putin's reign" consists in that "he was given a unique opportunity by history, a period of wealth and peace that he could have used to liberate his country from its dependence on oil and on authoritarian rule. He squandered that opportunity to unlease the source of Russia's true greatness—the still untapped skills and spirit of its people."{{Sfn|Lourie|2017|p=223}} And in conclusion predicts that:<blockquote> And because it did not involve the people enough, the House of Putin will, like the House of the Tsars and the House of the Communists, sooner or later come crashing down. When and with how much suffering is anyone's guess. {{sfn|Lourie|2017|p=224}}</blockquote>{{Expand section|date=February 2022}} ===The collapse of the USSR === During the [[Die Wende|collapse of the communist East German government]], Putin was working with the [[Stasi]] in Dresden. When they attacked the Ministry of Security, and then the Soviet KGB headquarters, he recounts that "we were forced to demonstrate our readiness to defend our building." {{sfn|Lourie|2017|p=48}} He went out with bodyguards and addressed the mob, but when they became aggressive again, he called for military backup and was told "We cannot do anything without orders from Moscow. And Moscow is silent." In response to this incident, Putin said, "That business of 'Moscow is Silent'-I got the feeling then that the country no longer existed. That it had disappeared … and had a terminal disease without a cure-a paralysis of power."{{sfn|Lourie|2017|p=48}} ==== Period of ([[Glasnost]] todo), ([[Perestroika]] todo), and the ([[Dissolution of the USSR]] todo ==== == Reunification of Germany and NATO's Eastward Expansion== [Richard Lourie]]'s positively reviews [[Tony Wood (historian)]]'s book, describing "Wood’s contrarian spirit extends to the West as well. He apportions it a share of the blame for the current tensions with Russia. {{blockquote|In 1990, [[Gorbachev|Gorbachev (todo)]] had been assured by [[James Baker|James Baker (todo)]] and [[George H. W. Bush|George H.W. Bush (todo)]] that if the two [[Reunification of Germany|Germanies were allowed to reunite (todo)]], [[NATO|NATO (todo)]] would not move “one inch east.” To Gorbachev’s enduring chagrin, the major [[Warsaw Pact|Warsaw Pact (todo)]] countries — Poland, Hungary, and the Czech Republic —were inducted into NATO nine years later, with [[Expansion of NATO|seven others, including three former Soviet republics]], following in 2004. [[George Kennan|George Kennan (todo)]], former US ambassador to the USSR and author of the [[Containment|containment theory (todo)]], was against the expansion. It would inevitably be taken as a hostile gesture, which would only increase nationalism and militarism in Russia. But the West was mighty, rich, and triumphant, and there was nothing Russia could do.|From Review of [[Tony Wood (historian)]]'s book (new article). {{cite news|url=https://lareviewofbooks.org/article/out-of-the-picture-on-tony-woods-russia-without-putin-money-power-and-the-myths-of-the-new-cold-war/|title=Out of the Picture: On Tony Wood’s "Russia Without Putin: Money, Power and the Myths of the New Cold War"|publisher=LA Review of Books|author-last=Lourie|author-first=Richard|author-link=Richard Lourie|date=29 January 2019}}}} <blockquote>For that reason, it became imperative for Moscow not to “lose” Ukraine to the EU and NATO. It would seem that the [[Annexation of Crimea by the Russian Federation|annexation of Crimea]], the proxy war in [[East Ukraine]], and the recent naval clashes in the Black Sea would indicate that Russia has now achieved its principal objective — creating enough conflict in Ukraine to disqualify it for membership in NATO, which does not accept countries with frozen conflicts or ongoing hostilities.</blockquote> "Wood sets himself the task of describing today’s Russia not as the result of one man’s will and vision but of the greater forces that preceded his assumption of office, function independently of him in the present, and will outlast him. This a work of background, context, and systemics, not history as biography."{{sfn|Lourie|2019}} ==Revolution and Civil War 1855-1923== [[1905 Revolution|Революция 1905]] года, или Первая русская революция [[February Revolution|Февральская революция]] 1917 года и [[October Revolution|Октябрьская революция]] 1917 года [[Red Terror|Красный террор]] == Lenin and [[Leninism]]== [[Lenin|Влади́мир Ильи́ч Ле́нин]] {{Empty section|date=February 2022}} {{cquote|In his quest for power, he promised people anything and everything. He offered simple solutions to complex problems. He lied unashamedly. He identified a scapegoat he could later label 'enemies of the people'. He justified himself on the basis that winning meant everything: the ends justified the means. ... Lenin was the godfather of wht commentators a century after his time call 'post-truth politics'.|author=Victor Sebestyen|title=Lenin: The Man, The Dictator, and the Master of Terror{{sfn|Sebestyen|2017|loc=Introduction, p. 3}}}} {{bquote|He built a system based on the idea that political terror against opponents was justified for a greater end. It was perfected by Stalin, but the ideas were Leninś. He had not always been a bad man, but he did terrible things. [[Angelica Balabanova]], one of his old comrades who admired him for many years but grew to fear and loathe him, said perceptively that 'Lenin's tragedy was, in [[Goethe]]'s phrase, he desired the good ... but created evil'.|author=Victor Sebestyen|title=Lenin: The Man, The Dictator, and the Master of Terror{{sfn|Sebestyen|2017|loc=Introduction, p. 3}}}} ===Dictatorship and Soviet Democracy=== {{cquote|Capitalism cannot be defeated and eradictated without the ruthless suppression of the resistence of the exploiters, who cannot at once be deprived of their wealth, of their superiority of organization and knowledge, and consequently for a fairly long period will inevitably try to overthrow the hateful rule of the poor; secondly, a great revolution, and a socialist revolution in particular, ev if there were no external war, is inconceivable without internal war, i.e. civil war, which is even more destructive than external war, and implies thousands and millions of cases of wavering and desertion from one side to another, implies a state of extreme indefiniteness, lack of equilibrium and chaos...|source=Lenin, Izbrannyie Proizvedeniya, Selected Works, Russian, Vol. 2, pp.277-78}} == Trotsky and [[Trotskyism]] == [[Leon Trotsky|Лев Дави́дович Тро́цкий]] == Welcome Competent Contributors == This original research project copied from [[w:User:Jaredscribe/Russia]] is intended to provide collection of analyses and quotes from [[WP:Reliable Sources]] that can be cited to fill historical gaps and correct biases on various wikipedia articles in the content field. This is a "choose your own adventure" course on the intellectual history of the ideologies that have shaped Russia and its sphere of influence, not a comprehensive history. It is intended to support self-directed study on topics of interest. could support improvement of linked articles on our sister project wikipedia, and might even bring peace in Euro-Asia. Historiographic perspectives outside the cold war binary of American imperialism/NATO expansionism vs. Marxist-Leninist anti-capitalism/Russian imperialism. I created the author pages for Lourie and Carr in the [[#Bibligraphy]] below, and have edited on all the others: but they all still need work. If you can acquire these books and summarize them, or quote them, on the author pages, please do. If your contributions are rejected, please add them on this UserWikiProject page, and we will refine and improve. You may contribute; includying copy-editing and adding wikilinks, but please don't delete or "edit" in substantial changes until after you've demonstrated competence at contributing. Unless you have demonstrated subject matter competence and good faith in your editing history; I will assume neither on this, because its my user subpage, and it is contentious subject matter where people in which major governments may be highly motivated. Therefore newbies and Anonymous IPs are always welcome to contribute on this page, but not to "edit" or "manage" other editors, nor to give decisive opinions in debate. ==Notes== {{reflist}} ==Bibliography== * {{cite book |title=Lenin: A New Biography |last=Volkogonov |first=Dmitri |author-link=Dmitri Volkogonov |year=1994 |translator-last=Shukman |translator-first=Harold |translator-link=Harold Shukman |publisher=HarperCollins |location=London |isbn=978-0-00-255123-6}} * {{cite book|author-first=Barnes|author-last=Carr|author-link=Barnes Carr|title=The Lenin Plot: The Unknown Story of America's War Against Russia|publisher=Pegasus Books|date=2020|isbn=978-1-64313-317-1}} * {{cite book|title=Trotsky: Fate of a Revolutionary|publisher=Stein & Day|location=New York|date=1982|ISBN=0-8128-2774-0|author-last=Wistrich|author-first=Robert S.|author-link=Robert Wistrich}} * {{cite book|author-link=Richard Lourie|author-last=Lourie|author-first=Richard|title=[[Vladimir Putin|Putin]]: His Downfall and Russia's Coming Crash|date=2017|publisher=St. Martin's Press|ISBN=978-0-312-53808-8}} * {{cite book|title=Russia Without Putin: Money, Power and the Myths of the New Cold War|date=2018|author-link=Tony Wood (historian)|author-last=Wood|author-first=Tony|ISBN=978-1788731249}} * {{cite book |title=Lenin: A Biography |edition=revised |last=Shub |first=David | author-link=David Shub |publisher=Pelican |location=London |year=1966}} * {{cite book |title=Lenin: A Biography |edition=revised |last=Shub |first=David | author-link=David Shub |publisher=Mentor Books |location=New York |year=1948|contribution=Appendix: [[David_Shub#Essentials_of_Leninism|Essentials of Leninism]]|contributor-last=Lenin|contributor-first=Vladimir|contributor-link=Vladimir Lenin}} * {{cite book|author-last=Sebestyen|author-first=Victor|author-link=Victor Sebestyen|title=Lenin: The Man, the Dictator, and the Master of Terror.|publisher=Pantheon Books|date=2017|ISBN=9781101871638}} * {{Cite news|url=https://harpers.org/archive/2023/06/why-are-we-in-ukraine/|title=Why Are We in Ukraine?: On the dangers of American hubris|last=Schwarz|first=Benjamin|work=Harper's Magazine|access-date=2023-06-23|last2=Layne|first2=Christopher|volume=June 2023|language=en|issn=0017-789X}} 8psednhh289f5yyiyo38t8shr46jj1y 2684013 2684011 2024-11-11T23:12:13Z Jaredscribe 2906761 2684013 wikitext text/x-wiki ''Migrating from [[w:en:User:Jaredscribe/Russia]]. TODO convert wikilinks'' [[Boris Savinkov|Бори́с Ви́кторович Са́винков]] writes 1921, ''"The Russian people do not want Lenin, Trotsky and Dzerzhinsky, not merely because the Bolsheviks mobilize them, shoot them, take their grain and are ruining Russia. The Russian people do not want them for the simple reason that .... nobody elected them."''{{sfn|Volkogonov|1994|p=72}} [[Dmitry Volkogonov|Дми́трий Анто́нович Волкого́нов]] writes "It never occured to us", he wrote, "that the [[October revolution|'breakthrough' of October 1917]] might be a counter-revolution, when compared to the [[February Revolution|events of February of that year]]."{{sfn|Volkogonov|1994|p=478}} Welcome to the "choose your own adventure" course through the ideological history of Russia and its sphere of influence. Self-direct your study on topics of interest, improve of linked articles on our sister project wikipedia, and try to work for a historically just peace in Euro-Asia. We aim for a historiographic perspective that is outside the cold war binary of progressive neo-liberalism vs. Marxist-Leninist anti-capitalist totalitarianism, as these have manifest through American imperialism and NATO expansionism vs. USSR and Russian imperialism. For wikidebate, see [[Should Ukraine surrender to Russia in 2022?#Russia should surrender and recognize Ukrainian independence|Should Ukraine surrender to Russia in 2022? Should Russia surrender and recognize Ukrainian independence]]? * [[Draft:De-Leninization]] * {{slink|Talk:Russian_Revolution#Major Ommissions and Leninist-Bolshevik POV}} ** {{slink|Wikipedia_talk:WikiProject_Russia#Neutral_rewrite_of_Russian_Revolution_lede_is_needed}} * {{slink|Talk:Enlargement_of_NATO#WP%3AWEIGHT_%22What_Gorbachev_heard%22%2C_and_what_did_the_Allied_negotiators_actually_say%3F}} == Post-Soviet Analysis== === On Ukraine and Crimea === [[Volodymyr Zelenskyy|Володимир Олександрович Зеленський]] lead actor [[Kvartal TV]] produced [[Servant_of_the_People_(TV_series)]], formed [[Servant_of_the_People_(political_party)]], 2019 elected Ukrainian president. [[Richard Lourie]] states that "the [[Orange Revolution|2004 Orange Revolution]] in [[Ukraine]] might have been seen by Putin as only an internal question if [[NATO]] had not at the same time conferred membership on seven former [[Eastern Bloc]] countries, three of them former Soviet republics, moving the alliance right up to Russia's western border."{{Sfn|Lourie|2017|p=224}} He predicts (2017) that Russia "will be satisfied with some low level of continued turmoil in [[eastern Ukraine]], because NATO will not offer membership to countries with frozen conflicts and border disputes."{{Sfn|Lourie|2017|p=148}} See also: [[War in Donbas]], part of the broader [[Russo-Ukrainian War]], in the aftermath of the [[2014 Ukrainian revolution]] and the [[Euromaidan]] movement. He suspects that Putin's other goal is to create a land bridge to [[Crimea]].{{Sfn|Lourie|2017|p=148}}{{Expand section|date=February 2022}} === On Putin and post-Communist Russia === Lourie's assesses that despite his status as the richest man in Russia and all Europe, the "failure at the core of Putin's reign" consists in that "he was given a unique opportunity by history, a period of wealth and peace that he could have used to liberate his country from its dependence on oil and on authoritarian rule. He squandered that opportunity to unlease the source of Russia's true greatness—the still untapped skills and spirit of its people."{{Sfn|Lourie|2017|p=223}} And in conclusion predicts that:<blockquote> And because it did not involve the people enough, the House of Putin will, like the House of the Tsars and the House of the Communists, sooner or later come crashing down. When and with how much suffering is anyone's guess. {{sfn|Lourie|2017|p=224}}</blockquote>{{Expand section|date=February 2022}} ===The collapse of the USSR === During the [[Die Wende|collapse of the communist East German government]], Putin was working with the [[Stasi]] in Dresden. When they attacked the Ministry of Security, and then the Soviet KGB headquarters, he recounts that "we were forced to demonstrate our readiness to defend our building." {{sfn|Lourie|2017|p=48}} He went out with bodyguards and addressed the mob, but when they became aggressive again, he called for military backup and was told "We cannot do anything without orders from Moscow. And Moscow is silent." In response to this incident, Putin said, "That business of 'Moscow is Silent'-I got the feeling then that the country no longer existed. That it had disappeared … and had a terminal disease without a cure-a paralysis of power."{{sfn|Lourie|2017|p=48}} ==== Period of ([[Glasnost]] todo), ([[Perestroika]] todo), and the ([[Dissolution of the USSR]] todo ==== == Reunification of Germany and NATO's Eastward Expansion== [Richard Lourie]]'s positively reviews [[Tony Wood (historian)]]'s book, describing "Wood’s contrarian spirit extends to the West as well. He apportions it a share of the blame for the current tensions with Russia. {{blockquote|In 1990, [[Gorbachev|Gorbachev (todo)]] had been assured by [[James Baker|James Baker (todo)]] and [[George H. W. Bush|George H.W. Bush (todo)]] that if the two [[Reunification of Germany|Germanies were allowed to reunite (todo)]], [[NATO|NATO (todo)]] would not move “one inch east.” To Gorbachev’s enduring chagrin, the major [[Warsaw Pact|Warsaw Pact (todo)]] countries — Poland, Hungary, and the Czech Republic —were inducted into NATO nine years later, with [[Expansion of NATO|seven others, including three former Soviet republics]], following in 2004. [[George Kennan|George Kennan (todo)]], former US ambassador to the USSR and author of the [[Containment|containment theory (todo)]], was against the expansion. It would inevitably be taken as a hostile gesture, which would only increase nationalism and militarism in Russia. But the West was mighty, rich, and triumphant, and there was nothing Russia could do.|From Review of [[Tony Wood (historian)]]'s book (new article). {{cite news|url=https://lareviewofbooks.org/article/out-of-the-picture-on-tony-woods-russia-without-putin-money-power-and-the-myths-of-the-new-cold-war/|title=Out of the Picture: On Tony Wood’s "Russia Without Putin: Money, Power and the Myths of the New Cold War"|publisher=LA Review of Books|author-last=Lourie|author-first=Richard|author-link=Richard Lourie|date=29 January 2019}}}} <blockquote>For that reason, it became imperative for Moscow not to “lose” Ukraine to the EU and NATO. It would seem that the [[Annexation of Crimea by the Russian Federation|annexation of Crimea]], the proxy war in [[East Ukraine]], and the recent naval clashes in the Black Sea would indicate that Russia has now achieved its principal objective — creating enough conflict in Ukraine to disqualify it for membership in NATO, which does not accept countries with frozen conflicts or ongoing hostilities.</blockquote> "Wood sets himself the task of describing today’s Russia not as the result of one man’s will and vision but of the greater forces that preceded his assumption of office, function independently of him in the present, and will outlast him. This a work of background, context, and systemics, not history as biography."{{sfn|Lourie|2019}} ==Revolution and Civil War 1855-1923== [[1905 Revolution|Революция 1905]] года, или Первая русская революция [[February Revolution|Февральская революция]] 1917 года и [[October Revolution|Октябрьская революция]] 1917 года [[Red Terror|Красный террор]] == Lenin and [[Leninism]]== [[Lenin|Влади́мир Ильи́ч Ле́нин]] {{Empty section|date=February 2022}} {{cquote|In his quest for power, he promised people anything and everything. He offered simple solutions to complex problems. He lied unashamedly. He identified a scapegoat he could later label 'enemies of the people'. He justified himself on the basis that winning meant everything: the ends justified the means. ... Lenin was the godfather of wht commentators a century after his time call 'post-truth politics'.|author=Victor Sebestyen|title=Lenin: The Man, The Dictator, and the Master of Terror{{sfn|Sebestyen|2017|loc=Introduction, p. 3}}}} {{bquote|He built a system based on the idea that political terror against opponents was justified for a greater end. It was perfected by Stalin, but the ideas were Leninś. He had not always been a bad man, but he did terrible things. [[Angelica Balabanova]], one of his old comrades who admired him for many years but grew to fear and loathe him, said perceptively that 'Lenin's tragedy was, in [[Goethe]]'s phrase, he desired the good ... but created evil'.|author=Victor Sebestyen|title=Lenin: The Man, The Dictator, and the Master of Terror{{sfn|Sebestyen|2017|loc=Introduction, p. 3}}}} ===Dictatorship and Soviet Democracy=== {{cquote|Capitalism cannot be defeated and eradictated without the ruthless suppression of the resistence of the exploiters, who cannot at once be deprived of their wealth, of their superiority of organization and knowledge, and consequently for a fairly long period will inevitably try to overthrow the hateful rule of the poor; secondly, a great revolution, and a socialist revolution in particular, ev if there were no external war, is inconceivable without internal war, i.e. civil war, which is even more destructive than external war, and implies thousands and millions of cases of wavering and desertion from one side to another, implies a state of extreme indefiniteness, lack of equilibrium and chaos...|source=Lenin, Izbrannyie Proizvedeniya, Selected Works, Russian, Vol. 2, pp.277-78}} == Trotsky and [[Trotskyism]] == [[Leon Trotsky|Лев Дави́дович Тро́цкий]] == Welcome Competent Contributors == This original research project copied from [[w:User:Jaredscribe/Russia]] is intended to provide collection of analyses and quotes from [[WP:Reliable Sources]] that can be cited to fill historical gaps and correct biases on various wikipedia articles in the content field. This is a "choose your own adventure" course on the intellectual history of the ideologies that have shaped Russia and its sphere of influence, not a comprehensive history. It is intended to support self-directed study on topics of interest. could support improvement of linked articles on our sister project wikipedia, and might even bring peace in Euro-Asia. Historiographic perspectives outside the cold war binary of American imperialism/NATO expansionism vs. Marxist-Leninist anti-capitalism/Russian imperialism. I created the author pages for Lourie and Carr in the [[#Bibligraphy]] below, and have edited on all the others: but they all still need work. If you can acquire these books and summarize them, or quote them, on the author pages, please do. If your contributions are rejected, please add them on this UserWikiProject page, and we will refine and improve. You may contribute; includying copy-editing and adding wikilinks, but please don't delete or "edit" in substantial changes until after you've demonstrated competence at contributing. Unless you have demonstrated subject matter competence and good faith in your editing history; I will assume neither on this, because its my user subpage, and it is contentious subject matter where people in which major governments may be highly motivated. Therefore newbies and Anonymous IPs are always welcome to contribute on this page, but not to "edit" or "manage" other editors, nor to give decisive opinions in debate. ==Notes== {{reflist}} ==Bibliography== * {{cite book |title=Lenin: A New Biography |last=Volkogonov |first=Dmitri |author-link=Dmitri Volkogonov |year=1994 |translator-last=Shukman |translator-first=Harold |translator-link=Harold Shukman |publisher=HarperCollins |location=London |isbn=978-0-00-255123-6}} * {{cite book|author-first=Barnes|author-last=Carr|author-link=Barnes Carr|title=The Lenin Plot: The Unknown Story of America's War Against Russia|publisher=Pegasus Books|date=2020|isbn=978-1-64313-317-1}} * {{cite book|title=Trotsky: Fate of a Revolutionary|publisher=Stein & Day|location=New York|date=1982|ISBN=0-8128-2774-0|author-last=Wistrich|author-first=Robert S.|author-link=Robert Wistrich}} * {{cite book|author-link=Richard Lourie|author-last=Lourie|author-first=Richard|title=[[Vladimir Putin|Putin]]: His Downfall and Russia's Coming Crash|date=2017|publisher=St. Martin's Press|ISBN=978-0-312-53808-8}} * {{cite book|title=Russia Without Putin: Money, Power and the Myths of the New Cold War|date=2018|author-link=Tony Wood (historian)|author-last=Wood|author-first=Tony|ISBN=978-1788731249}} * {{cite book |title=Lenin: A Biography |edition=revised |last=Shub |first=David | author-link=David Shub |publisher=Pelican |location=London |year=1966}} * {{cite book |title=Lenin: A Biography |edition=revised |last=Shub |first=David | author-link=David Shub |publisher=Mentor Books |location=New York |year=1948|contribution=Appendix: [[David_Shub#Essentials_of_Leninism|Essentials of Leninism]]|contributor-last=Lenin|contributor-first=Vladimir|contributor-link=Vladimir Lenin}} * {{cite book|author-last=Sebestyen|author-first=Victor|author-link=Victor Sebestyen|title=Lenin: The Man, the Dictator, and the Master of Terror.|publisher=Pantheon Books|date=2017|ISBN=9781101871638}} * {{Cite news|url=https://harpers.org/archive/2023/06/why-are-we-in-ukraine/|title=Why Are We in Ukraine?: On the dangers of American hubris|last=Schwarz|first=Benjamin|work=Harper's Magazine|access-date=2023-06-23|last2=Layne|first2=Christopher|volume=June 2023|language=en|issn=0017-789X}} 6mkalesaq9amavw8qyngp6jdutol7ea Surreal number 0 299370 2684014 2680017 2024-11-11T23:18:11Z Guy vandegrift 813252 /* Starting from zero */ 2684014 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\overbrace{\color{Red}\overline{1}}{\{0|\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 9135lxtn8qov3wo6735rioosjzxvtwk 2684015 2684014 2024-11-11T23:19:38Z Guy vandegrift 813252 /* With sets */ 2684015 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\overbrace{\color{Red}\overline{1}}^{\{0|\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] r5vfkzxjfk77h3qjtl2pr2w42pvvo2m 2684016 2684015 2024-11-11T23:20:34Z Guy vandegrift 813252 /* With sets */ 2684016 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\overbrace{\overline{1}}^{\{0|\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] kj1ikacl8av8bvki5nccie8hr01u33e 2684017 2684016 2024-11-11T23:21:58Z Guy vandegrift 813252 /* With sets */ 2684017 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\overbrace{1}^{\{0|\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] iy2tb1dit2kgwl0tihaxrckl2yxvjmx 2684018 2684017 2024-11-11T23:23:20Z Guy vandegrift 813252 /* With sets */ 2684018 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\underbrace{\overline 1}_{\{0|\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] nn67n3qstz8955x3m8p74sc9r79cpbz 2684019 2684018 2024-11-11T23:23:51Z Guy vandegrift 813252 /* With sets */ 2684019 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\underbrace{\overline 1}_{\{0|\,\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] lhzu630aw8a5h78p46gke09jlsooupa 2684020 2684019 2024-11-11T23:25:01Z Guy vandegrift 813252 /* With sets */ 2684020 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}{\overline 1}_{\{0|\,\}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] s6exekwafjsywjtww6pypny60tw0nqb 2684021 2684020 2024-11-11T23:27:42Z Guy vandegrift 813252 /* With sets */ 2684021 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\begin align{\overline 1}&{\{0|\,\}}\end align&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 59c0n7rfdm5cimnddy462vd6zkkd0zq 2684022 2684021 2024-11-11T23:28:41Z Guy vandegrift 813252 /* With sets */ 2684022 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\begin{align{{\overline 1}&{\{0|\,\}}\end{align}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] l0mtcteyal1pii373n6jdltib5j5aaf 2684023 2684022 2024-11-11T23:29:23Z Guy vandegrift 813252 /* With sets */ 2684023 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&\color{Red}\begin{align}{{\overline 1}&{\{0|\,\}}\end{align}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] fuzyvtb1hxirfon6fc6nn2jb9s33zbb 2684024 2684023 2024-11-11T23:32:04Z Guy vandegrift 813252 /* Starting from zero */ 2684024 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] mwx8wlx3w66xv1q8idckg3c97utuaqt 2684025 2684024 2024-11-11T23:34:22Z Guy vandegrift 813252 /* With sets */ 2684025 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align} a\\[0.6ex] b \end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 9deo7273njjhn6drlj42neewqfqht3k 2684026 2684025 2024-11-11T23:34:55Z Guy vandegrift 813252 /* With sets */ 2684026 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align} a\\[0.6ex] b \end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 7g7uumdozwwth7tsn2tf4huzjpjflml 2684027 2684026 2024-11-11T23:35:15Z Guy vandegrift 813252 /* With sets */ 2684027 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align} a\\[0.1ex] b \end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ie3boz41gbq2dqh7iqllxcka2nxa929 2684028 2684027 2024-11-11T23:36:09Z Guy vandegrift 813252 /* With sets */ 2684028 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[0.1ex]b\end{align}</math> <math>\begin{align}a\\b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] kxh6nwpqlwm07lrasak56udbvysovhu 2684029 2684028 2024-11-11T23:36:25Z Guy vandegrift 813252 /* With sets */ 2684029 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-0.1ex]b\end{align}</math> <math>\begin{align}a\\b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] o7likkl20d4syhtppi2w6qkzose1yt8 2684030 2684029 2024-11-11T23:36:57Z Guy vandegrift 813252 /* With sets */ 2684030 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-9ex]b\end{align}</math> <math>\begin{align}a\\b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] q94th8ltj0ef4ckzx9obr3tsf0il0du 2684031 2684030 2024-11-11T23:38:14Z Guy vandegrift 813252 /* With sets */ 2684031 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-1 ex]b\end{align}</math> <math>\begin{align}a\\b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] q7u7h8iborirtbnbayyxk8ij8bhgedx 2684032 2684031 2024-11-11T23:42:36Z Guy vandegrift 813252 /* With sets */ 2684032 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-.5 ex]b\end{align}</math> <math>\begin{align}a\\b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 9vywywupqp6pnviv196hzn5ti6jj1aa 2684033 2684032 2024-11-11T23:43:14Z Guy vandegrift 813252 /* With sets */ 2684033 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-.5 ex]b\end{align}</math> <math>\begin{align}a\\[-1 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 7tgnj7u2grbxz0ndufgrldki3ja5mp7 2684035 2684033 2024-11-11T23:43:48Z Guy vandegrift 813252 /* With sets */ 2684035 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-.5 ex]b\end{align}</math> <math>\begin{align}a\\[-2 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] g0obaecfkzd2allww5pxl926z1m9gr0 2684036 2684035 2024-11-11T23:44:00Z Guy vandegrift 813252 /* With sets */ 2684036 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\begin{align}a\\[-.5 ex]b\end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] asqc2rmsf8sqvp1kg96xmfljrqjtlgf 2684040 2684036 2024-11-11T23:47:48Z Guy vandegrift 813252 /* With sets */ 2684040 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== {\color{Red}\overline{1}} <math>\begin{align}{\color{Red}\overline{1}}\\[-.9 ex]b\end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] epe0fyw14zi1odq8hckjir096q53o9y 2684042 2684040 2024-11-11T23:49:58Z Guy vandegrift 813252 /* With sets */ 2684042 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== {\color{Red}\overline{1}} <math>\begin{align}{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qcruun61dclwul5y9vf3o61d58spqdz 2684045 2684042 2024-11-11T23:56:15Z Guy vandegrift 813252 /* With sets */ 2684045 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== {\color{Red}\overline{1}} <math>{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 2kmeas0tbdych22pydvwc0jzzvjes5o 2684046 2684045 2024-11-11T23:57:38Z Guy vandegrift 813252 /* With sets */ 2684046 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== \overset{a}{b} <math>{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qt2n4uv9x0m1lwgbv44xzgcq2xf2428 2684047 2684046 2024-11-11T23:57:58Z Guy vandegrift 813252 /* With sets */ 2684047 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\overset{a}{b}</math> <math>{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 3n78ipswez7owjw83lf2r4yo8t82aga 2684048 2684047 2024-11-11T23:58:16Z Guy vandegrift 813252 /* With sets */ 2684048 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>\overset{a}\underset{b}</math> <math>{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 1oxit9fphzlhsmhx1ggu4t9mig3c146 2684053 2684048 2024-11-12T00:08:47Z Guy vandegrift 813252 /* With sets */ 2684053 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>{\color{Red} \begin{matrix} \overline{1} \\ z \end{matrix}}</math> <math>{\color{Red} \overline{1}} \\[-.9 ex] \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 1ee4m4q4pwcxsagarbjunv9zkeph4df 2684054 2684053 2024-11-12T00:09:20Z Guy vandegrift 813252 /* With sets */ 2684054 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] z \end{matrix}}</math> <math>{\color{Red} \overline{1}} \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 5ftpl9qt4d9oghcaqk9kluk4qfhn70u 2684055 2684054 2024-11-12T00:10:11Z Guy vandegrift 813252 /* With sets */ 2684055 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] {\ L | R \} \end{matrix}}</math> <math>{\color{Red} \overline{1}} \{L|R\} \end{align}</math> <math>\begin{align}a\\[-.9 ex]b\end{align}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 4hs5p9bp2b03sjbfbx11qih8abvx5ql 2684057 2684055 2024-11-12T00:11:44Z Guy vandegrift 813252 /* With sets */ 2684057 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>{\color{Red} \begin{matrix} a \\[-.9 ex] b \end{matrix}}</math> <math>{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] {\ L | R \} \end{matrix}}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 8t9g0ehu5z1t9ppfzsjs2kkqll8v9bs 2684058 2684057 2024-11-12T00:12:29Z Guy vandegrift 813252 /* With sets */ 2684058 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math>{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] b \end{matrix}}</math> <math>{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ L | R \} \end{matrix}}</math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] h7bp1httfezwanw0t8h15qfekias2hu 2684061 2684058 2024-11-12T00:16:50Z Guy vandegrift 813252 /* With sets */ 2684061 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{0} \\[-.9 ex] \{ \; | \; \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] c90cnw1cqk39b68trweobtfw4bp5t0m 2684062 2684061 2024-11-12T00:18:33Z Guy vandegrift 813252 /* With sets */ 2684062 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] f28jaa3w9oovyqrd6j4rwzecgn957te 2684063 2684062 2024-11-12T00:26:14Z Guy vandegrift 813252 /* With sets */ 2684063 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] nvsr0dxosmm1coftdhg6z0j0cyx1lrm 2684065 2684063 2024-11-12T00:27:01Z Guy vandegrift 813252 /* With sets */ 2684065 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 21ll67p6f6la0lm4uewjo7p9mnx47q6 2684066 2684065 2024-11-12T00:29:37Z Guy vandegrift 813252 /* With sets */ 2684066 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red} \begin{matrix} \overline{3} \\[-.9 ex] \{ \; | 2 \} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red} \begin{matrix} \overline{4} \\[-.9 ex] \{ \; | 3 \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] afyfu6c97phuhftrslbb3t6sm56sfie 2684067 2684066 2024-11-12T00:31:28Z Guy vandegrift 813252 /* With sets */ 2684067 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} \overline{1} \\[-.9 ex] \{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | \overline{1} \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red} \begin{matrix} \overline{3} \\[-.9 ex] \{ \; | \overline{2} \} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red} \begin{matrix} \overline{4} \\[-.9 ex] \{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] i5czubm96nodhh98bcncjch1eum81yi 2684069 2684067 2024-11-12T00:41:11Z Guy vandegrift 813252 /* With sets */ 2684069 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{2} \\[-.9 ex] \{ \; | 1 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.9 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\begin{matrix}\overline{2} \\[-.9 ex]\{ \; | \overline{1} \} \end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\overline{3}\\[-.9 ex]\{\;|\overline{2}\}\end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\overline{4} \\[-.9 ex]\{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 8pkzfolldz81e1tr12e6ybg0i20v6st 2684070 2684069 2024-11-12T00:43:48Z Guy vandegrift 813252 /* With sets */ 2684070 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{\tfrac 1 2} \\[-.9 ex] \{ 1 | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.9 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\begin{matrix}\overline{2} \\[-.9 ex]\{ \; | \overline{1} \} \end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\overline{3}\\[-.9 ex]\{\;|\overline{2}\}\end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\overline{4} \\[-.9 ex]\{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] offbhcu4igkvsr44r0ugroiyo75rn6e 2684071 2684070 2024-11-12T00:44:52Z Guy vandegrift 813252 /* With sets */ 2684071 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{\tfrac 1 2} \\[-.5 ex] \{ 1 | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.9 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\begin{matrix}\overline{2} \\[-.9 ex]\{ \; | \overline{1} \} \end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\overline{3}\\[-.9 ex]\{\;|\overline{2}\}\end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\overline{4} \\[-.9 ex]\{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 1lwsnd70tb03skp1nvol9wlssvyr8q7 2684072 2684071 2024-11-12T00:46:09Z Guy vandegrift 813252 /* With sets */ 2684072 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{\tfrac 1 2} \\[-.5 ex] \{ 1 | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.5 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\begin{matrix}\overline{2} \\[-.5 ex]\{ \; | \overline{1} \} \end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\overline{3}\\[-.5 ex]\{\;|\overline{2}\}\end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\overline{4} \\[-.5 ex]\{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ke7eqgvqunq3zcld3gmd34mx2jic6xi 2684073 2684072 2024-11-12T00:52:21Z Guy vandegrift 813252 /* With sets */ 2684073 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{\tfrac 1 2} \\[-.5 ex] \{ 1 | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.5 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\overline{2} \\[-.5 ex]\{ \; | \overline{1} \} \end{matrix}} {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2} \end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\overline{3}\\[-.5 ex]\{\;|\overline{2}\}\end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\overline{4} \\[-.5 ex]\{ \; | \overline{3} \} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qqobe2msv2f0h46a9f9ewbxm4711sfn 2684074 2684073 2024-11-12T00:54:21Z Guy vandegrift 813252 /* With sets */ 2684074 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \overline{\tfrac 1 2} \\[-.5 ex] \{ 1 | 0 \} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.5 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] h8vy8etuly5p3evcvxq56h3ol0aa759 2684075 2684074 2024-11-12T01:00:06Z Guy vandegrift 813252 /* With sets */ 2684075 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\overline{1} \\[-.5 ex]\{ \; | 0 \} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] gtsqej9btke8n3xbbpo6e2vqvdk62d2 2684076 2684075 2024-11-12T01:01:28Z Guy vandegrift 813252 /* With sets */ 2684076 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\\overline{1}[-.5 ex] \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ae2m9vlp50d4xodsgdsbggm2383szok 2684077 2684076 2024-11-12T01:02:38Z Guy vandegrift 813252 /* With sets */ 2684077 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \[-.5 ex]\\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] gkseeu51a0vp1w2ylbs1knvpnyq8h1h 2684078 2684077 2024-11-12T01:03:57Z Guy vandegrift 813252 /* With sets */ 2684078 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] eu37tcqw3jq4m53lna4xc5mes1640t5 2684079 2684078 2024-11-12T01:05:23Z Guy vandegrift 813252 /* With sets */ 2684079 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red}\overline{\tfrac 1 2}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] s2ytkknpzs1dbsk81y668x74ql1436b 2684080 2684079 2024-11-12T01:09:44Z Guy vandegrift 813252 /* With sets */ 2684080 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 8dlrlhg8krhmyce1u8ws29h3t0z8vnk 2684081 2684080 2024-11-12T01:32:07Z Guy vandegrift 813252 /* With sets */ 2684081 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 2 | 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ 2 | 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] dxn0p2n1x7jb72as5ledobi4inniryw 2684084 2684081 2024-11-12T01:40:17Z Guy vandegrift 813252 /* With sets */ 2684084 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 3 | 2 \} \\[-.5 ex] \overline{2\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ 2 | 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 37omqt4ipryg9gzcine7baiw96pyg3f 2684085 2684084 2024-11-12T01:46:06Z Guy vandegrift 813252 /* With sets */ 2684085 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ \overline 3 | \overline 2 \} \\[-.5 ex] \overline{2\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ 2 | 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 09ffg5kqhzuzeckh9e4u7ib66sd2vaa 2684086 2684085 2024-11-12T01:47:12Z Guy vandegrift 813252 /* With sets */ 2684086 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ \overline 3 | \overline 2 \} \\[-.5 ex] \overline{2\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 2weysqlq4mrxzvzswz84dfb1yi5ulqv 2684087 2684086 2024-11-12T01:49:51Z Guy vandegrift 813252 /* With sets */ 2684087 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ \overline 3 | \overline 2 \} \\[-.5 ex] \overline{2\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | {0 \} \\[-.5 ex] {\color{Red}\overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] m2qntnp1vif0q0g7geip6nb4rkxm9e4 2684090 2684087 2024-11-12T01:53:18Z Guy vandegrift 813252 Undo revision [[Special:Diff/2684087|2684087]] by [[Special:Contributions/Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|talk]]) 2684090 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ \overline 3 | \overline 2 \} \\[-.5 ex] \overline{2\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 2weysqlq4mrxzvzswz84dfb1yi5ulqv 2684091 2684090 2024-11-12T01:54:29Z Guy vandegrift 813252 /* With sets */ 2684091 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 47budtcfsd8qjt9rz8oobysocgi0iet 2684092 2684091 2024-11-12T01:56:12Z Guy vandegrift 813252 /* With sets */ 2684092 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ga42njhbzkeso1hvwh929b1re90qsc9 2684093 2684092 2024-11-12T01:57:36Z Guy vandegrift 813252 /* With sets */ 2684093 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | }0{\color{Red} \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} } </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 2gxe2486kug1kmkmrvdxon3szzxy8d8 2684095 2684093 2024-11-12T01:58:16Z Guy vandegrift 813252 Undo revision [[Special:Diff/2684093|2684093]] by [[Special:Contributions/Guy vandegrift|Guy vandegrift]] ([[User talk:Guy vandegrift|talk]]) 2684095 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ga42njhbzkeso1hvwh929b1re90qsc9 2684096 2684095 2024-11-12T01:59:18Z Guy vandegrift 813252 /* With sets */ 2684096 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 } \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} } </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qsof1max29a9k9w6fm7hc8yorn37zhd 2684097 2684096 2024-11-12T01:59:47Z Guy vandegrift 813252 /* With sets */ 2684097 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 }{\color{Red} \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} } </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 0faz9pg0c66lgvobpaf2rd3papauykx 2684098 2684097 2024-11-12T02:01:09Z Guy vandegrift 813252 2684098 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ga42njhbzkeso1hvwh929b1re90qsc9 2684100 2684098 2024-11-12T02:02:46Z Guy vandegrift 813252 /* With sets */ 2684100 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} } </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 2132f0y33fm2babqa2vvj9t93kxh65x 2684102 2684100 2024-11-12T02:12:19Z Guy vandegrift 813252 /* With sets */ 2684102 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline 1 | } 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ \overline 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] mf9956pm1zs1bz508iragsxz1dqcas9 2684103 2684102 2024-11-12T02:13:22Z Guy vandegrift 813252 /* With sets */ 2684103 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline 1 | } 0 {\color{red} \}} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ \overline 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] p8tjfbg8ew5h9b66ypdkxg6y8trxpch 2684106 2684103 2024-11-12T02:18:23Z Guy vandegrift 813252 /* With sets */ 2684106 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline 1 | } 0 {\color{red} \}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& {\color{Red} \begin{matrix} \{ \overline 1 | 0 \} \\[-.5 ex] \overline{\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 4kgkjbrubpnsh38564u1sqr9ak965mr 2684107 2684106 2024-11-12T02:20:43Z Guy vandegrift 813252 /* With sets */ 2684107 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] r67758nyjw4zk75s9kqyoq9jtcqu2lj 2684109 2684107 2024-11-12T02:29:54Z Guy vandegrift 813252 /* With sets */ 2684109 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 0cdem775h4j5miogivt599mg0zodmpo 2684118 2684109 2024-11-12T03:04:49Z Guy vandegrift 813252 /* With sets */ 2684118 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \overline{1} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] rkti9mulbzobh17x9habr8xj6ajvst4 2684119 2684118 2024-11-12T03:05:36Z Guy vandegrift 813252 /* With sets */ 2684119 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] rymr3iynjp5oi77cgxq7mi41smrtlxf 2684120 2684119 2024-11-12T03:08:25Z Guy vandegrift 813252 /* With sets */ 2684120 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] pcmfrvqcm8uuttapekjtjutngnxnsol 2684121 2684120 2024-11-12T03:12:17Z Guy vandegrift 813252 2684121 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red} \begin{matrix}\{ \; | 0 \} \\[-.5 ex]\overline{1} \end{matrix}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] rymr3iynjp5oi77cgxq7mi41smrtlxf 2684122 2684121 2024-11-12T03:15:41Z Guy vandegrift 813252 /* With sets */ 2684122 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] fwmszpas1jw6msgg9vcqyupnp0mnac6 2684123 2684122 2024-11-12T03:18:02Z Guy vandegrift 813252 /* With sets */ 2684123 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] l6gnebntmto5itxeffec1lyig7ytdbm 2684124 2684123 2024-11-12T03:19:21Z Guy vandegrift 813252 /* With sets */ 2684124 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] f2h10wujrj82sssf8he8fwigljo88um 2684125 2684124 2024-11-12T03:19:46Z Guy vandegrift 813252 /* With sets */ 2684125 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 5se0az1icarrcch5waueeqpipo8uwwy 2684126 2684125 2024-11-12T03:20:36Z Guy vandegrift 813252 /* With sets */ 2684126 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] jjpnnvbelnid0ku6spu2iifgc7r252k 2684127 2684126 2024-11-12T03:23:02Z Guy vandegrift 813252 /* With sets */ 2684127 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ -1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] nusqc7l85m4wfdv7kx2muyyom3khosi 2684129 2684127 2024-11-12T03:36:04Z Guy vandegrift 813252 /* With sets */ 2684129 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ -1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] jbgnqrulfd3ieey4flpsq3iz9k0ctb8 2684130 2684129 2024-11-12T03:36:28Z Guy vandegrift 813252 /* With sets */ 2684130 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{1} } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 971nc21bpyi57f58tbrltuta4mauwjv 2684131 2684130 2024-11-12T03:37:30Z Guy vandegrift 813252 /* With sets */ 2684131 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 2} } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qb982o28aipbwr012wwb88era5m65qi 2684134 2684131 2024-11-12T03:38:27Z Guy vandegrift 813252 /* With sets */ 2684134 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \overline{2}\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 7m5l2ly9xmr1oreqoaby0vrtwn1y0yi 2684135 2684134 2024-11-12T03:40:49Z Guy vandegrift 813252 /* With sets */ 2684135 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \overline{1\tfrac 1 2} \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\overline{\tfrac 3 4} \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 4} } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] mnk58itl1qe7vle0rvu517t9batpq2j 2684137 2684135 2024-11-12T03:44:00Z Guy vandegrift 813252 /* With sets */ 2684137 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\overline{4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 30civ2ahxbmt0dxhkt5nb1asn1kjash 2684138 2684137 2024-11-12T03:46:34Z Guy vandegrift 813252 /* With sets */ 2684138 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] oqj38u2j9va6q1jm1ui3eyl7nqnyc9o 2684140 2684138 2024-11-12T03:54:21Z Guy vandegrift 813252 /* With sets */ 2684140 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\tfrac{\text{1} 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 671evs1epd0xbgo0c7hjgwncvtnyjd4 2684141 2684140 2024-11-12T03:55:52Z Guy vandegrift 813252 /* With sets */ 2684141 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{1}\tfrac{1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] iuvzmcmvv0j47v9mj3c5mi3swjd9beu 2684142 2684141 2024-11-12T03:56:59Z Guy vandegrift 813252 2684142 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \overline{3} \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\overline{\tfrac 1 8} } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] oqj38u2j9va6q1jm1ui3eyl7nqnyc9o 2684143 2684142 2024-11-12T04:01:54Z Guy vandegrift 813252 /* With sets */ 2684143 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 7rmvvz42l7esasa0wjxpccvh0f8kly2 2684144 2684143 2024-11-12T04:04:06Z Guy vandegrift 813252 /* With sets */ 2684144 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qrtju9zxl4fz2kxn3k9b0tkwz5rimyn 2684145 2684144 2024-11-12T04:05:36Z Guy vandegrift 813252 /* With sets */ 2684145 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline L | \overline{R} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline L | \overline{R} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline L | \overline{R} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline L | \overline{R} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] dpt5og7z2hmrug7g7ks94b7ntfaifnu 2684146 2684145 2024-11-12T04:16:24Z Guy vandegrift 813252 /* With sets */ 2684146 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] m9mhqqosv09qttea898sw7nj4vchngo 2684147 2684146 2024-11-12T04:20:13Z Guy vandegrift 813252 /* With sets */ 2684147 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> Σ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] r291q26i00h52qvtvgcwhchq2ayvhb2 2684148 2684147 2024-11-12T04:20:56Z Guy vandegrift 813252 /* Starting from zero */ 2684148 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] t8ve66zsxwh6s1jk4mdrrneytxg69tk 2684149 2684148 2024-11-12T04:22:35Z Guy vandegrift 813252 /* With sets */ 2684149 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 7buwa9745q71pouo96zqj40ufgwsfl0 2684150 2684149 2024-11-12T04:29:10Z Guy vandegrift 813252 /* With sets */ 2684150 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] pvgfgr2n88vzq5r1v82oz6canwx5z8m 2684151 2684150 2024-11-12T04:41:26Z Guy vandegrift 813252 /* With sets */ 2684151 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] j757j4i0d29mqwj4hwpu2zy7qk8fezc 2684152 2684151 2024-11-12T04:42:08Z Guy vandegrift 813252 /* With sets */ 2684152 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math> ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 7 8}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] okjf9lozfle4phvunmygl5hb3kqkezj 2684153 2684152 2024-11-12T04:43:57Z Guy vandegrift 813252 /* With sets */ 2684153 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- <small><math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] kxamuk0khadcee9wqcy172b2jowvbc9 2684154 2684153 2024-11-12T04:47:07Z Guy vandegrift 813252 /* With sets */ 2684154 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- <math display="block">\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] g1tp51qn00x900tq1tlyfludjghp35y 2684155 2684154 2024-11-12T04:48:19Z Guy vandegrift 813252 /* With sets */ 2684155 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] nttz82qvm4o33cydf0yildb9dfgz6uc 2684156 2684155 2024-11-12T04:55:54Z Guy vandegrift 813252 /* With sets */ 2684156 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- [[file:Example|thumb]] <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1\frac 1 2 | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] qpqsuhg0l7j0xh4n4e28o0on6ivt1xn 2684157 2684156 2024-11-12T05:08:01Z Guy vandegrift 813252 /* Starting from zero */ 2684157 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- [[file:Example|thumb]] <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 4xmnfm3oldh46sfijk7qcyz1rszv57f 2684158 2684157 2024-11-12T05:09:22Z Guy vandegrift 813252 /* With sets */ 2684158 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- [[file:Example.svg|thumb]] <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 43205jn85ejjansr7pp896s9b89fmhf 2684159 2684158 2024-11-12T05:13:08Z Guy vandegrift 813252 /* With sets */ 2684159 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- [[file:Example.svg|thumb]] <math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] 1xa3530vb9jolzclhcxgisauxmxcon8 2684160 2684159 2024-11-12T05:28:45Z Guy vandegrift 813252 /* With sets */ 2684160 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <math> {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} </math>x ----- <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] ahehpg3q7n1j7v0zlj36pmzorej0g5t 2684161 2684160 2024-11-12T05:31:21Z Guy vandegrift 813252 /* With sets */ 2684161 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== {{cot|under construction}} <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small>{{cob}} ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] n9t24de7qqqvbnxefrlm4bpizbkhnoh 2684162 2684161 2024-11-12T05:33:40Z Guy vandegrift 813252 /* With sets */ 2684162 wikitext text/x-wiki All readers are welcome to contribute to this resource. Try to follow the notation of [[Wikipedia:Surreal number]], but don't forget that on on Wikiversity, [https://www.youtube.com/watch?v=qo6lPifGnGA '''anything goes!'''] To create an essay or article start with a title that not already on the list below. It is very easy to change a title.. If you need help, leave a message at [[User talk:Guy vandegrift]]. {{RoundBoxTop|theme=1}}<inputbox> type=create width=110 buttonlabel=Create subpage break=no prefix={{FULLPAGENAME}}/ placeholder=Title of subpage </inputbox>{{RoundBoxBottom}} {{Special:Prefixindex/{{FULLPAGENAME}}/|hideredirects=0|stripprefix=1}} [[Category:Open essay collections]] ==Subpage abstracts== Each "abstract" begins with a and a link to a subpage. The abstract is just a [[w:transclusion|transclusion]] of the first few lines. ===Abstracts for beginners=== {{/The dyadics}}<br> {{/Root 2}}<br> {{/Counting}}<br>[[file:Pinocchio paradox Large Print.svg|thumb|right|140px|]] ■ '''[[Russell's paradox]]''' resembles [[w:Pinocchio paradox|Pinocchio paradox]] in that it involves self-referencing. {{:Russell's paradox}} ===Advanced abstracts=== {{/Why isn't half-omega the (left) child of omega?}} ----- {{/Simplicity}} [[Category:Open essay collections]] ---- ==Essential reading for advanced students== So far, the subpages to this resource are target the absolute beginner. I hope that changes, but for now people already familiar with the basics might want to look at the following websites: ===Meet the surreal numbers (Jim Simons)=== [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers'''] (by Jim Simons) is 39 pages long. The internet is full of introductions to surreal numbers. Many contain the same essential insight can be found on Wikipedia's '''[[w:Surreal number|Surreal number]]'''. But Jim Simon's article contains useful insights that most authors neglect to adequately cover. His discussion of [[w:Ordinal number|ordinal numbers]] begins with this introduction: :''Just as we don’t need much set theory, we don’t need to know much about ordinals, but it is helpful to know a little. Ordinals extend the idea of counting into the infinite in the simplest way imaginable: just keep on counting. So we start with the natural numbers: 0, 1, 2, 3, 4, . . ., but we don’t stop there, we keep on with a new number called ω, then ω + 1, ω + 2, ω + 3 and so on. After all those we come to ω + ω = ω·2. Carrying on we come to ω·3, ω·4 etc and so on to ω<sup>2</sup> . Carrying on past things like ω <sup>2</sup>·7 + ω·42 + 1, we’ll come to ω<sup>3</sup> , ω<sup>4</sup> and so on to ω<sup>ω</sup> , and this is just the beginning. To see a bit more clearly where this is heading, we’ll look at von Neumann’s construction of the ordinals.'' ====Simplicity theorem==== :'''''The Simplicity Theorem. (If) x is a number, and z is a number with the earliest possible birthday that lies strictly between the left and right options of x, then x = z''''' I find this easier to understand than the what appears in [[Wikipedia:Surreal number]]. ===A Short Guide to Hackenbush (Padraic Bartlett)=== [https://www.math.uchicago.edu/~may/VIGRE/VIGRE2006/PAPERS/Bartlett.pdf '''A Short Guide to Hackenbush'''] is 25 pages long. It will give insight as to what inspired the invention of surreal numbers. It turns out that the surreal numbers are inspired by an effort to attach a value to a game, not unlike [[w:Go (game)|go]] or [[w:Chess|chess]], but some peculiarities that make it easy to attach a rational number that predicts how the game will end if both sides play flawlessly. Non-negative values correspond to games where the person who moves first will lose, and the magnitude (absolute value) tells us something about the margin or victory. A value of zero corresponds to a position where the loser is the person whose turn it is to move (ties are impossible in red-blue [[w:Hackenbush|hackenbush]].) For those who love math as a beautiful tool for solving real-life problems, this application to game theory is the most likely way to make surreal numbers seem "useful". [[File:Surreal number tree.svg|thumb|500px|Tree diagram shown at [[Wikipedia:Surreal number]]]] ===Beyond ω (with Andi Fugard)=== '''[https://andifugard.info/surreal-numbers/ numbers – Andi Fugard]''' presents a slightly different picture of &omega;/2. The image to the right is from the Wikipedia article, and I am confused by the tree diagram starting at &omega;. Compare the image to the right with [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image]. All the dyadic (real) numbers are placed on a tree formation where each parent has two children. They display two types of infinite series: #The positive and negative integers are exterior elements and grow as <br>{{spaces|3}}{1, 2, 3,...}. #Interior dyadics cut as fractions that get smaller, for example as <br>{{spaces|3}}{ &frac12;, &frac14;, &frac18;, ...}. Look at the tree that begins at ω: Both sides match the tree that begins with 0, i.e., by adding or subtracting 1 from each previous element. To the left we get smaller with {ω, ω-1, ω-2,..., ω/2}. See also [https://andifugard.info/wp-content/uploads/2022/07/surreal_birthdays.png this image] and [https://andifugard.info/surreal-numbers/ this article]. I am quite confused by the fact that the left side of this tree doesn't continue with {ω, ω-1, ω-2,..., 0}.<ref>Here, 0 might not be a member of the set, but merely a point to which the series converges.</ref> It is true that the square root of ω is smaller than every element in the series {ω, ω-1, ω-2,..., 0}. But how do we know that 2ω has the same birthday as ω/2? '''Answer:''' Quoting page 30 of [https://www.m-a.org.uk/resources/downloads/4H-Jim-Simons-Meet-the-surreal-numbers.pdf '''Meet the surreal numbers''']: x = {ℕ | ω − ℕ} can hardly be ω − ω because that is equal to 0.<ref>Here, ℕ refers to <math>\mathbb{N}</math>, or the [[wikipedia:natural numbers|natural numbers]].</ref> So what it it? x = {ℕ | ω − ℕ}, and x + x = {x + ℕ | x + ω − ℕ}. Now x < ω − n for any n ∈ ℕ, so x + n < ω, ie so all the left option of x + x are less than ω, but are infinite. Similarly, x > n, so x + ω − n > ω, ie all the right options of x + x are bigger than ω. Therefore x + x = ω, and x = ω/2. === Surreal Numbers – An Introduction (Claus Tøndering) === [https://www.tondering.dk/download/sur.pdf '''Surreal Numbers – An Introduction'''] is 51 pages of careful rigor. It employs the notation of logic and set theory. Each surreal number can be expressed in a variety of "forms" (each consisting of a pair of sets.) On page 25 Tøndering proves that if x is the oldest surreal number between a and b, then {a | b} = x. ===Math576 Combinatorial Game Theory=== [https://people.math.sc.edu/lu/teaching/2020fall_576/note1.pdf Lecture note for Math576 Combinatorial Game Theory.pdf ] is an 84 page document that thoroughly connects surreal numbers to hackenbush. ===Surreal Numbers and Transseries=== [https://www.fields.utoronto.ca/talk-media/1/50/58/slides.pdf www.fields.utoronto.ca/talk-media/1/50/58/slides] concisely presents 12 pages of insight into how both real numbers, as well as von Neumann's ordinal numbers, embedded in the surreals. ===Video=== [https://www.youtube.com/watch?v=ZYj4NkeGPdM HACKENBUSH: a window to a new world of math] is an hour-long video that begins with a solid introduction to hackenbush, but also goes far beyond. === Other useful (but informal) discussions === * Mathematical Musings https://www.youtube.com/watch?v=QaK81xaIb-U * https://www.quora.com/What%E2%80%99s-the-difference-between-surreal-and-hyperreal-numbers-in-layman%E2%80%99s-terms ===Wikiversity/Wikipedia/Wikibooks=== {{colbegin}} *[[w:Surreal numbers]] *[[w:Ordinal arithmetic]] *[[w:Infinity#Real_analysis]] *[[w:Transfinite number#Examples]] *[[w:Hyperreal number]] *[[w:Von Neumann universe]] *[[Surreal_number/Simple_hackenbush#References]] *[[Introduction to Category Theory/Products and Coproducts of Sets]] *[[Introduction to Category Theory/Sets and Functions]] *[[Set theory]] *[[b:Surreal_Numbers_and_Games]] {{colend}} ===External links=== *[https://www.whitman.edu/documents/Academics/Mathematics/Grimm.pdf whitman.edu (Grimm.pdf)] 30 pages. Excellent resource with proofs and connection to hackenbush. A curious feature of this resource is that he claims that all red-blue hackenbush games are numbers. His argument that any non-zero hackenbush position can be used to create a zero position by subtracting a number that has been created by a collection of simple trees. Since every number can be represented by a simple hackenbush game, then every position can be "zeroed" by a simple game. Unfortunately, Grimm doesn't explain how omega can be represented by a hackenbush position. *[https://drive.google.com/file/d/1iVqRJJ4D0prkPboquCmGEVzOC0cdS5j-/view Steven Charlton - An Very Brief Introduction to Surreal Numbers] [https://guests.mpim-bonn.mpg.de/spc/talks/7_gandalf_surrealnumbers_notes.pdf (alternate link)] 6 pages. *[https://arxiv.org/pdf/1810.10373 Surreal Birthdays and Their Arithmetic (Matthew Roughan)] 13 pages. Directed Acyclic Graphs (DAG); 2*3 & 3/4 + 3/4/ (a bit complicated). *[https://medium.com/badiou-and-science/badiou-and-science-1-4-1-the-surreal-numbers-part-1-95dadcf4c554 badiou-and-science part-1] Nice graphs. 8 minute read. Seems identical to article at [https://www.scientificamerican.com/article/surreal-numbers-are-a-real-thing-heres-how-to-make-them/ scietificamerican.com], except the former has links to more game theory articles by same author. *[https://web.mit.edu/sp.268/www/surreal.pdf what is a game? (mit)] 13 pages.* *[https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers stackexchange definition of all dyadics] *[https://math.stackexchange.com/questions/926581/in-the-surreal-numbers-is-it-fair-to-say-0-9-repeating-is-not-equal-to-1 stackexchange on .9999] *See also [[Draft:Surreal_number#Collection_of_online_resources_saved_on_disk]] *[https://web.archive.org/web/20150429210249/http://euclid.colorado.edu/~monkd/m8714.html course notes on set theory] =====proof of conways simplicity rule===== https://math.stackexchange.com/questions/816540/proof-of-conways-simplicity-rule-for-surreal-numbers <math>0=\{|\}</math> <math>n+1=\{n|\}</math> <math>-n-1=\{|-n\}</math> <math>\tfrac{2p+1}{2^{q+1}}=\left\{ \tfrac{p}{2q} | \tfrac{p+1}{2q} \right\}</math> ====Limits and analysis==== Infinity is easy to imagine, but difficult to incorporate into rigorous mathematics. The following "logic" certainly violates the rules of mathematics and is therefore nonsensical: :<math>\lim_{\epsilon\to 0} \frac 1 \epsilon =\infty\;</math> and <math>\;\lim_{\epsilon\to 0} \frac 2 \epsilon =\infty\;</math> implies <math>\;\frac\infty\infty =2.</math> This is why expressions like <math>\infty/\infty</math> and <math>0/0</math> of often called [[wikt:indeterminant|indeterminant]]. Most of the time, mistakes like this can be avoided by utilizing concepts taught in a course on [[w:Mathematical analysis|mathematical analysis]]. ==Images== {{wide image|Positive surreals to seventh birthday.svg|2000px}} [[File:Números hiperreales.png|400px|thumb|Infinitesimals (ε) and infinities (ω) on the hyperreal number line (1/ε = ω/1). This image appears in the Wikipedia articles [[w:Hyperreal number]], [[w:Infinitesimal]], and [[w:Infinity]].]] {{clear}} ===Using Latex {matrix}=== With Latex, it is easier to use dots instead of arrows to highlight how parents give rise to children. The following two trees (starting from 1 and 0, respectively) are written as latex matrices:<small><math>\begin{matrix} &&&&&&&&&&&&&&& 1 &&&&&&&&&&&&&&& \\ &&&&&&& \tfrac 1 2&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&2 &&&&&&& \\ &&& \tfrac 1 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 3 4 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 3 &&& \\ &\tfrac 1 8 &\cdot&\cdot &\cdot& \tfrac 3 8 &\cdot&\cdot &\cdot& \tfrac 5 8 &\cdot&\cdot &\cdot& \tfrac 7 8 &\cdot&\cdot &\cdot& 1\tfrac 1 4 &\cdot&\cdot &\cdot& 1\tfrac 3 4 &\cdot&\cdot &\cdot& 2\tfrac 1 2 &\cdot&\cdot &\cdot& 4 & \\ \tfrac{1}{16} &\cdot& \tfrac{3}{16} &\cdot& \tfrac{5}{16} &\cdot& \tfrac{7}{16} &\cdot&\tfrac{9}{16} &\cdot& \tfrac{11}{16} &\cdot& \tfrac{13}{16} &\cdot& \tfrac{15}{16} &\cdot& 1\tfrac 1 8 &\cdot& 1\tfrac 3 8 &\cdot& 1\tfrac 5 8 &\cdot& 1\tfrac 7 8 &\cdot& 2\tfrac 1 4 &\cdot& 2\tfrac 3 4 &\cdot& 3\tfrac 1 2 &\cdot& 5 & \end{matrix}</math></small> ===Starting from zero=== <small><math>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&&{\color{Red}\overline{1}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&&{\color{Red}\overline{2}}&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&{\color{Red}\overline{\tfrac 1 2}}&\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot&\tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\ &{\color{Red}\overline{3}} &\cdot&\cdot &\cdot& {\color{Red}\overline{1\tfrac 1 2}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 3 4}} &\cdot&\cdot &\cdot& {\color{Red}\overline{\tfrac 1 4}} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\overline{4}} &\cdot& {\color{Red}\overline{2\tfrac 1 2}} &\cdot& {\color{Red}\overline{1\tfrac 3 4}} &\cdot& {\color{Red}\overline{1\tfrac 1 4}} &\cdot&{\color{Red}\overline{\tfrac 7 8}} &\cdot&{\color{Red}\overline{\tfrac 5 8}} &\cdot&{\color{Red}\overline{\tfrac 3 8}} &\cdot& {\color{Red}\overline{\tfrac 1 8}} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2\tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> ====With sets==== {{cot|under construction}} <math> {\color{Red}\begin{matrix}\{ \overline{L} | \overline{R} \} \\[-.5 ex]\text{-}a\tfrac b c\end{matrix}} </math> ----- <small><math display=block>\begin{matrix} &&&&&&&&&&&&&&& 0 &&&&&&&&&&&&&&& \\ &&&&&&& \begin{matrix} {\color{red}\{ \; | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}1 } \end{matrix} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& 1 &&&&&&&\\ &&& {\color{Red}\begin{matrix}\{ \; | \overline{1} \} \\[-.5 ex] \text{-}2\end{matrix}} &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot& \begin{matrix} {\color{red}\{ \overline 1 | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 2 } \end{matrix} &\cdot&\cdot &\cdot&\cdot&\cdot&\cdot&\cdot& \tfrac 1 2 &\cdot&\cdot&\cdot&\cdot&\cdot&\cdot&\cdot & 2 &&&\\&{\color{Red}\begin{matrix}\{\;|\overline{2}\}\\[-.5 ex] \text{-}3 \end{matrix}}&\cdot&\cdot &\cdot& {\color{Red} \begin{matrix} \{ \overline 2 | \overline 1 \} \\[-.5 ex] \text{-1}\tfrac 1 2 \end{matrix}} &\cdot&\cdot &\cdot& {\color{Red}\begin{matrix}\{ \overline{1} | \overline{\tfrac 1 2} \} \\[-.5 ex]\text{-}\tfrac 3 4 \end{matrix}} &\cdot&\cdot &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 2} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 4 } \end{matrix} &\cdot&\cdot &\cdot& \tfrac 1 4 &\cdot&\cdot &\cdot& \tfrac 3 4 &\cdot&\cdot &\cdot& 1\tfrac 1 2 &\cdot&\cdot &\cdot& 3 &\\ {\color{Red}\begin{matrix}\{ \; | \overline{3} \} \\[-.5 ex]\text{-4} \end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 3 | \overline{2} \} \\[-.5 ex]\text{-}2\tfrac 1 2\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{\overline{2} |\overline{1\tfrac 1 2} \} \\[-.5 ex]\text{-}1\tfrac 3 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline{1\frac 1 2} | \overline{1} \} \\[-.5 ex]\text{-}1\tfrac 1 4\end{matrix}} &\cdot& {\color{Red}\begin{matrix}\{ \overline 1 | \overline{\tfrac 3 4} \} \\[-.5 ex]\text{-}\tfrac 7 8\end{matrix}} &\cdot& {\color{Red}\overline{\tfrac 5 8}} &\cdot&{ \color{Red}\overline{\tfrac 3 8}} &\cdot& \begin{matrix} {\color{red}\{ \overline{\tfrac 1 4} | }0 {\color{red}\}} \\[-.5 ex] {\color{red}\text{-}\tfrac 1 8 } \end{matrix} &\cdot& \tfrac 1 8 &\cdot& \tfrac 3 8 &\cdot& \tfrac 5 8 &\cdot& \tfrac 7 8 &\cdot& 1\tfrac 1 4 &\cdot& 1\tfrac 3 4 &\cdot& 2 \tfrac 1 2 &\cdot& 4 \end{matrix}</math></small> {{cob}} ==Categories== [[Draft:Surreal number]] {{center|[[special:prefixindex/{{FULLPAGENAME}}/|<small>''Link to any subpages this page might have''</small>]]}} [[Category:Numbers]] c7nkugt8c60u7emwp0l0su1q2q9qq97 Large language models 0 302417 2683952 2683441 2024-11-11T17:06:29Z Conan 183430 /* Hugging Face docs */ pipeline 2683952 wikitext text/x-wiki Large language models (LLM's) are software programs that are also known as a form of "artificial intelligence" (AI); LLM's are specifically an aspect of generative AI. This wiki area is for learning, teaching, and research related to LLM's. {{RightTOC}} [[Image:Multiple attention heads.png|right|280px|thumb|An illustration of multiple attention heads, each having its own criteria of relevance of other tokens for one of the tokens within the scope of a context window. (For the purpose of illustration, the context window consists of only one sentence.]] ==Discourse and ideas== Here is discourse and ideas related to large language models. Perhaps once significantly developed/refined, some of these can have their own sub-page or become a unique learning resource. ===Learning wikis as training data=== Unless laws change, Creative Commons content appears to be valid training data for LLM's. As LLM's progress and advance, more and more data can be utilized to training increasingly complex models. Learning wikis devoted to learning, teaching, and resource, that allow for original research and original content creation (related to learning, teaching, and research), can potentially be extremely valuable (in terms of educational value) for large language models. Perhaps in the future (if this does not already exist), large language models will be able to continuously be trained on, retain, and learn from new data and information. Perhaps in the future, an open source large language model could only be trained on Creative Commons data, and therefore, all generated content would also be licensed under Creative Commons. ==Discussion questions== Here are some learning and teaching oriented discussion questions related to large language models. Humans can use language and mental effort to explore these ideas collaboratively, or some of these could be used as prompts to see how an LLM might respond. * Would a large language model that is only trained on Creative Commons licensed data only be capable of generating responses to prompts that can also be rightly and correctly licensed under a Creative Commons license? * How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)? * What are some ethical considerations related to large language models that should be considered? * What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think? * How can large language models help to advance and accelerate technological automation in ways that will benefit all of humanity? * In what ways can large language models help programmers to code? * Can music be thought of a language within the realm of large language models? * What is differentiable computing and how does differentiable computing relate to large language models? * How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? == Educational prompt ideas== These are original prompt ideas regarding ways to learn about large language models, and also to explore using LLM's for learning, teaching, and research. Input these into your preferred LLM (without quotes) to see what results are generated. LLM's might produce interesting or useful answers in response to these prompts. Some of these prompts may be interesting or useful for discussions among and between humans. * "Describe to me how large language models can be utilized for learning, teaching, and research. Do this in an about 200 word two paragraph mini essay. Explain it to me like I am a freshman in community college." * "Give me a list of 12 ways that large language models can be utilized for learning, teaching, and research." * "How can LLM's be utilized to accelerate the pace of research and scientific discovery?" * "What are some ethical considerations related to large language models that should be considered?" * "What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think?" * "What are some project ideas to integrate large language models in with humanoid robots, and/or other sorts of robots? Please give me 15 project ideas that can be relatively simple or extremely complex." * "Please search the Internet if possible. In what ways have university professors and academic researchers been using large language models in the last year? Please respond in list form." * "In what ways can large language models help programmers to code? Please provide me 8 examples and respond in list form." * "Can music be thought of a language within the realm of large language models?" * "What is differentiable computing and how does differentiable computing relate to large language models?" * "How can one fine tune an open source large language model?" * "What are some popular state of the art open source large language models. Please search the internet as helpful and respond to me in list form." * "Please give me a list of important terminology that I should be aware of when working with and training open source large language models. Please be comprehensive. Please respond in list form. And please search the internet as helpful." * "What sort of hardware should I utilize to run the most competent open source large language models that I want to utilize for learning, teaching, and research? Please search the internet as helpful." * "How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? Please respond in list form." * "How can researchers utilize large language models to create theories, hypothesis, and to formulate potential research studies? Please respond in short paragraphs, but in list form." ==Readings and learning media== ===External=== * [https://stpp.fordschool.umich.edu/tags/large-language-models Large Language Models] - Articles * [https://hai.stanford.edu/news/how-large-language-models-will-transform-science-society-and-ai How Large Language Models Will Transform Science, Society, and AI] * [https://insights.sei.cmu.edu/blog/harnessing-the-power-of-large-language-models-for-economic-and-social-good-foundations/ Harnessing the Power of Large Language Models For Economic and Social Good: Foundations] * [https://courses.grainger.illinois.edu/CS447/sp2023/Slides/Lecture27.pdf Lecture 27: Intro to Large Language Models] ====Hugging Face NLP==== A course about natural language processing (NLP) using libraries from the Hugging Face ecosystem &ndash; Transformers, Datasets, Tokenizers, and Accelerate. : [https://huggingface.co/learn/nlp-course/chapter0/1 Natural Language Processing (NLP) course] :: [https://huggingface.co/learn/nlp-course/chapter1/1 transformer models] :: [https://huggingface.co/learn/nlp-course/chapter2/1 using transformers]: ::: [https://huggingface.co/learn/nlp-course/chapter2/2 pipeline], [https://huggingface.co/learn/nlp-course/chapter2/3 models], [https://huggingface.co/learn/nlp-course/chapter2/4 tokenizer], [https://huggingface.co/learn/nlp-course/chapter2/5 batching], decoding, padding, attention mask :: [https://huggingface.co/learn/nlp-course/chapter3/1 fine-tuning a pretrained model]: ::: preprocessing, map, [https://huggingface.co/docs/datasets/index dataset], dynamic padding, batch, collate function, train, predict, evaluate, [https://github.com/huggingface/accelerate accelerate] :: [https://huggingface.co/learn/nlp-course/chapter4/1 sharing models and tokenizers]: ::: hub, model card :: [https://huggingface.co/learn/nlp-course/chapter5/1 the datasets library]: ::: batch, DataFrame, validation, splitting, embedding, FAISS :: [https://huggingface.co/learn/nlp-course/chapter6/1 the tokenizers library]: ::: [https://huggingface.co/learn/nlp-course/chapter6/2 training tokenizer], grouping, QnA, [https://huggingface.co/docs/tokenizers/api/normalizers normalizers], pre-tokenization, [https://huggingface.co/docs/tokenizers/api/models models],[https://huggingface.co/docs/tokenizers/api/trainers trainers]: BPE, WordPiece, Unigram, [https://huggingface.co/docs/tokenizers/api/post-processors post processors], [https://huggingface.co/docs/tokenizers/components#decoders decoders] :: [https://huggingface.co/learn/nlp-course/chapter7/1 main nlp tasks]: ::: [https://huggingface.co/learn/nlp-course/chapter7/2 token classification], metrics, perplexity, [https://huggingface.co/learn/nlp-course/chapter7/4 translation], [https://huggingface.co/learn/nlp-course/chapter7/5 summarization], [https://huggingface.co/learn/nlp-course/chapter7/6 training CLM], [https://huggingface.co/learn/nlp-course/chapter7/7 QnA], :: [https://huggingface.co/learn/nlp-course/chapter8/1 how to ask for help] :: [https://huggingface.co/learn/nlp-course/chapter9/1 building and sharing demos] ==== Hugging Face docs ==== : https://huggingface.co/docs :: Core libraries ::: [https://huggingface.co/docs/transformers Transformers] &ndash; State-of-the-art ML for Pytorch, TensorFlow, and JAX. :::: [https://huggingface.co/docs/transformers/main_classes/pipelines#transformers.pipeline pipeline] &ndash; simple interface for inference with models. ::: [https://huggingface.co/docs/datasets Datasets] &ndash; Access and share datasets for computer vision, audio, and NLP tasks. ::: [https://huggingface.co/docs/accelerate Accelerate] &ndash; Easily train and use PyTorch models with multi-GPU, TPU, mixed-precision. ::: [https://huggingface.co/docs/tokenizers Tokenizers] &ndash; Fast tokenizers, optimized for both research and production. :: [https://huggingface.co/docs/hub Hub] &ndash; Host Git-based models, datasets and Spaces on the Hugging Face Hub. :: [https://huggingface.co/docs/diffusers Diffusers] &ndash; State-of-the-art diffusion models for image and audio generation in PyTorch. :: [https://huggingface.co/docs/huggingface_hub Hub Python Library] &ndash; Client library for the HF Hub: manage repositories from your Python runtime. :: [https://huggingface.co/docs/huggingface.js Huggingface.js] &ndash; A collection of JS libraries to interact with Hugging Face, with TS types included. :: [https://huggingface.co/docs/transformers.js Transformers.js] &ndash; Community library to run pretrained models from Transformers in your browser. :: [https://huggingface.co/docs/api-inference Inference API (serverless)] &ndash; Experiment with over 200k models easily using the serverless tier of Inference Endpoints. :: [https://huggingface.co/docs/inference-endpoints Inference Endpoints (dedicated)] &ndash; Easily deploy models to production on dedicated, fully managed infrastructure. :: [https://huggingface.co/docs/peft PEFT] &ndash; Parameter efficient fine-tuning methods for large models ::: Soft prompting, LoRA, IA3 :: [https://huggingface.co/docs/optimum Optimum] &ndash; Fast training and inference of HF Transformers with easy to use hardware optimization tools. :: [https://huggingface.co/docs/optimum-neuron AWS Trainium &amp; Inferentia] &ndash; Train and Deploy Transformers &amp; Diffusers with AWS Trainium and AWS Inferentia via Optimum :: [https://huggingface.co/docs/evaluate Evaluate] &ndash; Evaluate and report model performance easier and more standardized. ::: types: metrics, comparisons, measurements :: [https://huggingface.co/tasks Tasks] ::: extraction, question answering, classification, generation ... :: [https://huggingface.co/docs/dataset-viewer Dataset viewer] &ndash; API to access the contents, metadata and basic statistics of all Hugging Face Hub datasets. ::: Splits and subsets, [https://github.com/huggingface/dataset-viewer dataset-viewer] :: [https://huggingface.co/docs/trl TRL] &ndash; Transformer Reinforcement Learning ::: reward modeling, fine-tuning, optimizations, :: [https://huggingface.co/docs/sagemaker Amazon SageMaker] &ndash; Train and Deploy Transformer models with Amazon SageMaker and Hugging Face Deep Learning Containers (DLC). :: [https://huggingface.co/docs/timm timm] &ndash; Pytorch Image Models. ::: State-of-the-art computer vision models, layers, optimizers, training/evaluation, and utilities. :: [https://huggingface.co/docs/safetensors Safetensors] &ndash; Simple, safe way to store and distribute neural networks weights. :: [https://huggingface.co/docs/text-generation-inference Text Generation Inference] &ndash; Toolkit to serve Large Language Models. :: [https://huggingface.co/docs/autotrain AutoTrain] &ndash; AutoTrain API and UI. ::: [https://huggingface.co/autotrain autotrain] :: [https://huggingface.co/docs/text-embeddings-inference Text Embeddings Inference] &ndash; Toolkit to serve Text Embedding Models. :: [https://huggingface.co/docs/competitions Competitions] &ndash; Create your own competitions on Hugging Face. :: [https://huggingface.co/docs/bitsandbytes Bitsandbytes] &ndash; Toolkit to optimize and quantize models. :: [https://huggingface.co/docs/optimum-tpu Google TPUs] &ndash; Deploy models on [https://cloud.google.com/tpu/docs Google TPUs] via Optimum. :: [https://huggingface.co/docs/chat-ui Chat UI] &ndash; Open source chat frontend, powers the [https://huggingface.co/chat HuggingChat] app. :: [https://huggingface.co/docs/leaderboards Leaderboards] &ndash; Create your own Leaderboards on Hugging Face. :: [https://huggingface.co/docs/hugs Hugging Face Generative AI Services (HUGS)] &ndash; optimized, zero-configuration inference microservices designed to simplify and accelerate the development of AI applications with open models. ===Videos=== * [https://www.youtube.com/watch?v=5sLYAQS9sWQ How Large Language Models Work] * [https://www.youtube.com/watch?v=JhCl-GeT4jw Large Language Models and The End of Programming - CS50 Tech Talk with Dr. Matt Welsh] * [https://www.youtube.com/watch?v=yBI1nPep72Q LMStudio Tutorial Run ANY Open-Source Model LOCALLY] * [https://www.youtube.com/watch?v=UU1WVnMk4E8 Create a Large Language Model from Scratch with Python – Tutorial] * [https://www.youtube.com/watch?v=eC6Hd1hFvos Fine-tuning Large Language Models (LLMs) | w/ Example Code] ===Wikipedia=== {{colbegin|5}} * [[w:Large language model|Large language model]] * [[w:Prompt engineering|Prompt engineering]] * [[w:GPT-4|GPT-4]] * [[w:Category:Large language models|Category:Large language models]] * [[w:LLaMA|LLaMA]] * [[w:Mistral AI|Mistral AI]] * [[w:Foundation model|Foundation model]] * [[w:Natural-language understanding|Natural-language understanding]] * [[w:Ethics of artificial intelligence|Ethics of artificial intelligence]] * [[w:Artificial general intelligence|Artificial general intelligence]] * [[w:Intelligence amplification|Intelligence amplification]] * [[w:Outline of artificial intelligence|Outline of artificial intelligence]] * [[w:Synthetic intelligence|Synthetic intelligence]] * [[w:Weak artificial intelligence|Weak artificial intelligence]] * [[w:History of artificial intelligence|History of artificial intelligence]] * [[w:Timeline of artificial intelligence|Timeline of artificial intelligence]] * [[w:Progress in artificial intelligence|Progress in artificial intelligence]] * [[w:History of natural language processing|History of natural language processing]] * [[w:Hardware for artificial intelligence|Hardware for artificial intelligence]] * [[w:AI safety|AI safety]] * [[w:Neural scaling law|Neural scaling law]] * [[w:Philosophy of artificial intelligence|Philosophy of artificial intelligence]] * [[w:Philosophy of mind|Philosophy of mind]] * [[w:Computational theory of mind|Computational theory of mind]] * [[w:Regulation of artificial intelligence|Regulation of artificial intelligence]] * [[w:LangChain|LangChain]] * [[w:Generative pre-trained transformer|Generative pre-trained transformer]] * [[w:GitHub Copilot|GitHub Copilot]] * [[w:ChatGPT|ChatGPT]] * [[w:Generative artificial intelligence|Generative artificial intelligence]] * [[w:Category:Generative artificial intelligence|Category:Generative artificial intelligence]] * [[w:Music and artificial intelligence|Music and artificial intelligence]] * [[w:Workplace impact of artificial intelligence|Workplace impact of artificial intelligence]] * [[w:Applications of artificial intelligence|Applications of artificial intelligence]] * [[w:Artificial intelligence in Wikimedia projects|Artificial intelligence in Wikimedia projects]] * [[w:Wikipedia:Artificial intelligence|Wikipedia:Artificial intelligence]] * [[w:Artificial intelligence in healthcare|Artificial intelligence in healthcare]] * [[w:Automated reasoning|Automated reasoning]] * [[w:Machine learning in physics|Machine learning in physics]] * [[w:Quantum neural network|Quantum neural network]] * [[w:ChatGPT in education|ChatGPT in education]] * [[w:Artificial intelligence content detection|Artificial intelligence content detection]] * [[w:Turing test|Turing test]] * [[w:List of datasets for machine-learning research|List of datasets for machine-learning research]] * [[w:Fine-tuning (deep learning)|Fine-tuning (deep learning)]] * [[w:Attention (machine learning)|Attention (machine learning)]] * [[w:Mixture of experts|Mixture of experts]] * [[w:Gemini (language model)|Gemini (language model)]] * [[w:Auto-GPT|Auto-GPT]] * [[w:VideoPoet|VideoPoet]] {{colend}} ==See also== * [[Artificial intelligence]] * [[Artificial Intelligence & Machine Learning]] * [[Artificial Intelligence and Robotics Laboratory]] * [[Computer science]] * [[Artificial Consciousness]] * [[Supersymmetric Artificial Neural Network]] * [[History of artificial intelligence]] [[Category: Computer science]] [[Category: Machine learning]] [[Category: Artificial intelligence]] hxywem81mpoumyxmz0fg797hzvlzea3 2683954 2683952 2024-11-11T17:48:54Z Conan 183430 /* Hugging Face docs */ Auto classes ... 2683954 wikitext text/x-wiki Large language models (LLM's) are software programs that are also known as a form of "artificial intelligence" (AI); LLM's are specifically an aspect of generative AI. This wiki area is for learning, teaching, and research related to LLM's. {{RightTOC}} [[Image:Multiple attention heads.png|right|280px|thumb|An illustration of multiple attention heads, each having its own criteria of relevance of other tokens for one of the tokens within the scope of a context window. (For the purpose of illustration, the context window consists of only one sentence.]] ==Discourse and ideas== Here is discourse and ideas related to large language models. Perhaps once significantly developed/refined, some of these can have their own sub-page or become a unique learning resource. ===Learning wikis as training data=== Unless laws change, Creative Commons content appears to be valid training data for LLM's. As LLM's progress and advance, more and more data can be utilized to training increasingly complex models. Learning wikis devoted to learning, teaching, and resource, that allow for original research and original content creation (related to learning, teaching, and research), can potentially be extremely valuable (in terms of educational value) for large language models. Perhaps in the future (if this does not already exist), large language models will be able to continuously be trained on, retain, and learn from new data and information. Perhaps in the future, an open source large language model could only be trained on Creative Commons data, and therefore, all generated content would also be licensed under Creative Commons. ==Discussion questions== Here are some learning and teaching oriented discussion questions related to large language models. Humans can use language and mental effort to explore these ideas collaboratively, or some of these could be used as prompts to see how an LLM might respond. * Would a large language model that is only trained on Creative Commons licensed data only be capable of generating responses to prompts that can also be rightly and correctly licensed under a Creative Commons license? * How might large language models affect learning and research. Will LLM's eventually seen like calculators are in math and sciences now? But for everything (all subjects/topics, including math, physics, ethics, biology, psychology, chemistry, engineering, art)? * What are some ethical considerations related to large language models that should be considered? * What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think? * How can large language models help to advance and accelerate technological automation in ways that will benefit all of humanity? * In what ways can large language models help programmers to code? * Can music be thought of a language within the realm of large language models? * What is differentiable computing and how does differentiable computing relate to large language models? * How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? == Educational prompt ideas== These are original prompt ideas regarding ways to learn about large language models, and also to explore using LLM's for learning, teaching, and research. Input these into your preferred LLM (without quotes) to see what results are generated. LLM's might produce interesting or useful answers in response to these prompts. Some of these prompts may be interesting or useful for discussions among and between humans. * "Describe to me how large language models can be utilized for learning, teaching, and research. Do this in an about 200 word two paragraph mini essay. Explain it to me like I am a freshman in community college." * "Give me a list of 12 ways that large language models can be utilized for learning, teaching, and research." * "How can LLM's be utilized to accelerate the pace of research and scientific discovery?" * "What are some ethical considerations related to large language models that should be considered?" * "What are some pros and cons to open source large language models? Will open source LLM's likely become more advanced the propriety LLM's eventually? What do you think?" * "What are some project ideas to integrate large language models in with humanoid robots, and/or other sorts of robots? Please give me 15 project ideas that can be relatively simple or extremely complex." * "Please search the Internet if possible. In what ways have university professors and academic researchers been using large language models in the last year? Please respond in list form." * "In what ways can large language models help programmers to code? Please provide me 8 examples and respond in list form." * "Can music be thought of a language within the realm of large language models?" * "What is differentiable computing and how does differentiable computing relate to large language models?" * "How can one fine tune an open source large language model?" * "What are some popular state of the art open source large language models. Please search the internet as helpful and respond to me in list form." * "Please give me a list of important terminology that I should be aware of when working with and training open source large language models. Please be comprehensive. Please respond in list form. And please search the internet as helpful." * "What sort of hardware should I utilize to run the most competent open source large language models that I want to utilize for learning, teaching, and research? Please search the internet as helpful." * "How can teachers utilize large language models to help accelerate student learning and to help students learn more efficiently? Please respond in list form." * "How can researchers utilize large language models to create theories, hypothesis, and to formulate potential research studies? Please respond in short paragraphs, but in list form." ==Readings and learning media== ===External=== * [https://stpp.fordschool.umich.edu/tags/large-language-models Large Language Models] - Articles * [https://hai.stanford.edu/news/how-large-language-models-will-transform-science-society-and-ai How Large Language Models Will Transform Science, Society, and AI] * [https://insights.sei.cmu.edu/blog/harnessing-the-power-of-large-language-models-for-economic-and-social-good-foundations/ Harnessing the Power of Large Language Models For Economic and Social Good: Foundations] * [https://courses.grainger.illinois.edu/CS447/sp2023/Slides/Lecture27.pdf Lecture 27: Intro to Large Language Models] ====Hugging Face NLP==== A course about natural language processing (NLP) using libraries from the Hugging Face ecosystem &ndash; Transformers, Datasets, Tokenizers, and Accelerate. : [https://huggingface.co/learn/nlp-course/chapter0/1 Natural Language Processing (NLP) course] :: [https://huggingface.co/learn/nlp-course/chapter1/1 transformer models] :: [https://huggingface.co/learn/nlp-course/chapter2/1 using transformers]: ::: [https://huggingface.co/learn/nlp-course/chapter2/2 pipeline], [https://huggingface.co/learn/nlp-course/chapter2/3 models], [https://huggingface.co/learn/nlp-course/chapter2/4 tokenizer], [https://huggingface.co/learn/nlp-course/chapter2/5 batching], decoding, padding, attention mask :: [https://huggingface.co/learn/nlp-course/chapter3/1 fine-tuning a pretrained model]: ::: preprocessing, map, [https://huggingface.co/docs/datasets/index dataset], dynamic padding, batch, collate function, train, predict, evaluate, [https://github.com/huggingface/accelerate accelerate] :: [https://huggingface.co/learn/nlp-course/chapter4/1 sharing models and tokenizers]: ::: hub, model card :: [https://huggingface.co/learn/nlp-course/chapter5/1 the datasets library]: ::: batch, DataFrame, validation, splitting, embedding, FAISS :: [https://huggingface.co/learn/nlp-course/chapter6/1 the tokenizers library]: ::: [https://huggingface.co/learn/nlp-course/chapter6/2 training tokenizer], grouping, QnA, [https://huggingface.co/docs/tokenizers/api/normalizers normalizers], pre-tokenization, [https://huggingface.co/docs/tokenizers/api/models models],[https://huggingface.co/docs/tokenizers/api/trainers trainers]: BPE, WordPiece, Unigram, [https://huggingface.co/docs/tokenizers/api/post-processors post processors], [https://huggingface.co/docs/tokenizers/components#decoders decoders] :: [https://huggingface.co/learn/nlp-course/chapter7/1 main nlp tasks]: ::: [https://huggingface.co/learn/nlp-course/chapter7/2 token classification], metrics, perplexity, [https://huggingface.co/learn/nlp-course/chapter7/4 translation], [https://huggingface.co/learn/nlp-course/chapter7/5 summarization], [https://huggingface.co/learn/nlp-course/chapter7/6 training CLM], [https://huggingface.co/learn/nlp-course/chapter7/7 QnA], :: [https://huggingface.co/learn/nlp-course/chapter8/1 how to ask for help] :: [https://huggingface.co/learn/nlp-course/chapter9/1 building and sharing demos] ==== Hugging Face docs ==== : https://huggingface.co/docs :: Core libraries ::: [https://huggingface.co/docs/transformers Transformers] &ndash; State-of-the-art ML for Pytorch, TensorFlow, and JAX. :::: [https://huggingface.co/docs/transformers/main_classes/pipelines#transformers.pipeline pipeline] &ndash; simple interface for inference with models. :::: [https://huggingface.co/docs/transformers/model_doc/auto#auto-classes Auto classes]: AutoConfig, AutoModel, and AutoTokenizer. The from_pretrained method. :::: [https://huggingface.co/docs/transformers//main_classes/trainer#transformers.Trainer Trainer] and [https://huggingface.co/docs/transformers/main_classes/trainer#transformers.TrainingArguments TrainingArguments] ::: [https://huggingface.co/docs/datasets Datasets] &ndash; Access and share datasets for computer vision, audio, and NLP tasks. ::: [https://huggingface.co/docs/accelerate Accelerate] &ndash; Easily train and use PyTorch models with multi-GPU, TPU, mixed-precision. ::: [https://huggingface.co/docs/tokenizers Tokenizers] &ndash; Fast tokenizers, optimized for both research and production. :: [https://huggingface.co/docs/hub Hub] &ndash; Host Git-based models, datasets and Spaces on the Hugging Face Hub. :: [https://huggingface.co/docs/diffusers Diffusers] &ndash; State-of-the-art diffusion models for image and audio generation in PyTorch. :: [https://huggingface.co/docs/huggingface_hub Hub Python Library] &ndash; Client library for the HF Hub: manage repositories from your Python runtime. :: [https://huggingface.co/docs/huggingface.js Huggingface.js] &ndash; A collection of JS libraries to interact with Hugging Face, with TS types included. :: [https://huggingface.co/docs/transformers.js Transformers.js] &ndash; Community library to run pretrained models from Transformers in your browser. :: [https://huggingface.co/docs/api-inference Inference API (serverless)] &ndash; Experiment with over 200k models easily using the serverless tier of Inference Endpoints. :: [https://huggingface.co/docs/inference-endpoints Inference Endpoints (dedicated)] &ndash; Easily deploy models to production on dedicated, fully managed infrastructure. :: [https://huggingface.co/docs/peft PEFT] &ndash; Parameter efficient fine-tuning methods for large models ::: Soft prompting, LoRA, IA3 :: [https://huggingface.co/docs/optimum Optimum] &ndash; Fast training and inference of HF Transformers with easy to use hardware optimization tools. :: [https://huggingface.co/docs/optimum-neuron AWS Trainium &amp; Inferentia] &ndash; Train and Deploy Transformers &amp; Diffusers with AWS Trainium and AWS Inferentia via Optimum :: [https://huggingface.co/docs/evaluate Evaluate] &ndash; Evaluate and report model performance easier and more standardized. ::: types: metrics, comparisons, measurements :: [https://huggingface.co/tasks Tasks] ::: extraction, question answering, classification, generation ... :: [https://huggingface.co/docs/dataset-viewer Dataset viewer] &ndash; API to access the contents, metadata and basic statistics of all Hugging Face Hub datasets. ::: Splits and subsets, [https://github.com/huggingface/dataset-viewer dataset-viewer] :: [https://huggingface.co/docs/trl TRL] &ndash; Transformer Reinforcement Learning ::: reward modeling, fine-tuning, optimizations, :: [https://huggingface.co/docs/sagemaker Amazon SageMaker] &ndash; Train and Deploy Transformer models with Amazon SageMaker and Hugging Face Deep Learning Containers (DLC). :: [https://huggingface.co/docs/timm timm] &ndash; Pytorch Image Models. ::: State-of-the-art computer vision models, layers, optimizers, training/evaluation, and utilities. :: [https://huggingface.co/docs/safetensors Safetensors] &ndash; Simple, safe way to store and distribute neural networks weights. :: [https://huggingface.co/docs/text-generation-inference Text Generation Inference] &ndash; Toolkit to serve Large Language Models. :: [https://huggingface.co/docs/autotrain AutoTrain] &ndash; AutoTrain API and UI. ::: [https://huggingface.co/autotrain autotrain] :: [https://huggingface.co/docs/text-embeddings-inference Text Embeddings Inference] &ndash; Toolkit to serve Text Embedding Models. :: [https://huggingface.co/docs/competitions Competitions] &ndash; Create your own competitions on Hugging Face. :: [https://huggingface.co/docs/bitsandbytes Bitsandbytes] &ndash; Toolkit to optimize and quantize models. :: [https://huggingface.co/docs/optimum-tpu Google TPUs] &ndash; Deploy models on [https://cloud.google.com/tpu/docs Google TPUs] via Optimum. :: [https://huggingface.co/docs/chat-ui Chat UI] &ndash; Open source chat frontend, powers the [https://huggingface.co/chat HuggingChat] app. :: [https://huggingface.co/docs/leaderboards Leaderboards] &ndash; Create your own Leaderboards on Hugging Face. :: [https://huggingface.co/docs/hugs Hugging Face Generative AI Services (HUGS)] &ndash; optimized, zero-configuration inference microservices designed to simplify and accelerate the development of AI applications with open models. ===Videos=== * [https://www.youtube.com/watch?v=5sLYAQS9sWQ How Large Language Models Work] * [https://www.youtube.com/watch?v=JhCl-GeT4jw Large Language Models and The End of Programming - CS50 Tech Talk with Dr. Matt Welsh] * [https://www.youtube.com/watch?v=yBI1nPep72Q LMStudio Tutorial Run ANY Open-Source Model LOCALLY] * [https://www.youtube.com/watch?v=UU1WVnMk4E8 Create a Large Language Model from Scratch with Python – Tutorial] * [https://www.youtube.com/watch?v=eC6Hd1hFvos Fine-tuning Large Language Models (LLMs) | w/ Example Code] ===Wikipedia=== {{colbegin|5}} * [[w:Large language model|Large language model]] * [[w:Prompt engineering|Prompt engineering]] * [[w:GPT-4|GPT-4]] * [[w:Category:Large language models|Category:Large language models]] * [[w:LLaMA|LLaMA]] * [[w:Mistral AI|Mistral AI]] * [[w:Foundation model|Foundation model]] * [[w:Natural-language understanding|Natural-language understanding]] * [[w:Ethics of artificial intelligence|Ethics of artificial intelligence]] * [[w:Artificial general intelligence|Artificial general intelligence]] * [[w:Intelligence amplification|Intelligence amplification]] * [[w:Outline of artificial intelligence|Outline of artificial intelligence]] * [[w:Synthetic intelligence|Synthetic intelligence]] * [[w:Weak artificial intelligence|Weak artificial intelligence]] * [[w:History of artificial intelligence|History of artificial intelligence]] * [[w:Timeline of artificial intelligence|Timeline of artificial intelligence]] * [[w:Progress in artificial intelligence|Progress in artificial intelligence]] * [[w:History of natural language processing|History of natural language processing]] * [[w:Hardware for artificial intelligence|Hardware for artificial intelligence]] * [[w:AI safety|AI safety]] * [[w:Neural scaling law|Neural scaling law]] * [[w:Philosophy of artificial intelligence|Philosophy of artificial intelligence]] * [[w:Philosophy of mind|Philosophy of mind]] * [[w:Computational theory of mind|Computational theory of mind]] * [[w:Regulation of artificial intelligence|Regulation of artificial intelligence]] * [[w:LangChain|LangChain]] * [[w:Generative pre-trained transformer|Generative pre-trained transformer]] * [[w:GitHub Copilot|GitHub Copilot]] * [[w:ChatGPT|ChatGPT]] * [[w:Generative artificial intelligence|Generative artificial intelligence]] * [[w:Category:Generative artificial intelligence|Category:Generative artificial intelligence]] * [[w:Music and artificial intelligence|Music and artificial intelligence]] * [[w:Workplace impact of artificial intelligence|Workplace impact of artificial intelligence]] * [[w:Applications of artificial intelligence|Applications of artificial intelligence]] * [[w:Artificial intelligence in Wikimedia projects|Artificial intelligence in Wikimedia projects]] * [[w:Wikipedia:Artificial intelligence|Wikipedia:Artificial intelligence]] * [[w:Artificial intelligence in healthcare|Artificial intelligence in healthcare]] * [[w:Automated reasoning|Automated reasoning]] * [[w:Machine learning in physics|Machine learning in physics]] * [[w:Quantum neural network|Quantum neural network]] * [[w:ChatGPT in education|ChatGPT in education]] * [[w:Artificial intelligence content detection|Artificial intelligence content detection]] * [[w:Turing test|Turing test]] * [[w:List of datasets for machine-learning research|List of datasets for machine-learning research]] * [[w:Fine-tuning (deep learning)|Fine-tuning (deep learning)]] * [[w:Attention (machine learning)|Attention (machine learning)]] * [[w:Mixture of experts|Mixture of experts]] * [[w:Gemini (language model)|Gemini (language model)]] * [[w:Auto-GPT|Auto-GPT]] * [[w:VideoPoet|VideoPoet]] {{colend}} ==See also== * [[Artificial intelligence]] * [[Artificial Intelligence & Machine Learning]] * [[Artificial Intelligence and Robotics Laboratory]] * [[Computer science]] * [[Artificial Consciousness]] * [[Supersymmetric Artificial Neural Network]] * [[History of artificial intelligence]] [[Category: Computer science]] [[Category: Machine learning]] [[Category: Artificial intelligence]] 2m102aqhqzsutp166z7oah5231vg6mt Does Israel commit genocide in Israel–Hamas war? 0 305611 2683997 2633042 2024-11-11T21:30:28Z Jaredscribe 2906761 [[Guidelines#Neutral_point_of_view]] 2683997 wikitext text/x-wiki {{Wikidebate}} Disclaimer: Getting the debate right about this highly controversial/emotionally charged topic is difficult, given it is written by non-professionals and is not reviewed by professionals. ==Israel commits genocide in Israel–Hamas war== ===Pro=== * {{Argument for}} The commitment of genocide is plausible per preliminary ruling of International Court of Justice (ICJ), as per [[Wikipedia: Allegations of genocide in the 2023 Israeli attack on Gaza]]. ** {{Objection}} Mere plausibility is far removed from establishing the truth of the accusation. * {{Argument for}} Arguably, the rather indiscriminate large-scale bombing of civilian infrastructure creates conditions for large-scale loss of life by starvation, etc., and it is hard to see how this is not part of the intent. ** {{Objection}} If Egypt allows Gazans as refugees into its territory (an if) and if international aid can be provided there, starvation should be avoidable. Therefore, starvation is not necessary outcome. *** {{Comment}} Then, it is at least ethnic cleansing, creating conditions that make it hard for Gazans to return to their homes after the conflict. ===Con=== * {{Argument against}} Genocide is a technical term and cannot be decided using lay understanding and analysis. The motion should therefore be dismissed, not because it is necessarily false, but rather because it is not fit for the kind of lay analysis attempted in a Wikidebate. ** {{Objection}} This proposition assumes that all wikidebate participants in the past, present and future cannot possibly complete "expert technical analysis", which is not necessarily true. * {{Argument against}} Israel is attacking Hamas, not civilians; the civilians are collateral damage. * {{Argument against}} Expanding on the above, if Israel was attacking civilians at large scale with the intent to decimate the Gaza population as much as possible, there would be much huger loss of Gazan life. Even with the Hamas-stated loss of 35,562 Gazan lives (May 21)<ref>[[Wikipedia: Casualties of the Israel–Hamas war]]</ref> (possibly inaccurate, and some of them are likely members of Hamas rather than civilians), that amounts to 1.5% of the Gaza population of 2,375,259<ref>[[Wikipedia: Gaza Strip]]</ref>. ** {{Objection}} In so far as the definition of genocide allows destruction of the group ''in part'', even such a relatively low percentage can fit the bill. ** {{Objection}} If all it took to bar the genocide claim was to claim that the people killed make up a small percentage of the targeted population, ICJ would have never declared genocide to be ''plausible''. * {{Argument against}} Expanding on the above, as per Times of Israel, the combatant-to-civilian ratio in the war is 13:17, a witness to aim to protect civilian life (the ratio is made using Hamas-supplied total casualties and Israel-supplied Hamas combatant casualties).<ref>[https://www.timesofisrael.com/the-genocide-claim-against-israel-doesnt-add-up/ The genocide claim against Israel doesn't add up | The Times of Israel], 2 June 2024, timesofisrael.com</ref> ** {{Objection}} The source of the ratio is not neutral/independent. == Have Hamas, Palestinian Islamic Jihad, and their allies attempted genocide of the Jewish people? == === Pro - yes, they attempted genocide of the Jews === === Con - no, they merely tried to conquer Israel and free Palestine === ==References== <references/> ==Further reading== Wikipedia and Wikisource: * {{W|Allegations of genocide in the 2023 Israeli attack on Gaza}}, wikipedia.org * {{W|Palestinian genocide accusation}}, wikipedia.org -- this is not specifically about the Israel–Hamas war * [[Wikisource: South Africa v. Israel (Order of 26 January 2024)]] Non-Wikipedia: * [https://www.quora.com/Do-you-believe-that-Israel-is-committing-genocide-in-Gaza-against-Palestinians Do you believe that Israel is committing genocide in Gaza against Palestinians?], quora.com * [https://www.bbc.com/news/world-middle-east-68667556 Gaza war: UN rights expert accuses Israel of acts of genocide], bbc.com * [https://www.ajc.org/news/israel-is-not-committing-genocide Israel Is Not Committing Genocide], American Jewish Committee, ajc.org * [https://www.aei.org/op-eds/israel-is-not-committing-genocide-in-gaza/ Israel Is Not Committing “Genocide” in Gaza], American Enterprise Institute, aei.org * [https://www.commondreams.org/opinion/israel-is-committing-genocide-in-gaza Opinion | It’s Not Complicated: Israel is Committing Genocide in Gaza], commondreams.org [[Category:Israel]] l8rssz8ldjvu8w33q0yrwe0eoy3h615 Motivation and emotion/Book/2024/Comprehensive action determination model 0 305986 2684056 2683445 2024-11-12T00:10:47Z Jtneill 10242 /* Overview */ Move scenario 2684056 wikitext text/x-wiki {{title|Comprehensive action determination model:<br>What is the CADM and how can it be applied to understanding human motivation?}} <div align=center></div> {{MECR3|1=https://youtu.be/Fde1L08wMl4}} <div align=center></div> __TOC__ ==Overview== {{RoundBoxTop|theme=3}}{{Image|float=right|pad=20px|name=Footprint water.png|width=300px|caption=Figure 1: Water footprint}}'''Scenario:''' You're exploring how university students’ water use habits relate to their broader attitudes towards sustainability. Specifically, you’ve noticed that some students leave taps running or wastewater during breaks, and you want to understand why this happens. You’re curious about the internal and external factors that influence this behaviour, like whether students are unaware of the environmental impact of their actions, or if they just don’t prioritize sustainability in their daily routines. Additionally, you want to investigate how their broader attitudes toward the environment influence their actions. You have come across an “integrated model” of behaviour. This model combines elements from various theories to provide a more comprehensive understanding of how people act. You think this model could be useful for analysing why students might neglect simple conservation practices like turning off taps, despite being able to adopt more sustainable habits. {{RoundBoxBottom}} The Comprehensive Action Determination Model is a theoretical framework designed to explain human behaviour. It proposes that behaviour is directly predicted by three processes: habitual, situational, and intentional, and indirectly influenced by normative processes. This complex model can aid research in understanding human motivation by breaking down the processes, evaluating the outcomes, and examining the underlying context behind behaviour. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What is motivation? * Why is understanding motivation important? * What is the Comprehensive Action Determination Model (CADM)? * What are the underpinning theories behind the CADM? * How can the CADM be applied to understanding human motivation? {{RoundBoxBottom}} == What is Motivation? == [[File:Maslow's Hierarchy of Needs.svg|thumb|442x442px|Figure 2: Pyramid depicting the structure of Maslow's hierarchy of needs. ]] To understand [[motivation]], we must first define behaviour. Behaviour can be defined as the way an individual acts, the way they talk, the way they communicate, and how they conduct themselves. Essentially, behaviour encompasses all our actions. Motivation, on the other hand, is the "why" behind our behaviour — the reasons underlying why we act in certain ways. Theorists explain motivation as the attribute that moves us to do or not to do something (Lai, 2011). The word ''motivation'' comes from the Latin verb ''movere'', meaning "to move." This is a fitting term, as motivation is what moves a person to make certain choices, act, expend effort, and persist in those actions (Dörnyei & Ushioda, 2021). Motivation also has significant effects on our [[Emotion|emotions]]. For example, when individuals achieve their set goals, they experience joy and satisfaction, which can further drive motivation in the future. However, the reverse can also occur: a lack of motivation can lead to negative emotions and frustration toward a certain behaviour, which may then affect future behaviour (Bradley & Lang, 2007). Motivation is said to have three important components that drive behaviour: direction, intensity, and persistence. Direction refers to how motivation influences the choices we make and the goals we set. Intensity refers to how motivation influences how hard we work toward achieving our goals. Finally, persistence refers to how motivation affects how long we continue to work toward our goals (Dörnyei & Ushioda, 2021). Over the years, many theories have been developed to understand motivation. These include Herzberg's [[wikipedia:Two-factor_theory|Two-Factor Theory]] (Herzberg et al., 1959; Herzberg et al., 2011), [[Self-determination theory|Self-Determination Theory]] (Deci, 1972, 2000), and probably the most famous of them all, [[wikipedia:Maslow's_hierarchy_of_needs|Maslow's Hierarchy of Needs]] (Maslow, 1943). As depicted in Figure 2, Maslow’s hierarchy is a 5-step pyramid where "higher" needs (such as self-actualization) can only be achieved by satisfying "lower" order needs (such as physiological needs). Theorists argue that it is unrealistic to create an elaborate super-theory to understand motivation due to its complexity and the countless variables that affect it. They contend that the complexity of motivation cannot be fully understood through a single theory or model (Dörnyei & Ushioda, 2021). So, how can we understand human motivation? Are there any theories or models that can be applied to this complex phenomenon? == Comprehensive Action Determination Model (CADM) == The Comprehensive Action Determination Model was first proposed by Klöckner and Blöbaum in 2010 (Klöckner & Blöbaum, 2010). They argue that one of the main goals of [[environmental psychology]] is to understand what determines people's actions, particularly in relation to environmental influences. Klöckner and Blöbaum also note that several well-established models—or, as they term them, "action models" or "action determination models"—have been proposed. However, none of these models alone provide an adequate representation of the multiple factors that determine behaviour (Klöckner & Blöbaum, 2010). They further argue that integrated approaches combining two models—the [[wikipedia:Theory_of_planned_behavior|Theory of Planned Behaviour]] (Ajzen, 1991) and the Norm-Activation Model (Schwartz, 1977)—have shown promise (Onwezen et al., 2013; Liu et al., 2017), especially when the concept of [[wikipedia:Habit|habit]] is incorporated (Klöckner et al., 2003). Additionally, Klöckner and Blöbaum highlight that the Ipsative Theory of Behaviour offers a valuable perspective on the situational determination of behaviour (Klöckner & Blöbaum, 2010). However, while these theories (the Theory of Planned Behaviour and the Norm-Activation Model) have proven successful in specific domains, all models exhibit limitations in other areas (Klöckner & Blöbaum, 2010). The CADM unifies the Theory of Planned Behaviour, the Norm-Activation Model, the Ipsative Theory of Behavior, and the concept of habit into one integrated framework. Klöckner and Blöbaum propose that combining these existing theories into a single model may result in a more universally applicable framework that accounts for all relevant factors and influences affecting behavior, thereby providing a comprehensive explanation of behavioral outcomes (Klöckner & Blöbaum, 2010). === Underpinning theories of CADM: === To understand the comprehensive action determination model, we must first understand the underpinning models, theories and theoretical concepts. As stated in the previous paragraph these are the theory of planned behaviour, the Norm-activation model, the Ipsative theory of behaviour and the theoretical concept of habit. ==== Theory of Planned Behaviour: ==== [[File:Theory of planned behaviour.png|thumb|405x405px|Figure 3: Flow diagram of the Theory of Planned Behaviour ]] The [[wikipedia:Theory_of_planned_behavior|Theory of Planned Behaviour]] was first proposed by Ajzen in 1991 (Ajzen, 1991). The theory consists of three constructs: behavioural intention, attitude toward behaviour, and subjective norms. Firstly, behavioural intention refers to the motivation behind a behaviour; the stronger the intention, the more likely the behaviour is to be performed. Secondly, attitude refers to how positively or negatively a person evaluates a specific behaviour. Thirdly, subjective norms refer to the social pressures to perform or not perform a given behaviour. Perceived behavioural control is also a key construct in the Theory of Planned Behaviour, and it refers to how a person perceives the difficulty of performing a specific behaviour (Asare, 2015). The theory suggests that attitudes toward the behaviour, subjective norms, and perceived behavioural control all influence behavioural intention, which in turn leads to behaviour, as depicted in Figure 3. Klockner and Blobaum (2010) argue that the Theory of Planned Behaviour focuses too much on intention while neglecting the role of objective situational constraints, habits, and personal norms. ==== Norm-Activation Model: ==== The Norm-Activation Model was first proposed by Schwartz in 1977 (Schwartz, 1977). The model suggests that behaviour is predicted by personal norms. Schwartz (1977) defines personal norms as “feelings of moral obligation, not as intentions” (Onwezen et al., 2013). The model posits that personal norms are influenced by two factors: awareness of consequences and awareness of needs (sometimes referred to as the ascription of responsibility). Awareness of consequences refers to the understanding that performing or not performing a certain behaviour leads to specific outcomes. Awareness of needs involves the feeling of responsibility to perform a particular behaviour (Onwezen et al., 2013; Klöckner & Blöbaum, 2010). As depicted in Figure 4, both awareness of consequences and awareness of needs predict personal norms, which in turn predict behaviour. Klockner and Blobaum (2010) identify limitations of the model, stating that “The Norm-Activation Model focuses on personal norms but underestimates the roles of habits, intentions, attitudes, and the situational context.” [[File:Norm activation model.png|center|thumb|610x610px|Figure 4: Flow diagram of the Norm-Activation Model ]] ==== Ipsative Theory of Behaviour: ==== The Ipsative theory of behaviour was proposed by Frey (1988). The theory suggests that a person's behaviour can be limited or obstructed by the absence of genuine or perceived opportunities, influenced by both internal and external circumstances (Tanner, 1999). The theory consists of three presumptions about human behaviour. Firstly, objective constraints are assumed to influence behaviour. These constraints determine what a person can do, what they ought to do, or what they are permitted to do within a specific society. These variables make up the "objective possibility set," which limits or hinders people's ability to engage in certain activities. Notably, these constraints exist independently of individual perceptions (Tanner, 1999). Secondly, ipsative constraints prevent the activation of alternative behaviours. Ipsative constraints form the "ipsative possibility set," which individuals regard as relevant to their behavioural decisions (Tanner, 1999; Klockner & Blobaum, 2010). Finally, subjective constraints are believed to directly affect preferences rather than determining participation in specific actions. In essence, they influence a person's willingness to act (Tanner, 1999). Klockner and Blobaum (2010) argue that while the Ipsative theory of behaviour effectively outlines the objective and subjective aspects of situations as predictors of behaviour, it overlooks intentional, habitual, and normative processes. ==== Habits: ==== The theoretical concept of [[wikipedia:Habit|habit]] was incorporated into the CADM to address limitations found in the Theory of Planned Behaviour and the Norm-Activation Model in predicting repetitive behaviours (Klockner & Blobaum, 2010). Habits can be defined as learned tendencies to repeat previous behaviours. They are activated by contextual elements that are often linked to past performances, such as specific locations, preceding actions in a sequence, and particular individuals (Woods & Neal, 2007). The concept of habit was added to account for structural differences between actions that are frequent and those that are rare or performed for the first time. When decisions are frequently made with satisfying outcomes, the influence of decision-making in given situations decreases, resulting in more automated behavioural patterns (Triandis, 1979; Klockner & Blobaum, 2010). Klockner and Blobaum (2010) note that although the concept of habit recognizes the interaction between intentions and habits, it does not fully account for non-automatic situational facilitation, constraints on behaviour, or normative processes. === How does the CADM work? === The Comprehensive Action Determination Model proposes that behaviour is determined by three possible direct sources or processes: habitual, intentional, and situational as depicted in figure 5. Habitual processes include schemata, heuristics, and associations of behaviour; intentional processes include attitudes and intentions behind behaviour; and situational processes include both objective and subjective constraints on behaviour. A fourth process, the normative process, is also present, but it does not directly affect behaviour. Instead, it influences intentional and habitual processes. The normative process includes social norms, personal norms, and awareness of needs and consequences. Klockner and Blobaum (2010) explain that attitudes, subjective constraints (e.g., [[wikipedia:Perceived_control|perceived behavioural control]]), and personal and social norms are used to generate intentions. They further explain that attitudes reflect cognitive and emotional beliefs about behaviour, while perceived behavioural control represents beliefs about the degree of control or determination one has over their actions. Additionally, personal and social norms shape the moral framework that guides the decision-making process leading to behaviour. Personal norms are rooted in an individual’s value system and can be seen as the motivations behind decision-making (Klockner & Blobaum, 2010). All these factors integrate in what Klockner and Blobaum (2010) describe as the "integrating stage," which generates intentions just before behaviour occurs. However, the normative process also influences habits, as it has higher temporal stability compared to attitudes and perceived behavioural control. Situational processes and perceived behavioural control are also thought to activate personal norms by creating awareness of needs and consequences, which then generate the formation of intentions. Habitual and situational processes are believed to interfere with intentional processes and can moderate the influence of intentions on behaviour. Perceived behavioural control is essential for activating both normative and intentional processes. As a result, situational influences affect both normative and intentional processes. Furthermore, habits are said to form through the successful execution of behaviour in specific situations, meaning situational processes also influence habitual behaviours. Finally, behaviour influences changes in personal norms, and habits, in turn, affect future behaviour (Klockner & Blobaum, 2010). [[File:Comprehensive action determination model.png|center|thumb|508x508px|Figure 5: Simplified flow diagram of the Comprehensive Action Determination Model ]] {{RoundBoxTop|theme=7}}{{image|name= Comprehensive Action Determination Model water usage behaviour.png|width=450px|pad=20px|caption=Figure 6: Detailed flow diagram of Comprehensive Action Determination Model In context to water usage behaviours|float=right}}'''Example:''' Utilizing the scenario presented at the start of the chapter, we can apply the Comprehensive Action Determination Model to analyse the situation in greater depth (Figure 6). According to Klockner and Blobaum (2010), behaviour is primarily predicted by intentions and perceived behavioural control. Intentions, in turn, are generated from perceived behavioural control, social norms, and attitudes. In this scenario, habitual processes, such as water usage habits, directly predict the likelihood of engaging in water conservation efforts and moderate the relationship between intention and conservation behaviour. While personal norms are identified as predictors of intention, they do not directly predict conservation behaviour. Personal norms are shaped by awareness of environmental needs and consequences and are activated through perceived behavioural control, which creates a sense of moral obligation. Moreover, social norms influence personal norms, as they are internalized from broader societal expectations and adapted into an individual’s value system (Klockner & Blobaum, 2010). Personal norms, being a stable psychological construct, also influence the formation of habits. Klockner and Blobaum (2010) further argue that both subjective constraints (such as perceived behavioural control) and objective constraints (such as access to water-saving tools or technologies) are direct predictors of conservation behaviour. Since habits tend to demonstrate long-term stability, water usage habits (a habitual process) should be influenced by perceived behavioural control and the availability of water-saving options. Both perceived behavioural control and access to water-saving technologies also act as mediators in the relationship between intention and water conservation behaviour. In other words, individuals’ intentions to conserve water are likely influenced by their existing water-related habits and the perceived control they have over their water usage. Finally, conservation behaviour feeds back onto personal norms and habits {{RoundBoxBottom}} === Current research on the CADM: === Since its proposal in 2010, the Comprehensive Action Determination Model has gained some traction in recent literature. The research on this model is primarily focused on environmental behaviour (link to wiki) (Klockner, 2013). Environmental behaviour refers to actions, attitudes, and practices related to the environment. It encompasses how people interact with their physical surroundings, how they perceive environmental issues, and how their behaviours impact the environment, either positively or negatively. Current research applying the CADM includes studies on sustainable farming (Tan, 2024), food waste behaviour (Cheng et al., 2024), reducing personal clothing consumption (Joanes et al., 2020), and recycling behaviours (Klockner & Oppedal, 2011; Fang et al., 2021; Ofstad et al., 2017). Research conducted by Tan (2024) on sustainable farming found that the CADM was the most effective model for analysing and predicting persistent agricultural practices, contributing to a deeper understanding of behavioural determinants in sustainable agriculture. Cheng and colleagues (2024) also found the CADM to be effective in exploring food waste behaviours. The model showed positive results in studies of recycling behaviour (Klockner & Oppedal, 2011; Fang et al., 2021; Ofstad et al., 2017) and clothing consumption (Joanes et al., 2020). Although the CADM has shown notable success in recent applications and studies, it is important to recognize that the existing body of literature remains relatively limited. As such, there is a pressing need for further research to enhance the generalizability of these findings and ensure their applicability across a broader range of contexts and scenarios. === Limitations to the CADM: === The Comprehensive Action Determination Model has two notable limitations: complexity and being data intensive. The model’s complex nature can be seen as a significant drawback. It can be difficult to interpret initially, as it combines elements from the Theory of Planned Behaviour, the Norm-Activation Model, the Ipsative Theory of Behaviour, and the concept of habit. This complexity is further compounded by the presence of numerous variables that not only influence each other but also interact in intricate ways, with some variables acting as mediators, moderators, or both. These interrelationships make it challenging to fully understand how each factor contributes to the overall behaviour being studied. The interplay between these variables often requires careful analysis to untangle their individual and combined effects on the model’s outcomes. The complex nature of the CADM may not be practical in situations where quick decisions are needed, as the analysis of CADM is typically too thorough for such rapid decision-making. Secondly, the model is limited by its data-intensive nature. As noted earlier, its complexity means that analysing each variable within the dataset can be challenging. This data analysis process is often time-consuming and labour-intensive, making it difficult to replicate the model with different populations or in various contexts. The need for large, detailed datasets also poses challenges for scalability and generalization, further complicating its application across diverse groups or settings. As a result, its practical use may be constrained in environments where data availability is limited or where the computational resources required for analysis are not feasible. == CADM and understanding human motivation == === Examining context: === The comprehensive action determination model allows researchers to examine the context behind human behaviour. Examining the context behind our behaviour helps researchers gain deeper insights into the motivations that drive specific behaviours. Furthermore, it allows researchers to assess the strength of the motivation in relation to the context. Additionally, Normative process such as personal norms and social norms are known to influence intentions which lead to behaviour. Based on the behaviour, researchers can identify if social norms such as cultural norms or societal expectations have a stronger influence on intentions more than personal norms, even though it is said by Klockner and Blobaum (2010) that personal norms are affected by social norms. The use of the CADM in behavioural research provides a framework for breaking down the contexts underlying behaviours and the motivations that are involved, offering valuable insights into both individual and collective action. === Evaluating outcomes: === Using the Comprehensive Action Determination Model in longitudinal studies helps researchers explore how past behaviours influence future actions. By following participants over time, these studies offer insights into how behaviours, habits, and perceived control in specific situations shape future behaviour. The CADM allows researchers to track patterns and identify the motivations driving behaviour change. One key area where CADM is valuable is studying habit formation. Repeated behaviours can become automatic over time, requiring less mental effort and fostering a sense of control. The model helps explain how certain behaviour turn into habits by examining past actions, the emotional and cognitive states tied to them, and the environments in which they occur. Researchers can track how habits develop, strengthen, or fade, and how they motivate future decisions. The CADM also emphasizes the role of feedback loops in behaviour change. Positive or negative outcomes from past behaviours can strengthen or weaken future actions. These feedback loops can either reinforce existing behaviours or lead to changes. The model allows researchers to trace these feedback mechanisms and how they impact future behaviour. By using CADM in longitudinal studies, researchers can better understand how past behaviour’s motivate future actions. This approach sheds light on the role of habits, perceived control, situational factors, and feedback in shaping behaviour over time. The insights gained can help develop more effective strategies for behaviour change and intervention, providing a deeper understanding of the factors that motivate long-term behaviour. === Understanding behavioural processes: === The Comprehensive Action Determination Model offers a valuable framework for understanding human motivation by systematically breaking down the various behavioural processes that drive actions. This model allows researchers to dissect the factors influencing motivation at different stages, such as habitual and situational processes. By applying the CADM, studies can identify specific points in the motivational process where individuals may excel such as during moments of strong goal commitment or accomplishment as well as areas where motivation may falter, such as in the face of adversity or lack of support. The CADM provides a deeper understanding of how different variables interact to either enhance or undermine motivation, ultimately helping to design more effective strategies for fostering sustained effort and engagement across various contexts. == Conclusion == Motivation is the fundamental "why" behind everything we do; it fuels our drive to pursue goals, overcome challenges, and sustain effort over time. It is the explanation behind our behaviour. Understanding motivation is important because it helps us identify the driving forces behind behaviour. The Comprehensive Action Determination Model explains how individuals make decisions in relation to habitual, intentional, situational and normative processes, all of which affect each other in complex ways. The CADM integrates preexisting "action determination models," such as the Theory of Planned Behaviour, the Norm-Activation Model, the Ipsative Theory of Behaviour, and the theoretical concept of habit, into what is believed to be a comprehensive model of behaviour. The CADM can be applied to understanding human motivation by examining the context behind our behaviour and the underlying motives that influence such contexts. It can be used to evaluate outcomes to investigate how past behaviour can motivate and shape future actions. Finally, by understanding the behavioural processes within the CADM, researchers can identify where motivation may excel or falter, depending on the outcomes of behaviour. Motivation is the core driver of our behaviour, influencing how we set and achieve goals. The Comprehensive Action Determination Model helps explain how motivation interacts with various factors like habits, intentions, and situational influences. By understanding this model, we can gain insight into the underlying motives behind our actions and improve decision-making, ultimately shaping future behaviour. ==Learning features== <quiz display="simple"> {Motivation is a predictor of behaviour: |type="()"} + True - False {Exploring correlations between variables relating to certain behaviour is an application to the CADM |type="()"} + True - False </quiz> ==See also== * [[Motivation and emotion/Book/2013/Environmental behaviour|Environmental behaviour]] (Book chapter, 2013) * [[Motivation and emotion/Book/2024/Environmental cues and habits|Environmental cues and habits]] (Book chapter, 2024) * [[Motivation and emotion/Book/2015/Extrinsic motivation and antisocial behaviour in children|Extrinsic motivation and antisocial behaviour in children]] (Book chapter, 2015) ==References== {{Hanging indent|1=Ajzen, I. (1991). The Theory of planned behavior. Organizational Behavior and Human Decision Processes. Asare, M. (2015). USING THE THEORY OF PLANNED BEHAVIOR TO DETERMINE THE CONDOM USE BEHAVIOR AMONG COLLEGE STUDENTS. American Journal of Health Studies, 30(1), 43. Bradley, M. M., & Lang, P. J. (2007). Emotion and motivation. In J. T. Cacioppo, L. G. Tassinary, & G. G. Berntson (Eds.), Handbook of psychophysiology (3rd ed., pp. 581–607). Cambridge University Press. https://doi.org/10.1017/CBO9780511546396.025 Cheng, X., Zhang, J., & Li, W. (2024). What shapes food waste behaviors? New insights from a comprehensive action determination model. Waste Management, 181, 188–198. https://doi.org/10.1016/j.wasman.2024.04.017 Deci, E. L. (1971). Effects of externally mediated rewards on intrinsic motivation. Journal of Personality and Social Psychology, 18(1), 105–115. https://doi.org/10.1037/h0030644 Fang, W.-T., Huang, M.-H., Cheng, B.-Y., Chiu, R.-J., Chiang, Y.-T., Hsu, C.-W., & Ng, E. (2021). Applying a Comprehensive Action Determination Model to Examine the Recycling Behavior of Taipei City Residents. Sustainability, 13(2), 490–490. https://doi.org/10.3390/su13020490 Frey, B. S. (1988). Ipsative and objective limits to human behavior. Journal of Behavioral Economics, 17(4), 229–248. https://doi.org/10.1016/0090-5720(88)90012-5 Frey, B.S. (1992). An Ipsative Theory of Human Behaviour. In: Economics As a Science of Human Behaviour. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1374-0_12 Herzberg, F., Mausner, B., & Snyderman, B. B. (2011). The motivation to work. Herzbert, F., Mausner, B., & Snyderman, B. (1959). The Motivation to Work. Nueva York. Joanes, T., Gwozdz, W., & Klöckner, C. A. (2020). Reducing personal clothing consumption: A cross-cultural validation of the comprehensive action determination model. Journal of Environmental Psychology, 71, 101396–101396. https://doi.org/10.1016/j.jenvp.2020.101396 Klöckner, C. A. (2013). A comprehensive model of the psychology of environmental behaviour—A meta-analysis. Global Environmental Change, 23(5), 1028–1038. https://doi.org/10.1016/j.gloenvcha.2013.05.014 KLöckner, C. A., Matthies, E., & Hunecke, M. (2003). Problems of Operationalizing Habits and Integrating Habits in Normative Decision‐Making Models1. Journal of Applied Social Psychology, 33(2), 396–417. https://doi.org/10.1111/j.1559-1816.2003.tb01902.x Klöckner, C. A., & Oppedal, I. O. (2011). General vs. domain specific recycling behaviour—Applying a multilevel comprehensive action determination model to recycling in Norwegian student homes. Resources Conservation and Recycling, 55(4), 463–471. https://doi.org/10.1016/j.resconrec.2010.12.009 Lai, E. R. (2011). Motivation: A literature review. Person Research’s Report, 6, 40-41. Liu, Y., Sheng, H., Mundorf, N., Redding, C., & Ye, Y. (2017). Integrating Norm Activation Model and Theory of Planned Behavior to Understand Sustainable Transport Behavior: Evidence from China. International Journal of Environmental Research and Public Health, 14(12), 1593–1593. https://doi.org/10.3390/ijerph14121593 Maslow, A. H. (1943). A theory of human motivation. Psychological Review google scholar, 2, 21-28. Ofstad, S., Tobolova, M., Alim Nayum, & Klöckner, C. (2017). Understanding the Mechanisms behind Changing People’s Recycling Behavior at Work by Applying a Comprehensive Action Determination Model. Sustainability, 9(2), 204–204. https://doi.org/10.3390/su9020204 Onwezen, M. C., Antonides, G., & Bartels, J. (2013). The Norm Activation Model: An exploration of the functions of anticipated pride and guilt in pro-environmental behaviour. Journal of Economic Psychology, 39, 141–153. https://doi.org/10.1016/j.joep.2013.07.005 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Schwartz, S. H. (1977). Normative Influences on Altruism. Advances in Experimental Social Psychology, 221–279. https://doi.org/10.1016/s0065-2601(08)60358-5 Tan, J. J. H. (2024). Sustaining Sustainable Farming: An Evaluation of the Reasoned Action and Comprehensive Action Determination Frameworks for Persistence (Master's thesis, California Polytechnic State University). TANNER, C. (1999). CONSTRAINTS ON ENVIRONMENTAL BEHAVIOUR. Journal of Environmental Psychology, 19(2), 145–157. https://doi.org/10.1006/jevp.1999.0121 Triandis, H. C. (1979). Values, attitudes, and interpersonal behavior. Nebraska Symposium on Motivation, 27, 195–259. Wood, W., & Neal, D. T. (2007). A new look at habits and the habit-goal interface. Psychological review, 114(4), 843. Zoltán Dörnyei, & Ushioda, E. (2021). Teaching and Researching Motivation. In Routledge eBooks. Informa. https://doi.org/10.4324/9781351006743 }} ==External links== * [https://www.healthdirect.gov.au/motivation-how-to-get-started-and-staying-motivated Motivation] (Healthdirect) * [[wikipedia:Theory_of_planned_behavior|Theory of planned behaviour]] (Wikipedia) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Behaviour]] [[Category:Motivation and emotion/Book/Environment]] 561udgfgaqhmcuaffmdbzm8ytyoe5su Motivation and emotion/Book/2024/Free will and neuroscience 0 306527 2684172 2683434 2024-11-12T08:38:42Z Sienna04 2989037 2684172 wikitext text/x-wiki {{title|Free will and neuroscience:<br>What does neuroscience reveal about the concept of free will?}} {{MECR3|1=https://youtu.be/gSb9VbNwGbI}} __TOC__ ==Overview== {{RoundBoxTop|theme=5}} If you were asked if you had free will would you say yes? More specifically, would you be able to name a scenario when you acted of your own free will? And if you could name a scenario, how does the biological functions of your brain fit into it? {{RoundBoxBottom}} This chapter considers the neurological relationship to free will in order to understand how the biological functions of our brains fit into free will. The idea of free will has been around since the early Greeks. With neuroscience being in circulation since the early Greeks it is surprising that there are not a large number of connections between free will and neuroscience. Relating these two topics help us in understanding both conscious and unconscious actions. The idea of free will is relatively difficult to identify in people as there are so many influences in the world which could affect our will. This book chapter examines theories and articles to understand the influence of neurological processes on free will. ==Background== Before learning about the connections of free will and neuroscience it is important to understand some cases in neuroscience in order to understand what neuroscience does and how it might assist in learning about free will. It is also important to learn about the early theorists and philosophers that had differing ideas of what free will is. === What is neuroscience? === Neuroscience is defined as "any or all of the sciences, such as neurochemistry and experimental psychology, which deal with the structure or function of the nervous system and brain" (Nordqvist, 2013). ==== History of neuroscience ==== Neuroscience has been recorded to have originated with the understanding of the brain's role of behaviour (“History of Neurobiology,” 2021). Three case studies discussed below follow the history of neuroscience. ===== The case of Phineas Gage ===== As unfortunate as his case was, Phineas Gage's case has gone down in history memorably. Gage was working as a railroad worker when a very long iron rod shot through the front of his skull and went straight through (Damasio et al., 1994). Gage survived the accident and doctors recorded the changes in his behaviour after his accident. "Once a responsible, appropriate, and hard-working an, Phineas became irresponsible, socially inappropriate, and unable to work again" ("History of Neurobiology," 2021). Phineas Gage's study helped scientists understand what the frontal lobes role was within behaviour (Damasio et al., 1994). ===== The case of Mr. Tan ===== Have you ever heard of Broca's area? Well, the case study of Mr. Tan explains how this came to be. A French physician and neurosurgeon, Pierre Paul Broca, "was studying the brain and attempting to determine whether localisation was a legitimate scientific idea" ("History of Neurobiology," 2021). The localisation discussed was, at the time, phrenology "the study of brain functioning as it relates to bumps and indentations on the head" ("History of Neurobiology," 2021). Mr. Tan was examined by Dr. Broca as he was losing his speech and he could only say 'tan' ("History of Neurobiology," 2021). Unfortunately, Mr. Tan had died shortly after the examination, however, Dr. Broca did an autopsy and found that there was a legion in the left of his frontal lobe ("History of Neurobiology," 2021). Mr. Tan's brain underwent neuroimaging studies posthumously confirming the damage to exist within Broca's area (Teive et al., 2011). ===== The case of H.M. ===== H.M. had been experiencing seizures and underwent brain surgery to try and control them as it was thought he would die from them if not controlled ("History of Neurobiology," 2021). In this surgery H.M. had his hippocampus removed which both controlled his seizures and gave him anterograde amnesia, meaning that he could not make new memories ("History of Neurobiology," 2021). The case of H.M. is helpful in understanding the use of the hippocampus in memory (Eichenbaum, 2013). === What is free will? === Free will is defined as the ability to choose one's own actions and act voluntarily without feeling necessity or the constraint of fate (Britannica 2024). ==== History of free will ==== The idea of free will has been alive for a very long time. From Homer and the Iliad to Wittgenstein, Dilman (1999/2013), outlines this historical and philosophical roots of free will. Many popular and well known psychologists are discussed by Dilman in his book. Names like Plato, Aristotle, Descartes, Kant, and Freud all have a place in the history of free will. ===== Plato ===== According to Dilman (1999/2013), Plato's view was that being evil created a lack of free will, likewise achieving self mastery is what helps someone have autonomy or free will. Why is it that someone who is evil does not have free will while someone who has 'self mastery' does? It seems that there is a flaw in the idea of good, evil and self-mastery. This flaw being that Plato's idea of evil may be based off someone who is acting in a way that would not have been deemed societally acceptable. If someone was acting out of societal expectations and doing whatever they want or even breaking the law does that not appear to be free will? It appears that anyone can have self mastery when they choose when and what to do and not do. ===== Aristotle ===== Where Plato's contribution was philosophical Aristotle's is analytical (Dilman, 1999/2013). Aristotle believed that "human beings pursue ends in accordance with reason, they form intentions, make choices, and act on them" (Dilman, 1999/2013) and were not just put on this earth to seek food and sensation. Dilman (1999/2013), states that Aristotle believed that Plato's ideas of evil and self-mastery were flawed. Instead Aristotle believed that when a person makes a choice of any kind they are using their will (Dilman, 1999/2013). This idea seems to be a good way to explain free will. The ability to make choices as humankind seems to help us enact of our own will. ===== Descartes ===== Descartes separated the mind from the body in his theory of dualism (Dilman, 1999/2013). Dilman (1999/2013), stated that "the 'act of will' is voluntary for Descartes, but the movement it brings about is not". Movement being involuntary seems to make sense. If you were to look at reflexes and how quick they are in response to say a hit to the knee it would appear that there was little time to think about them. Likewise, some people can be shocked that a reflex happened in response to such a small tap to the knee. Descartes is seemingly describing neurological processes as involuntary movements. ===== Kant ===== According to Dilman (1999/2013) "Kant... claims that the will can and ought to be determined by reason". Dilman (1999/2013) also stated that Kant had difficulty accepting his own ideas as he had opposing concepts of free will and causality of which he did not believe that free will could exist at the same time. The idea of Kant's free will theory is once again different from the other influential names in history. ===== Freud ===== "Freud... thought that we identify free will with indifference and so are most inclined to believe in its reality where very little hangs on what we do" (Dilman, 1999/2013). Under this banner would fall small choices made in day to day life like, what shirt you choose to wear or what time to eat lunch. In the sense of choice Freud's view is similar to Aristotle's with one main difference being that, in Freud's case, the choices connected to free will are only small choices.{{RoundBoxTop|theme=2}}<quiz> Which theorist/s believed in the free will of choice? </quiz> {{RoundBoxBottom}} === Free will in neuroscience === According to Brass et al. (2019), "the main contribution of neuroscience to the free will debate has revolved around the question whether conscious decisions can be predicted from brain activation preceding such decisions". Burns and Bechara (2007) explain that there are twos systems involved in will. These systems being impulsive and reflective, which could also be labeled as impulsive and inhibition systems as the reflective system controls the impulsive system. These systems could help explain the free will of neuroscience and help understand if there is a choice to be had as Aristotle believes. == Theories == Roediger and colleagues (2008), outline conscious control of behaviour with four studies, tying neuroscience to psychology. === The response - choice paradigm === The first of the studies is the response – choice paradigm utilised by Benjamin Libet. Libet studied the relationship between the readiness potential and conscious thought to understand how they create a motor movement. “At the time that Libet began his research that prior to motor movement there was an electrical change on the area of the scalp above the premotor cortex. This is known as the readiness potential” (Roediger et al., 2008). During his study Libet had his participants read off of a specially made clock and note the time they became aware of the intention to move (Roediger et al., 2008; Pockett, 2007; Cardoso, 2021). But how does this study tie into free will? This study seemingly disproves the idea of free will as there is a specific electrical charge that causes the action. Libet (1999), states that this study does not disprove free will as there is a period of time between when the participants become aware of their intention to act and when the action happens where the participants could choose to stop the behaviour. <u>With the being said free will wasn't the main point of Libet's research or any point. It was only after the study had been completed that Libet released an article about free will using his previous experiment as an example</u>. Libet's response-choice paradigm aligns with Descartes perspective of free will. === The stop signal paradigm === The second of the four studies is the stop signal paradigm created by Gordon Logan and his colleagues. Logan and colleagues had their participants "perform repeated trials of a simple task (usually discriminating X from O). On a portion of the trials (usually around 20%), a tone is emitted at some point after the go stimulus (the X or O) has been presented but before the subject has responded to that stimulus. Subjects are instructed to stop performing the discrimination task (the go task) when they hear the tone (the stop signal)" (Roediger et al., 2008). The reaction time was measured in this study. This paradigm is best used to understand response inhibition within a laboratory setting (Verbruggen & Logan, 2008). The stop signal paradigm helps understand free will by understanding inhibitions and the use of 'free won't'. === The process dissociation procedure === The third of the four studies is the process-disassociation procedure utilised by Larry Jacoby and colleagues. "The process-dissociation procedure has been used to estimate the separate contributions of consciously controlled and nonconsciously controlled, or automatic, processes to performance on memory tasks" (Roediger et al., 2008). The process dissociation procedure has to do with more multiple process working together than one single process by itself (Roediger et al., 2008). In order for this to happen, an opposition procedure needs to be used. An opposition procedure involves "the two types of mental processes (e.g. conscious vs unconscious, controlled vs automatic) that are presumably tapped by a given cognitive task are set in opposition to each other" (Roediger et al., 2008). The process dissociation procedure helps understand free will by comparing conscious and unconscious thought. This can then be related back to other studies or theorists like Aristotle who believed that choice reflected will. === The forced report procedure === The final of the four studies is the forced report procedure utilised by Asher Koriat and Morris Goldsmith. The forced report procedure "focuses on the role that report option, the decision to volunteer or withhold information, plays in determining performance on memory tasks" (Roediger et al., 2008). This can help in understanding free will through the choice of volunteering or withholding the information. Once again this relates back to Aristotles' theory of choice, more importantly the ability to choose being our free will. ==Conclusion== This chapter explored the different definitions, histories and theories of both free will and neuroscience both separate and combined. The conclusion about free will is one that may be a mystery for a long time, however it has become apparent that Aristotle's idea of choice in relation to free will seems to have been related back to often. Through the theories it all had to do with physical processes and whether or not a person can choose to fulfil that action. So it seems that a conclusion has been reached on what neuroscience says about free will and that is that it exists in the form of choices. ==See also== * [[Motivation and emotion/Book/2015/Willpower#Theories|Willpower]] - Book Chapter (2015) * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive Dissonance and motivation]] - Book Chapter (2021) * [[Motivation and emotion/Book/2017/Compatibilism|Compatibilism]] - Book Chapter (2017) == Quotes == #"any or all of the sciences, such as neurochemistry and experimental psychology, which deal with the structure or function of the nervous system and brain" [https://neuro.georgetown.edu/about-neuroscience/ (Nordqvist, 2013)] #"Once a responsible, appropriate, and hard-working an, Phineas became irresponsible, socially inappropriate, and unable to work again" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"was studying the brain and attempting to determine whether localisation was a legitimate scientific idea" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"the study of brain functioning as it relates to bumps and indentations on the head" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"human beings pursue ends in accordance with reason, they form intentions, make choices, and act on them" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"the 'act of will' is voluntary for Descartes, but the movement it brings about is not" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"Kant... claims that the will can and ought to be determined by reason" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"Freud... thought that we identify free will with indifference and so are most inclined to believe in its reality where very little hangs on what we do" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"the main contribution of neuroscience to the free will debate has revolved around the question whether conscious decisions can be predicted from brain activation preceding such decisions" [https://d1wqtxts1xzle7.cloudfront.net/61943295/Why_neuroscience_does_not_disprove_free_will20200130-82782-1ks0blh-libre.pdf?1580410156=&response-content-disposition=inline%3B+filename%3DWhy_neuroscience_does_not_disprove_free.pdf&Expires=1723813701&Signature=UwZrGyYBGHUjODEBJj6tKV1fZjJs458xX6YAgSExn5Ey5oYC320DVWytqfaKd3bjZwRxPSf5qnin0d92ss9PgHEdX8wGWNnq1W2AOUAi4ffbnla4ml2cKoJReX3ERyBka2GjlssSinhTSX0xgDXgObLaxlfHaiy1AVR8z5vWo5W~UpAIuCQBlMe~2FkPe2vTCvudnXtxs4StCes8wbMGJz2BdZssWCFqJvu3U1KZoAdi66RN1P~szs-rqPp~sCEHt6VyzlI3lj3UFGbh0vSPRdaIGwVAgRqWgWhGM3lHjaaJk9kphqY-LGDyxSo9y-PzxbPTAnZRYWhvoWqRrr8MFQ__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA (Brass et al., 2019)] #“At the time that Libet began his research that prior to motor movement there was an electrical change on the area of the scalp above the premotor cortex. This is known as the readiness potential” [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"perform repeated trials of a simple task (usually discriminating X from O). On a portion of the trials (usually around 20%), a tone is emitted at some point after the go stimulus (the X or O) has been presented but before the subject has responded to that stimulus. Subjects are instructed to stop performing the discrimination task (the go task) when they hear the tone (the stop signal)" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"The process-dissociation procedure has been used to estimate the seperate contributions of consciously controlled and nonconsciously controlled, or automatic, processes to performance on memory tasks" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"the two types of mental processes (e.g. conscious vs unconscious, controlled vs automatic) that are presumably tapped by a given cognitive task are set in opposition to each other" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"focuses on the role that report option, the decision to volunteer or withhold information, plays in determining performance on memory tasks" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] ==References== {{Hanging indent|1= Brass, M., Furstenberg, A., & Mele, A. R. (2019). Why neuroscience does not disprove free will. ''Neuroscience & Biobehavioral Reviews'', ''102'', 251–263. https://doi.org/10.1016/j.neubiorev.2019.04.024 Britannica, T. Editors of Encyclopaedia (2024, October 3). free will. Encyclopedia Britannica. https://www.britannica.com/topic/free-will Burns, K., & Bechara, A. (2007). Decision making and free will: a neuroscience perspective. ''Behavioral Sciences & the Law'', ''25''(2), 263–280. https://doi.org/10.1002/bsl.751 Cardoso, R. C. (2021). Neurolaw and the Neuroscience of Free Will: an Overview. ''SCIO: Revista de Filosofía'', ''21'', 55–81. https://doi.org/10.46583/scio_2021.21.843 Damasio, H., Grabowski, T., Frank, R., Galaburda, A. M., & Damasio, A. R. (1994). The Return of Phineas Gage: Clues About the Brain from the Skull of a Famous Patient. Science, 264(5162), 1102–1105. JSTOR. http://www.antoniocasella.eu/dnlaw/Damasio_1994.pdf Eichenbaum, H. (2013). What H.M. Taught Us. Journal of Cognitive Neuroscience, 25(1), 14–21. https://doi.org/10.1162/jocn_a_00285 History of Neurobiology. (2021). In ''connect.springerpub.com''. Springer Publishing Company. https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 Ilham Dilman. (2013). ''Free Will An Historical and Philosophical Introduction''. Routledge. http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Original work published 1999) Libet, B. (1999). Do we have Free Will? ''Journal of Consciousness Studies'', ''6''(8-9), 47–57. https://spot.colorado.edu/~tooley/Benjamin%20Libet.pdf Nordqvist, C. (2013). ''About Neuroscience - Department of Neuroscience''. Department of Neuroscience. https://neuro.georgetown.edu/about-neuroscience/ Pockett, S. (2007). The concept of free will: philosophy, neuroscience and the law. ''Behavioral Sciences & the Law'', ''25''(2), 281–293. https://doi.org/10.1002/bsl.743 Roediger, H. L., Goode, M. K., & Zarombe, F. M. (2008). Free Will and the Control of Action. In J. Baer, J. C. Kaufman, & R. F. Baumeister (Eds.), ''Are we free? Psychology and Free Will'' (pp. 205–225). Oxford University Press. https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf Teive, H. A. G., Munhoz, R. P., & Caramelli, P. (2011). Historical aphasia cases: “Tan-tan”, “Vot-vot”, and “Cré nom!” Arquivos de Neuro-Psiquiatria, 69(3), 555–558. https://doi.org/10.1590/s0004-282x2011000400027 Verbruggen, F., & Logan, G. D. (2008). Response inhibition in the stop-signal paradigm. ''Trends in Cognitive Sciences'', ''12''(11), 418–424. https://doi.org/10.1016/j.tics.2008.07.005 }} == External links == == Interesting extras == * [https://www.youtube.com/watch?v=vCGtkDzELAI Determinism vs Free will] (Crash Course) * [https://www.youtube.com/watch?v=OjCt-L0Ph5o The Libet Experiment: Is Free Will Just an Illusion?] (BBC radio 4) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Neuroscience]] [[Category:Motivation and emotion/Book/Will]] sdggwgw4l7euyxj8gsaepi8z7j89jav 2684173 2684172 2024-11-12T08:47:32Z Sienna04 2989037 2684173 wikitext text/x-wiki {{title|Free will and neuroscience:<br>What does neuroscience reveal about the concept of free will?}} {{MECR3|1=https://youtu.be/gSb9VbNwGbI}} __TOC__ ==Overview== {{RoundBoxTop|theme=5}} If you were asked if you had free will would you say yes? More specifically, would you be able to name a scenario when you acted of your own free will? And if you could name a scenario, how does the biological functions of your brain fit into it? {{RoundBoxBottom}} This chapter considers the neurological relationship to free will in order to understand how the biological functions of our brains fit into free will. The idea of free will has been around since the early Greeks. With neuroscience being in circulation since the early Greeks it is surprising that there are not a large number of connections between free will and neuroscience. Relating these two topics help us in understanding both conscious and unconscious actions. The idea of free will is relatively difficult to identify in people as there are so many influences in the world which could affect our will. This book chapter examines theories and articles to understand the influence of neurological processes on free will. ==Background== Before learning about the connections of free will and neuroscience it is important to understand some cases in neuroscience in order to understand what neuroscience does and how it might assist in learning about free will. It is also important to learn about the early theorists and philosophers that had differing ideas of what free will is. === What is neuroscience? === Neuroscience is defined as "any or all of the sciences, such as neurochemistry and experimental psychology, which deal with the structure or function of the nervous system and brain" (Nordqvist, 2013). ==== History of neuroscience ==== Neuroscience has been recorded to have originated with the understanding of the brain's role of behaviour (“History of Neurobiology,” 2021). Three case studies discussed below follow the history of neuroscience. ===== The case of Phineas Gage ===== As unfortunate as his case was, Phineas Gage's case has gone down in history memorably. Gage was working as a railroad worker when a very long iron rod shot through the front of his skull and went straight through (Damasio et al., 1994). Gage survived the accident and doctors recorded the changes in his behaviour after his accident. "Once a responsible, appropriate, and hard-working an, Phineas became irresponsible, socially inappropriate, and unable to work again" ("History of Neurobiology," 2021). Phineas Gage's study helped scientists understand what the frontal lobes role was within behaviour (Damasio et al., 1994). ===== The case of Mr. Tan ===== Have you ever heard of Broca's area? Well, the case study of Mr. Tan explains how this came to be. A French physician and neurosurgeon, Pierre Paul Broca, "was studying the brain and attempting to determine whether localisation was a legitimate scientific idea" ("History of Neurobiology," 2021). The localisation discussed was, at the time, phrenology "the study of brain functioning as it relates to bumps and indentations on the head" ("History of Neurobiology," 2021). Mr. Tan was examined by Dr. Broca as he was losing his speech and he could only say 'tan' ("History of Neurobiology," 2021). Unfortunately, Mr. Tan had died shortly after the examination, however, Dr. Broca did an autopsy and found that there was a legion in the left of his frontal lobe ("History of Neurobiology," 2021). Mr. Tan's brain underwent neuroimaging studies posthumously confirming the damage to exist within Broca's area (Teive et al., 2011). ===== The case of H.M. ===== H.M. had been experiencing seizures and underwent brain surgery to try and control them as it was thought he would die from them if not controlled ("History of Neurobiology," 2021). In this surgery H.M. had his hippocampus removed which both controlled his seizures and gave him anterograde amnesia, meaning that he could not make new memories ("History of Neurobiology," 2021). The case of H.M. is helpful in understanding the use of the hippocampus in memory (Eichenbaum, 2013). === What is free will? === Free will is defined as the ability to choose one's own actions and act voluntarily without feeling necessity or the constraint of fate (Britannica 2024). ==== History of free will ==== The idea of free will has been alive for a very long time. From Homer and the Iliad to Wittgenstein, Dilman (1999/2013), outlines this historical and philosophical roots of free will. Many popular and well known psychologists are discussed by Dilman in his book. Names like Plato, Aristotle, Descartes, Kant, and Freud all have a place in the history of free will. ===== Plato ===== According to Dilman (1999/2013), Plato's view was that being evil created a lack of free will, likewise achieving self mastery is what helps someone have autonomy or free will. Why is it that someone who is evil does not have free will while someone who has 'self mastery' does? It seems that there is a flaw in the idea of good, evil and self-mastery. This flaw being that Plato's idea of evil may be based off someone who is acting in a way that would not have been deemed societally acceptable. If someone was acting out of societal expectations and doing whatever they want or even breaking the law does that not appear to be free will? It appears that anyone can have self mastery when they choose when and what to do and not do. ===== Aristotle ===== Where Plato's contribution was philosophical Aristotle's is analytical (Dilman, 1999/2013). Aristotle believed that "human beings pursue ends in accordance with reason, they form intentions, make choices, and act on them" (Dilman, 1999/2013) and were not just put on this earth to seek food and sensation. Dilman (1999/2013), states that Aristotle believed that Plato's ideas of evil and self-mastery were flawed. Instead Aristotle believed that when a person makes a choice of any kind they are using their will (Dilman, 1999/2013). This idea seems to be a good way to explain free will. The ability to make choices as humankind seems to help us enact of our own will. ===== Descartes ===== Descartes separated the mind from the body in his theory of dualism (Dilman, 1999/2013). Dilman (1999/2013), stated that "the 'act of will' is voluntary for Descartes, but the movement it brings about is not". Movement being involuntary seems to make sense. If you were to look at reflexes and how quick they are in response to say a hit to the knee it would appear that there was little time to think about them. Likewise, some people can be shocked that a reflex happened in response to such a small tap to the knee. Descartes is seemingly describing neurological processes as involuntary movements. ===== Kant ===== According to Dilman (1999/2013) "Kant... claims that the will can and ought to be determined by reason". Dilman (1999/2013) also stated that Kant had difficulty accepting his own ideas as he had opposing concepts of free will and causality of which he did not believe that free will could exist at the same time. The idea of Kant's free will theory is once again different from the other influential names in history. ===== Freud ===== "Freud... thought that we identify free will with indifference and so are most inclined to believe in its reality where very little hangs on what we do" (Dilman, 1999/2013). Under this banner would fall small choices made in day to day life like, what shirt you choose to wear or what time to eat lunch. In the sense of choice Freud's view is similar to Aristotle's with one main difference being that, in Freud's case, the choices connected to free will are only small choices.{{RoundBoxTop|theme=2}}<quiz display=simple> Which theorist/s believed in the free will of choice?} + Aristotle + Freud - Kant - Plato </quiz> {{RoundBoxBottom}} === Free will in neuroscience === According to Brass et al. (2019), "the main contribution of neuroscience to the free will debate has revolved around the question whether conscious decisions can be predicted from brain activation preceding such decisions". Burns and Bechara (2007) explain that there are twos systems involved in will. These systems being impulsive and reflective, which could also be labeled as impulsive and inhibition systems as the reflective system controls the impulsive system. These systems could help explain the free will of neuroscience and help understand if there is a choice to be had as Aristotle believes. == Theories == Roediger and colleagues (2008), outline conscious control of behaviour with four studies, tying neuroscience to psychology. === The response - choice paradigm === The first of the studies is the response – choice paradigm utilised by Benjamin Libet. Libet studied the relationship between the readiness potential and conscious thought to understand how they create a motor movement. “At the time that Libet began his research that prior to motor movement there was an electrical change on the area of the scalp above the premotor cortex. This is known as the readiness potential” (Roediger et al., 2008). During his study Libet had his participants read off of a specially made clock and note the time they became aware of the intention to move (Roediger et al., 2008; Pockett, 2007; Cardoso, 2021). But how does this study tie into free will? This study seemingly disproves the idea of free will as there is a specific electrical charge that causes the action. Libet (1999), states that this study does not disprove free will as there is a period of time between when the participants become aware of their intention to act and when the action happens where the participants could choose to stop the behaviour. <u>With the being said free will wasn't the main point of Libet's research or any point. It was only after the study had been completed that Libet released an article about free will using his previous experiment as an example</u>. Libet's response-choice paradigm aligns with Descartes perspective of free will. === The stop signal paradigm === The second of the four studies is the stop signal paradigm created by Gordon Logan and his colleagues. Logan and colleagues had their participants "perform repeated trials of a simple task (usually discriminating X from O). On a portion of the trials (usually around 20%), a tone is emitted at some point after the go stimulus (the X or O) has been presented but before the subject has responded to that stimulus. Subjects are instructed to stop performing the discrimination task (the go task) when they hear the tone (the stop signal)" (Roediger et al., 2008). The reaction time was measured in this study. This paradigm is best used to understand response inhibition within a laboratory setting (Verbruggen & Logan, 2008). The stop signal paradigm helps understand free will by understanding inhibitions and the use of 'free won't'. === The process dissociation procedure === The third of the four studies is the process-disassociation procedure utilised by Larry Jacoby and colleagues. "The process-dissociation procedure has been used to estimate the separate contributions of consciously controlled and nonconsciously controlled, or automatic, processes to performance on memory tasks" (Roediger et al., 2008). The process dissociation procedure has to do with more multiple process working together than one single process by itself (Roediger et al., 2008). In order for this to happen, an opposition procedure needs to be used. An opposition procedure involves "the two types of mental processes (e.g. conscious vs unconscious, controlled vs automatic) that are presumably tapped by a given cognitive task are set in opposition to each other" (Roediger et al., 2008). The process dissociation procedure helps understand free will by comparing conscious and unconscious thought. This can then be related back to other studies or theorists like Aristotle who believed that choice reflected will. === The forced report procedure === The final of the four studies is the forced report procedure utilised by Asher Koriat and Morris Goldsmith. The forced report procedure "focuses on the role that report option, the decision to volunteer or withhold information, plays in determining performance on memory tasks" (Roediger et al., 2008). This can help in understanding free will through the choice of volunteering or withholding the information. Once again this relates back to Aristotles' theory of choice, more importantly the ability to choose being our free will. ==Conclusion== This chapter explored the different definitions, histories and theories of both free will and neuroscience both separate and combined. The conclusion about free will is one that may be a mystery for a long time, however it has become apparent that Aristotle's idea of choice in relation to free will seems to have been related back to often. Through the theories it all had to do with physical processes and whether or not a person can choose to fulfil that action. So it seems that a conclusion has been reached on what neuroscience says about free will and that is that it exists in the form of choices. ==See also== * [[Motivation and emotion/Book/2015/Willpower#Theories|Willpower]] - Book Chapter (2015) * [[Motivation and emotion/Book/2021/Cognitive dissonance and motivation|Cognitive Dissonance and motivation]] - Book Chapter (2021) * [[Motivation and emotion/Book/2017/Compatibilism|Compatibilism]] - Book Chapter (2017) == Quotes == #"any or all of the sciences, such as neurochemistry and experimental psychology, which deal with the structure or function of the nervous system and brain" [https://neuro.georgetown.edu/about-neuroscience/ (Nordqvist, 2013)] #"Once a responsible, appropriate, and hard-working an, Phineas became irresponsible, socially inappropriate, and unable to work again" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"was studying the brain and attempting to determine whether localisation was a legitimate scientific idea" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"the study of brain functioning as it relates to bumps and indentations on the head" [https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 (“History of Neurobiology,” 2021)] #"human beings pursue ends in accordance with reason, they form intentions, make choices, and act on them" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"the 'act of will' is voluntary for Descartes, but the movement it brings about is not" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"Kant... claims that the will can and ought to be determined by reason" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"Freud... thought that we identify free will with indifference and so are most inclined to believe in its reality where very little hangs on what we do" [http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Dilman, 1999/2013)] #"the main contribution of neuroscience to the free will debate has revolved around the question whether conscious decisions can be predicted from brain activation preceding such decisions" [https://d1wqtxts1xzle7.cloudfront.net/61943295/Why_neuroscience_does_not_disprove_free_will20200130-82782-1ks0blh-libre.pdf?1580410156=&response-content-disposition=inline%3B+filename%3DWhy_neuroscience_does_not_disprove_free.pdf&Expires=1723813701&Signature=UwZrGyYBGHUjODEBJj6tKV1fZjJs458xX6YAgSExn5Ey5oYC320DVWytqfaKd3bjZwRxPSf5qnin0d92ss9PgHEdX8wGWNnq1W2AOUAi4ffbnla4ml2cKoJReX3ERyBka2GjlssSinhTSX0xgDXgObLaxlfHaiy1AVR8z5vWo5W~UpAIuCQBlMe~2FkPe2vTCvudnXtxs4StCes8wbMGJz2BdZssWCFqJvu3U1KZoAdi66RN1P~szs-rqPp~sCEHt6VyzlI3lj3UFGbh0vSPRdaIGwVAgRqWgWhGM3lHjaaJk9kphqY-LGDyxSo9y-PzxbPTAnZRYWhvoWqRrr8MFQ__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA (Brass et al., 2019)] #“At the time that Libet began his research that prior to motor movement there was an electrical change on the area of the scalp above the premotor cortex. This is known as the readiness potential” [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"perform repeated trials of a simple task (usually discriminating X from O). On a portion of the trials (usually around 20%), a tone is emitted at some point after the go stimulus (the X or O) has been presented but before the subject has responded to that stimulus. Subjects are instructed to stop performing the discrimination task (the go task) when they hear the tone (the stop signal)" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"The process-dissociation procedure has been used to estimate the seperate contributions of consciously controlled and nonconsciously controlled, or automatic, processes to performance on memory tasks" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"the two types of mental processes (e.g. conscious vs unconscious, controlled vs automatic) that are presumably tapped by a given cognitive task are set in opposition to each other" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] #"focuses on the role that report option, the decision to volunteer or withhold information, plays in determining performance on memory tasks" [https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf (Roediger and colleagues, 2008)] ==References== {{Hanging indent|1= Brass, M., Furstenberg, A., & Mele, A. R. (2019). Why neuroscience does not disprove free will. ''Neuroscience & Biobehavioral Reviews'', ''102'', 251–263. https://doi.org/10.1016/j.neubiorev.2019.04.024 Britannica, T. Editors of Encyclopaedia (2024, October 3). free will. Encyclopedia Britannica. https://www.britannica.com/topic/free-will Burns, K., & Bechara, A. (2007). Decision making and free will: a neuroscience perspective. ''Behavioral Sciences & the Law'', ''25''(2), 263–280. https://doi.org/10.1002/bsl.751 Cardoso, R. C. (2021). Neurolaw and the Neuroscience of Free Will: an Overview. ''SCIO: Revista de Filosofía'', ''21'', 55–81. https://doi.org/10.46583/scio_2021.21.843 Damasio, H., Grabowski, T., Frank, R., Galaburda, A. M., & Damasio, A. R. (1994). The Return of Phineas Gage: Clues About the Brain from the Skull of a Famous Patient. Science, 264(5162), 1102–1105. JSTOR. http://www.antoniocasella.eu/dnlaw/Damasio_1994.pdf Eichenbaum, H. (2013). What H.M. Taught Us. Journal of Cognitive Neuroscience, 25(1), 14–21. https://doi.org/10.1162/jocn_a_00285 History of Neurobiology. (2021). In ''connect.springerpub.com''. Springer Publishing Company. https://connect.springerpub.com/content/book/978-0-8261-0923-1/chapter/ch01 Ilham Dilman. (2013). ''Free Will An Historical and Philosophical Introduction''. Routledge. http://www.amas.hk/pdf/shijianshenxue/6/388)Free%20Will%20-%20Historical%20and%20Philosophical%20Introduction%20(Ilham%20Dilman)%20.pdf (Original work published 1999) Libet, B. (1999). Do we have Free Will? ''Journal of Consciousness Studies'', ''6''(8-9), 47–57. https://spot.colorado.edu/~tooley/Benjamin%20Libet.pdf Nordqvist, C. (2013). ''About Neuroscience - Department of Neuroscience''. Department of Neuroscience. https://neuro.georgetown.edu/about-neuroscience/ Pockett, S. (2007). The concept of free will: philosophy, neuroscience and the law. ''Behavioral Sciences & the Law'', ''25''(2), 281–293. https://doi.org/10.1002/bsl.743 Roediger, H. L., Goode, M. K., & Zarombe, F. M. (2008). Free Will and the Control of Action. In J. Baer, J. C. Kaufman, & R. F. Baumeister (Eds.), ''Are we free? Psychology and Free Will'' (pp. 205–225). Oxford University Press. https://www.researchgate.net/profile/Henry-Roediger-2/publication/285124681_Free_Will_and_the_Control_of_Action/links/586d271e08aebf17d3a717c1/Free-Will-and-the-Control-of-Action.pdf Teive, H. A. G., Munhoz, R. P., & Caramelli, P. (2011). Historical aphasia cases: “Tan-tan”, “Vot-vot”, and “Cré nom!” Arquivos de Neuro-Psiquiatria, 69(3), 555–558. https://doi.org/10.1590/s0004-282x2011000400027 Verbruggen, F., & Logan, G. D. (2008). Response inhibition in the stop-signal paradigm. ''Trends in Cognitive Sciences'', ''12''(11), 418–424. https://doi.org/10.1016/j.tics.2008.07.005 }} == External links == == Interesting extras == * [https://www.youtube.com/watch?v=vCGtkDzELAI Determinism vs Free will] (Crash Course) * [https://www.youtube.com/watch?v=OjCt-L0Ph5o The Libet Experiment: Is Free Will Just an Illusion?] (BBC radio 4) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Neuroscience]] [[Category:Motivation and emotion/Book/Will]] phucu9uofgcxbnkook45lzstddjic00 Motivation and emotion/Book/2024/Solitary confinement 0 306596 2683450 2676197 2024-11-11T12:03:29Z Ubaldo111 2987891 removed template thing 2683450 wikitext text/x-wiki {{title|Solitary confinement:<br>What are its motivational and emotional processes and impacts?}} {{MECR3|1=https://youtu.be/hu8yfthZmqo}} <div align=center></div> __TOC__ ==Overview == {{RoundBoxTop|theme=3}} [[File:Solitary Confinement (52164007181).jpg|thumb|'''Figure 1'''. Officer standing in a solitary confinement cell]] ;Scenario You have been arrested supposedly in connection with a terrible crime. You are placed into custody in a dark room measuring 2m x 3m by yourself with only a small hole for light in the door. The space is bare, containing only a small bed and a sink, and smelling stagnant and musty. You are not sure how long you will be kept in this room that has no contact with the outside world. Time starts to blur as you sit alone in silence, trapped in a seemingly endless isolation, with only your thoughts to accompany you. {{RoundBoxBottom}} [[wikipedia:Solitary_confinement|Solitary confinement]] (solitary) in a small dark cell uses [[wikipedia:Sensory_deprivation|sensory deprivation]] and [[wikipedia:Social_isolation|social isolation]] to break the will of those in it and induce [[w:Learned helplessness|learned helplessness]]. Solitary confinement is mainly used to punish, extract information from, torture, and/or to closely supervise a person. This chapter examines the processes and impacts of solitary confinement for the motivation and emotion(s) of those subjected to it. It refers to research and the knowledge from key psychological theories including the [[wikipedia:Self-determination_theory|self determination theory]] (SDT), basic needs theory (BNT), and relationship motivation theory (RMT), as well as Maslow's [[wikipedia:Maslow's_hierarchy_of_needs|hierarchy of needs]]. To maximise the ease and engagement of learning, the chapter uses case studies, links to YouTube videos and some quick quizzes. This chapter does not include the processes or impacts of physical abuse which is sometimes also used in conjunction with solitary confinement. {{RoundBoxTop|theme=3}} '''Focus questions:''' * What psychological processes are involved in solitary confinement? * What are its impacts on motivation? * What are its impacts on emotion? {{RoundBoxBottom}} == Psychological processes involved in solitary confinement == Solitary confinement acts most commonly as a positive or negative [[wikipedia:Punishment_(psychology)#Positive|punishment]]. It aims to reduce the frequency of any unwanted behaviours. The specific behaviours solitary confinement aims to discourage include keeping information secret from authorities, violent crime, political activism or war with that country by threatening to take prisoners of war (Haney, 2003). The punishment itself comes from several well documented mechanisms. Firstly, solitary confinement is often used in tandem with [[wikipedia:Sleep_deprivation|sleep deprivation]] which is a form of psychological torture (Reyes, 2007). Secondly, solitary confinement creates an environment which over time, removes a person's privacy, intimacy, trust, and connection with others, as well as their sense of self and security (Physicians for Human Rights, 2005). Thirdly, the processes of solitary confinement induce compliance to authority by reducing a prisoner's sense of self-efficacy (Wortman & Brehm, 1975). Solitary confinement does this by creating a place where a person has little to no control over what happens at any time. The [[wikipedia:Central_Intelligence_Agency|Central Intelligence Agency (CIA)]] wrote a training manual in 1983 which has recently{{when}} been declassified, entitled "Human Resource Exploitation". It says that the psychological processes of solitary confinement are the ideal conditions to debilitate a person with aversive stimuli and create dependency on an interrogator to extract information from them (CIA, 2023). [[wikipedia:Martin_Seligman|Seligman]] wrote during his work on learned helplessness that, given the right conditions, helplessness can be induced (Hiroto & Seligman, 1975). Solitary confinement is also used under a different name, medical housing units (MHUs). MHUs surveil the mentally or medically unwell to make sure they remain alive in custody. This is done with the intention to deter [[wikipedia:Hunger_strike|hunger striking]] and suicide attempts, particularly of political activists (Cho & Naples-Mitchell, 2021). The use of this type of solitary confinement has been heavily criticised as MHUs actually worsen the condition of the prisoner and rates of suicide are higher in them (Cassese, 1991). This is why they are known colloquially as suicide watch cells (Cassese). In rare cases, solitary confinement is seen as a positive tool for de-escalating bad or violent situations in prisons (Laws, 2021). A systematic review found that the use of solitary confinement has increased in recent{{when}} decades. It also found very high rates of psychological distress meaning the justification for positive use could not be generalised and that solitary confinement should be avoided in almost all cases (Haney, 2018). In [[wikipedia:Eastern_culture|Eastern culture]], specifically some in [[wikipedia:Buddhism#Worldview|Buddhist]] circles, a certain amount of self-imposed solitary confinement is considered to be a good thing. It is believed that the processes of solitary confinement act on the mind and can bring a person closer to inner peace or "[[wikipedia:Buddhism#Liberation|Liberation]]". Monks who have used this practice successfully speak about how they became more forgiving and patient of others after the experience. However, this sample is potentially biased as the monks for whom confinement was not enjoyable or did not work are not heard from. Interestingly, there are programs teaching the principles of Buddhist meditation to prison inmates to counter the psychological processes of solitary confinement (McIvor, 2011). === Case study: Julian Assange === {{Robelbox|width=30|theme={{{theme|3}}}|title=}} <div style="{{Robelbox/pad}}"> [[File:A Julian Assange activist in London's Piccadilly Circus carries a sign declaring 'I stand with Julian.'.jpg|thumb|340px|'''Figure 2'''. Activist in London carries a sign declaring "I stand with Julian", 2023]] [[wikipedia:Julian_Assange|Julian Assange]], the founder and editor of [[wikipedia:WikiLeaks|WikiLeaks]], faced a variety of criminal charges in 2012 and went into [[wikipedia:Right_of_asylum|political asylum]] at the Ecuadorian Embassy until 2019 when that was revoked<ref name=":0">Bowater, D. (2012, June 20). ''Julian Assange faces re-arrest over breaching his bail condition by seeking asylum in Ecuador''. The Telegraph. https://www.telegraph.co.uk/news/worldnews/wikileaks/9343630/Julian-Assange-faces-re-arrest-over-breaching-his-bail-condition-by-seeking-asylum-in-Ecuador.html</ref>. Having already been confined to the embassy or having faced arrest since 2012<ref name=":0" />, from April 2019 until June of 2024 he was placed into solitary and other highly restrictive forms of jail in Belmarsh prison whilst awaiting extradition to the United States<ref>Rebaza, C., Fox, K., & Cotovio, V. (2021, January 4). ''UK judge denies US request to extradite Julian Assange''. CNN. https://edition.cnn.com/2021/01/04/uk/julian-assange-extradition-wikileaks-us-gbr-intl/index.html</ref>(see Figure 2). The United Nations sent a special rapporteur on torture and other cruel, inhuman or degrading treatment or punishment to visit Assange in prison. The special rapporteur, wrote a report on Assange’s mental and physical state. The report concluded that Assange displayed all the symptoms of a victim of psychological torture including paranoia, chronic anxiety, and intense psychological trauma<ref>Booth, W. (2019, May). U.N. official says Julian Assange is a victim of ‘psychological torture,’ warns against U.S. extradition. https://www.washingtonpost.com/world/europe/un-official-says-assange-is-a-victim-ofpsychological-torture-warns-against-extradition-to-the-us/2019/05/31/cca722e0-5f84-11e9-bf24-db4b9fb62aa2_story.html</ref>. He struck a plea deal with the U.S. for his part in leaking the classified documents<ref>Leigh, D. (2010, November 28). ''US embassy cables leak sparks global diplomatic crisis''. The Guardian. https://www.theguardian.com/world/2010/nov/28/us-embassy-cable-leak-diplomacy-crisis</ref> and was released in June 2024. On the first of October 2024, Assange gave a statement to the Parliamentary Assembly of the Council of Europe where he spoke about the impacts of his imprisonment in solitary confinement. Please see [https://www.msn.com/en-us/video/news/assange-makes-1st-public-appearance-after-detention/vi-AA1rxpre?t=74 the video] of that. </div> {{Robelbox/close}} === Quiz 1 === <quiz display="simple"> {Is solitary confinement always a punishment? |type="()"} - Yes + No {The UN special rapporteur did not support Assange's confinement: |type="()"} + True - False </quiz> ==Psychological perspectives== This section examines psychological perspectives and theories that can help understand how solitary confinement. The theories will act as a reference point allowing us to determine how solitary confinement's processes stop people from meeting their physiological and psychological needs. === Maslow's hierarchy of needs === [[File:Maslow's Hierarchy of Needs2.svg|thumb|'''Figure 3'''. Maslow's hierarchy of needs model|260x260px]] [[wikipedia:Abraham_Maslow#Hierarchy_of_needs|Maslow's]] [[wikipedia:Maslow's_hierarchy_of_needs|hierarchy of needs]] (see Figure 3) classifies needs into a pyramid. The basic needs and psychological needs are described as deficiency needs in that when they are not met an individual becomes increasingly more motivated to meet them. Once they have been met the self-fulfilment needs can be met. There is [[wikipedia:Maslow's_hierarchy_of_needs#Criticism|criticism]] of the model, mostly about order of the needs. Using the model, it is clear how the processes of solitary confinement stop people from meeting their deficiency and growth needs. Self-esteem and belonging require there to be positive interactions with others and something to work towards. Thus, there is little to no possibility for a person who is locked up alone and not in control of their environment to meet their psychological needs. Physiologically, in solitary confinement (depending on how extreme it is) at least some of the basic needs like water, food, and shelter are met. However, the same cannot be said for safety, security, rest, or warmth. This is because solitary is designed to prevent the majority of psychological and physiological needs from being met as a punitive measure. === Self-determination theory and mini-theories === [[File:Self-determination-theory-three-needs.webp|thumb|303x303px|'''Figure 4'''. Self-determination theory]] The [[wikipedia:Self-determination_theory|Self-determination theory]] (SDT) has three [[wikipedia:Self-determination_theory#Basic_psychological_needs|basic needs]], all of which relate to and have implications for solitary confinement (see Figure 4). They are innate needs for autonomy, competence, and relatedness (Ryan & Deci, 2000). As distinct from Maslow's pyramid, SDT needs are strictly psychological and could occur anywhere given the right conditions. Fulfilling these needs is necessary in order to create and maintain motivation (Ryan & Deci{{when}}). In solitary confinement, however, the conditions making it possible to fulfil these needs are purposefully removed. [[wikipedia:Self-determination_theory#Summary_of_the_SDT_mini-theories|The basic needs theory]] (BNT) is a mini-theory of the SDT. It says that meeting the three basic needs of the SDT is important for several factors relating to motivation (Reeve, 2012). The factors are intrinsic motivation, effective functioning, high quality engagement, and psychological well-being. Therefore not being able to meet these needs due to solitary confinement would create issues according to the BNT. Finally, [[wikipedia:Self-determination_theory#Summary_of_the_SDT_mini-theories|the relationship motivation theory]] (RMT) mini-theory says that the third need of the SDT, relatedness, is the most important. This is because high quality relationships can meet all three basic needs described in BNT and SDT (Deci & Ryan 2014). In solitary confinement there is a distinct lack of any quality relationships. Thus, despite what the RMT suggests about relationships being able to provide support for autonomy and competence when they cannot be met once again, this is not possible{{rewrite}}. Overall, all three theories, Maslow's hierarchy, and the SDT, BNT and RMT theories, explain elements of why the processes of solitary confinement inhibit the satisfying of physiological and psychological needs. The SDT and mini-theories have more empirical evidence to support them than Maslow's hierarchy as even in extreme situations such as solitary confinement people are still motivated to seek the three basic needs (autonomy, competence, and relatedness) according to BNT (Visser, 2020). === Case study: Nelson Mandela === {{Robelbox|width=30|theme={{{theme|3}}}|title=}} <div style="{{Robelbox/pad}}"> [[File:Mandela voting in 1994.jpg|thumb|'''Figure 5'''. Nelson Mandela voting for the first time 1994|190px]] [[wikipedia:Nelson_Mandela|Nelson Mandela]] was an anti-[[wikipedia:Apartheid|apartheid]] activist. He was jailed for a total of 27 years, much of that time in [[wikipedia:Robben_Island_(prison)|Robben Island prison]]. There, he was placed in solitary confinement many times and had his privileges revoked on many occasions<ref>Benson, M. (1986). ''Nelson Mandela''. GB : Penguin Books.</ref>. His eyesight and back were permanently affected as a result. Mandela went on to become the first president of South Africa elected by all of its' peoples in 1994 (see Figure 5). He stated that his lengthy time in prison led him to be more understanding of the challenges facing all South Africans. In response to how he and other activists were treated the UN introduced [https://www.un.org/en/events/mandeladay/mandela_rules.shtml the Nelson Mandela Rules] in 2015. </div> {{Robelbox/close}} === Quiz 2 === <quiz display="simple"> {Does solitary confinement inhibit the components of the SDT? |type="()"} + Yes - No {The Nelson Mandela Rules limit the amount of days a prisoner can be placed in solitary confinement consecutively: |type="()"} + True - False </quiz> ==Impacts of solitary confinement == The processes of and psychological theories relating to need fulfilment in solitary confinement have been covered. Futhermore, the potential issues coming from solitary have been made clear. Thus, the impacts are now examined and discussed. The impacts of solitary confinement are split between motivation and emotion. === Motivation === Humans have a combination of basic and complex physical and psychological needs. When in solitary confinement these needs can only be met partially if at all. This has a destabilising and de-energising effect on motivation. According to the late U.S. senator [[wikipedia:John_McCain#Prisoner_of_war|John McCain]], being in solitary takes away your will to live (Gawande, 2009). Research conducted on 229,000 released prisoners over a 15 year period found that those who had been in solitary for any amount of time during their incarceration were 78% more likely to die from suicide and 54% more from murder within 1 year of release than other prisoners (Brinkley-Rubinstein et al., 2019). The same research also showed a 127% greater likelihood of opioid overdose within the first two weeks of release. These findings could be partially explained by the modified cognitive functioning seen in rats after solitary confinement. In the experiments, the rats had their brain activity measured before and after they were placed in solitary confinement. As a result of being in solitary confinement for 24 hours their brain activity changed, provoking social avoidance (Blanco-Suarez, 2017; Matthews et al., 2016). These same effects on personality have been observed in humans after solitary confinement. They are described as continuing patterns of social intolerance and incapability (Grassian, 2006). The impact of sensory deprivation combined with unmet psychological needs causes an effect called [https://dictionary.apa.org/personality-disintegration personality disintegration] (Physicians for Human Rights, 2005; Reyes, 2007). There is a bidirectional relationship between the brain and the social environment. This is because both social connection and brain function play a key part of healthy brain function (Coppola, 2019). This means that solitary confinement also impacts cognitive function, making it more difficult to find the motivation to return to a normal life (Scientific American, 2013). Even with less than one month of solitary confinement inmates have impairments to their impulse control, social cue recognition, memory, and concentration (Hresko, 2006). These changes can alter the brain's structure permanently (Supreme Court of the United States, 2016). === Emotion === Being unable to meet psychological and physiological needs due to solitary can be emotionally de-regulating and provoke negative emotions. The emotions include, fear and anxiety (Hresko, 2006). The de-regulation can cause panic attacks, perceptual hallucinations and violent fantasies (Hresko). There is some disagreement as to the characterisation of those upon whom solitary confinement has the most emotionally destabilising effect. In the CIA training manual from 1983, it was suggested that the better adjusted someone is (meaning how normally functioning they are) the more they will be affected (CIA, 2023). More recently, however, evidence shows that those who are already at risk of or currently suffering from depression or mood disorders are the most emotionally affected (Haney, 2003). Current and former solitary confinement inmates are commonly diagnosed with [[wikipedia:Post-traumatic_stress_disorder|post traumatic stress disorder]] (PTSD) which causes fear and stress responses with or without conscious awareness (Witte, 2007). Specifically in PTSD related to solitary confinement, there is a disruption in the normal response of the [[wikipedia:Neurotransmitter|neurotransmitter]] system to an [[wikipedia:Arousal|aroused]] state. The system produces and releases higher levels of [[wikipedia:Norepinephrine|norepinephrine]] for a longer time (Costanzo & Gerrity, 2009). The physiological brain changes occurring as a result of solitary confinement were first studied at scale in 1992. 57 prisoners of war with a mean age of 32 years were released after being held in solitary confinement for an average of 6 months. They underwent brain scans which showed their brains were dull, similar to people who had sustained a [[wikipedia:Traumatic_brain_injury|traumatic brain injury]] from a from a car crash (Vrca, et al., 1996). The changes to brain structures from solitary confinement which effect emotion are the [[wikipedia:Hippocampus|hippocampus]] and the [[wikipedia:Amygdala|amygdala]]. They are the regions associated with learning and memory and threat response, respectively. The hippocampus loses neuroplasticity, shrinks and begins to fail however, the amygdala shows increased activation and size (Blanco-Suarez, 2019). As a result, there is impairment to learning and memory formation and a loss of emotional and stress control (Lobel & Akil, 2018). With in some cases, permanent changes in mood like depression (Lobel & Akil). The impacts of solitary confinement emotionally are long lasting and difficult or impossible to recover from (Physicians for Human Rights, 2005). This is because solitary forces individuals to cope by using [[wikipedia:Coping#Negative_techniques_(maladaptive_coping_or_non-coping)|maladaptive behaviours]] (Coppola, 2019). [[wikipedia:Craig_Haney|Craig Haney]] says that those who have adapted to solitary confinement are more frequently released than those who have not. However, these people are maladapted and no longer capable of emotional readjustment (Gawande, 2009). === Case study: Chelsea Manning === {{Robelbox|width=30|theme={{{theme|3}}}|title=}} <div style="{{Robelbox/pad}}"> [[wikipedia:Chelsea_Manning|Chelsea Manning]], a former US army intelligence officer passed some 250,000 classified US documents onto Julian Assange<ref>Leigh, D. (2010, November 28). ''US embassy cables leak sparks global diplomatic crisis''. The Guardian. https://www.theguardian.com/world/2010/nov/28/us-embassy-cable-leak-diplomacy-crisis</ref><ref>White, G. (2011). ''This is the Wikileak that sparked the Tunisian crisis''. Business Insider. https://www.businessinsider.com/tunisia-wikileaks-2011-1</ref>. The documents contained information detailing how the U.S. had acted improperly towards civilians in Iraq and Afghanistan. Manning was charged under several serious national security provisions including the [[wikipedia:Espionage_Act_of_1917|Espionage Act]]. Demonstrating concerning self-harming behaviour, she was placed under [[wikipedia:Chelsea_Manning#Detention|prevention of injury status]] (POI). All of this meant that Manning was held in solitary confinement with no visits and no outside contact between July 2010 and April 2011. She has been open about how solitary confinement has negatively impacted her life and wellbeing including, several suicide attempts, frequent panic attacks, and an inability to function socially well past being pardoned by President Barack Obama in 2017. Watch this interview→ [https://www.youtube.com/shorts/3_5K8kOksck clip] ← which went viral worldwide showing how Manning has become accustomed to her own silence. The silence in the clip lasts only seconds, but according to the interviewer the unedited silence lasted for more than 10 minutes. </div> {{Robelbox/close}} === Quiz 3 === <quiz display="simple"> {It is not possible to recover from the impacts of solitary confinement. |type="()"} + True - False {Has Manning readjusted back to normal life? |type="()"} - Yes + No </quiz> ==Conclusion== The psychological processes which make solitary confinement such a powerful punishment come from the environment that it creates. The isolation and lack of all control of the environment cause people to lose their connection with others and ultimately their own sense of self. Compliance and learned helplessness generally occur as a result and when they do not, MHUs are used to further induce them. In some types of Buddhism, solitary confinement is used by monks in order to achieve liberation because of its psychological processes. The psychological theories analysed to understand these processes were Maslow's hierarchy of basic, psychological and fulfilment needs, SDT, BNT, and relationship motivation theory. In combination with the psychological processes, the theories clearly demonstrate how and why solitary confinement inhibits physiological and psychological needs from being met, as demonstrated by the Assange and Mandela case studies. The impacts of solitary confinement arising from both physiological and psychological needs not being met on motivation include: an increased rate of suicide after release, social avoidance and/or lack of social skills, memory and attention decline, and personality disintegration. These all stem from the modified cognitive functioning which occurs as a result of the human brain trying to adapt to solitary confinement's environment. Emotionally, solitary confinement causes increased arousal and fear responses. This causes physiological structural changes in the brain, specifically shrinking of the hippocampus and growth of the amygdala. Therefore, the emotional impacts of solitary confinement are commonly permanent and inclusive of both PTSD and a de-regulated production of neurotransmitters, mostly norepinephrine. The effect of the processes and impact of solitary confinement on motivation and emotion on a person are captured in Manning's interview from her case study. ==See also== * [[wikipedia:Chelsea_Manning|Chelsea Manning]] (Wikipedia) * [[wikipedia:Julian_Assange|Julian Assange]] (Wikipedia) * [[wikipedia:Nelson_Mandela|Nelson Mandela]] (Wikipedia) * [[Motivation and emotion/Book/2023/Torture interrogation, motivation, and emotion]] (Book chapter, 2023) * [[Motivation and emotion/Book/2021/Torture motivation]] (Book chapter, 2021) * [[wikipedia:Solitary confinement#Torture|Solitary confinement as torture]] (Wikipedia) * [https://www.youtube.com/watch?v=8UNCvk9YXOo TED Talk on solitary confinement] (YouTube) ==References== {{Hanging indent|1= Brinkley-Rubinstein, L., Sivaraman, J., Rosen, D. L., Cloud, D. H., Junker, G., Proescholdbell, S., Shanahan, M. E., & Ranapurwala, S. I. (2019). Association of restrictive housing during incarceration with mortality after release. ''JAMA Network Open'', ''2''(10). https://doi.org/10.1001/jamanetworkopen.2019.12516 Cho, E., & Naples-Mitchell, J. (2021). Solitary confinement and segregation without medical justification. ''In Behind Closed Doors Abuse and Retaliation Against Hunger Strikers in U.S. Immigration Detention (1st ed., pp. 40–44)''. essay, ''American Civil Liberties Union And Physicians for Human Rights.'' Coppola, F. (2019). The brain in solitude: an (other) eighth amendment challenge to solitary confinement. ''Journal of Law and the Biosciences, 6(1), 184–225''. https://doi.org/10.1093/jlb/lsz014 Costanzo, M. A., & Gerrity, E. (2009). The effects and effectiveness of using torture as an interrogation device: Using research to inform the policy debate. ''Social Issues and Policy Review, 3(1), 179–210.'' https://doi.org/10.1111/j.1751-2409.2009.01014.x Deci, E. L., & Ryan, R. M. (2014). Autonomy and need satisfaction in close relationships: Relationships motivation theory. ''Human Motivation and Interpersonal Relationships, 1(1), 53–73.'' https://doi.org/10.1007/978-94-017-8542-6_3 Gawande, A. (2009, March 23). Is long-term solitary confinement torture?. ''The New Yorker''. https://www.newyorker.com/magazine/2009/03/30/hellhole Grassian, S. (2006). Psychiatric effects of solitary confinement. ''Washington University Journal of Law and Policy, 22(1), 327–380.'' https://doi.org/https://openscholarship.wustl.edu/cgi/viewcontent.cgi?article=1362&context=law_journal_law_policy Haney, C. (2003). Mental health issues in long-term solitary and “Supermax” confinement. ''Crime &amp; Delinquency, 49(1), 124–156.'' https://doi.org/10.1177/0011128702239239 Haney, C. (2018, March 9). The psychological effects of solitary confinement: a systematic critique. ''University of Chicago Press, 47(1):000-000'' https://doi.org/10.1086/696041 Health Consequences of Psychological Torture. (2005). 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F., Izadmehr, E. M., Thomas, R. E., Lacy, G. D., Wildes, C. P., Ungless, M. A., & Tye, K. M. (2016). Dorsal raphe dopamine neurons represent the experience of social isolation. ''Cell, 164(4), 617–631''. https://doi.org/10.1016/j.cell.2015.12.040 McIvor, P. (2011). Outsider Buddhism : a study of Buddhism and Buddhist education in the U.S. prison system. ''Core.ac.uk. oai:uir.unisa.ac.za:10500/5105'' Reyes, H. (2007) ‘The worst scars are in the mind: psychological torture’, ''International Review of the Red Cross, 89(867), pp. 591–617''. doi:10.1017/s1816383107001300. Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. ''American Psychologist, 55(1), 68–78''. https://doi.org/10.1037//0003-066x.55.1.68 Scientific American. (2013, March). Solitary confinement is cruel and ineffective. ''Scientific American''. https://www.scientificamerican.com/article/solitary-confinement-cruel-ineffective-unusual/ Supreme Court of the United Sates, “Brief of medical and other scientific and health-related professionals as amici curiae in support of respondents and affirmance,” ''25'' Vrca, A., Bozikov, V., Brzović, Z., Fuchs, R., & Malinar, M. (1996). Visual evoked potentials in relation to factors of imprisonment in detention camps. ''International Journal of Legal Medicine, 109(3), 114–117''. https://doi.org/10.1007/bf01369669 Wortman, C. B., & Brehm, J. W. (1975). Responses to uncontrollable outcomes: An integration of reactance theory and the learned helplessness model. ''Advances in Experimental Social Psychology, 8, 277–336''. https://doi.org/10.1016/s0065-2601(08)60253-1 Witte, K. (2007). Fear as motivator, fear as inhibitor. ''Handbook of Communication and Emotion, 423–450''. https://doi.org/10.1016/b978-012057770-5/50018-7 }} ==External links== * [https://www.cia.gov/readingroom/home The CIA h''uman resource exploitation training manual 1983''] (CIA.gov) * [https://www.psychologytoday.com/us/blog/brain-chemistry/201902/the-effects-solitary-confinement-the-brain The effects of solitary confinement on the brain] (Psychology Today) * [https://www.un.org/en/events/mandeladay/mandela_rules.shtml The Nelson Mandela Rules] (UN.org) * [https://www.psychologytoday.com/us/blog/brain-chemistry/201712/the-neuroscience-loneliness The neuroscience of loneliness] (Psychology Today) ;Case study links [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Forensic]] [[Category:Motivation and emotion/Book/Self]] h2b7e872f43iv94bek1spkt2xchwis8 Motivation and emotion/Book/2024/Theory of positive disintegration and personal growth 0 306598 2684174 2681783 2024-11-12T09:47:52Z Jtneill 10242 /* Overview */ Move case study to beginning 2684174 wikitext text/x-wiki {{title|Theory of positive disintegration and personal growth:<br>What is the TPD and how can it be applied to personal growth?}} {{MECR3|1=https://youtu.be/ceKgUSKfyv8}} <div align=center></div> __TOC__{{RoundBoxTop|theme=13}}Focus questions: How can high developmental potential impact decision making? What is the TPD and how can it be applied to personal growth? How can TPD be motivational to individuals experiencing the disintegration of their personality? {{RoundBoxBottom}} ==Overview== {{RoundBoxTop|theme=13}} ;Case study example When Wyoh was in high school, they began to question "why?". Why are people so cruel? Why do I have to go to school? Why do I have to wear these clothes when I'd rather wear what I want to? As a response to this, Wyoh began to make decisions about what they did, based on their own interest, but also about what they thought was just and right. They started wearing lots of elastic wristbands and changed their hairstyle. Sometimes they would skip school because they thought it was not helpful or worth going. These decisions exist on a singular level. There was no "right" or "wrong" decision here. Their decisions had consequences, but did not greatly change the way they though of themself. In doing this, Wyoh had begun their journey into positive disintegration. Over the next few years, Wyoh would travel back and forth between states of primary integration and unilateral disintegration, without ever moving past this point. Wyoh made many friends from different cliques and social groups throughout high school, due to their ever changing personality. When Wyoh started at university, it became clear that their decisions had clear impacts on not only themself, but others as well. Their decisions would have clear right and wrong alternatives, and over time, their decisions reflected their morals and expectations of themself. Wyoh had finally progressed into the third stage of positive disintegration. {{RoundBoxBottom}} The Theory of positive disintegration (TPD) is a theory of personality development, developed by Polish psychologist [[wikipedia:Kazimierz_Dąbrowski|Kazimierz Dąbrowski]], in which emotions play an essential role in motivation. TPD theorizes that personality development progresses from a state of primary integration, in which decisions are based off of [[mwod:egocentrism#:~:text=noun,or%20in%20disregard%20of%20others|egocentrism]], upward to intentional [https://plato.stanford.edu/entries/altruism/ altruism] and decisions influenced by empathy, compassion and self awareness. This ultimate level of personality development is known as secondary integration. Between primary and secondary integration, there exist three stages of disintegration. Within these stages of disintegration, the initial personality of a person, shaped over the course of their life by [[wikipedia:Impulsivity|biological impulse]] and social and environmental adherence, is dismantled, to be ultimately replaced by a conscious and self-aware, self-created personality. Dąbrowski theorized that for personality to develop in full, integrated aspects of personality based on instinct and social learning must be broken down, or ''disintegrated''. (Dąbrowski, K., 1970)[[File:Battling PTSD (4949341330) (cropped).jpg|thumb|Figure 1. War Veteran (Tense events contribute to multilevel disintegration)|238x238px]]Importantly, TPD posits that personality development does not follow a time schedule, nor is significantly aligned with physical developmental milestones, such as puberty, pregnancy or menopause, however these milestones may include stressors which may influence the onset or continuation of positive disintegration. Positive disintegration can frequently occur during periods of intense stress. See Figure 1. Whilst not following a time schedule, TPD postulates that it always progresses in the same sequence; the five stages of positive disintegration, always in the same order. During these stages of personality disintegration, development forces the person to make decisions, early on being unilateral, with no clear right or wrong decision, and later being multilevel decisions, where morally right and wrong decisions exist. Ultimately, morally correct decisions will be chosen the vast majority of the time, allowing the person to progress to secondary integration. Not all people who begin their journey through positive disintegration will complete their personality development. In fact, some may shift back and forth between stages and until finally completing the development of their ideal personality, and others may never complete this journey. Some people may never leave the first stage of primary disintegration. This is dependent on developmental potential. Developmental potential refers to the influence of biological impulse, social and environmental adherence, overexcitability, abilities and talents, and motivation. People with a high enough developmental potential will generally undergo a complete remodelling of their personality through positive disintegration, so much so, that when an individual with a high developmental potential does not undergo positive disintegration, it is a statistical outlier. (Dąbrowski, K., 1970) Dąbrowski believed (Dabrowski, Kawczak, & Piechowski, 1970) that an individual must develop their own hierarchy of values and emotional reactions to develop their personality, as well as recognition, appreciation and utilisation of their own autonomy. The majority of psychological theories surrounding personality and individual differences do not consider emotional reaction and response to play a key role in its production, where TPD does. TPD proposes that the way one reacts to emotional stimuli contributes greatly to the creation of their individual ''personality ideal'', which acts as the end-goal of self-development. == Development potential == Dąbrowski ideated ''Development Potential (DP)'', a way of measuring a response to stimuli.(Dabrowski, Kawczak, & Piechowski, 1970). Whether positive or negative, a strong DP means that the environment will play little role in the personality development. A weak DP means that the environment plays a more significant role. Dąbrowski highlights three major aspects of development potential as ''Overexcitability, Abilities and Talents, and the 'Third Factor' -'' an increased drive for autonomous growth. ==== First factor: biological impulse ==== People who direct their energy and talents to serve egocentric goals and their biological needs, based on survival and self advancement are highly guided by this factor. (Tillier, W., 1998). ==== Second factor: social/environmental adherence ==== The second factor, based on the social environment and peer pressure, encourages mob mentality through the restriction of individual expression and creativity. This discourages individual thought. Parallel to the hive-mind effect seen commonly in cults, social forces shape individual behaviour. Behaviour is not in line with free will concepts, instead being reflective or conducive of social norms. In this factor, talents, behaviours, and creative outlets are redirected to follow the existing social morals and values. (Tillier, W., 1998). Whilst this sounds like it opposes free will, people influenced by this factor are likely to behave ethically, as their conscience is formed by social context, as long as the social standards within the society are ethical. The concern is when these standards are not ethical, or become corrupt. In this case, people who are influenced greatly by the second factor are not likely to act against the unethical standards of the group. David C. Thomasma argues people within a society face challenges which may either allow the individual to grow, or push them to decay, throughout the course of their lives. These challenges impede their free choices and their ability to make customarily good choices, or even just to make their own decisions at all. (Thomasma and Weisstub, 2004. p10). In general, when socialization occurs within this factor without an individual examining themself, they live a life parallel to that of a drone — robotic. Dąbrowski argues that a significant majority of the general population are primarily motivated by the second factor.(Dąbrowski, K., 1964). === Overexcitability (OE) === In the context of TPD, overexcitability refers to the ways in which 'gifted' individuals have an increased capacity for experiencing stimuli, whether internal or external. These individuals experience stimuli more intensely than others, and this overexcitability is a prerequisite to positive disintegration. (Mendaglio and Tillier, 2006). {{RoundBoxTop|theme=9}}Research study A 2017 Hong Kong study was conducted on the relationship between Overexcitabilities (OEs) and creativity, aligning with Dabrowski's theory. It found that individuals with higher levels of imaginational OE, followed by intellectual, emotional, sensual, and psychomotor OEs, tend to exhibit greater creativity with an astounding 71.8% accuracy rate among participants. The research suggests that OEs can be a useful indicator for identifying creatively gifted individuals. However, the study's reliance on the overexcitability questionnaire two (OEQII) as the sole measure of OEs is a limitation. Future research should consider employing diverse assessment methods and acknowledge the inherent limitations of self-report measures. Further, the study’s age range of the participants was a limitation as it only focused on students from grade 7-11. Which posits that the same research may be invalid in varying age ranges, future studies may benefit from gaining a broader understanding of the true relationship between OE and creativity (He et al., 2017).{{RoundBoxBottom}} === Types of overexcitability === Overexcitability is a broad subject, leading Dabrowski (Dabrowski, K, 1996) and Piechowski (Piechowski, M., 1986) to divide the topic into five distinct types. ==== Psychomotor overexcitability ==== Psychomotor overexcitability refers to an increased amount of energy. This may look like increased psychomotor arousal, or nervousness. The individual may engage in more [[wikipedia:Stimming|self stimulatory behaviours]] (stimming, fidgeting), in order to address excess psychomotor energy. (Piechowski, M.,1986) ==== Sensual overexcitability ==== Individuals with sensual overexcitability experience sensory pleasures more intensely than others. Piechowski, a close collaborator with Dabrowski, quotes a "keen sensual alliveness" (Piechowski, M., 1986, pp.90). He stated in his 1986 publication, that sensual OE is expressed through looking for sensual outlets for internal tensions, notably through overeating and sexual experience. (Nelson, K., 1989). ==== Imaginational overexcitability ==== People who experience this form of overexcitability have an increased sense of imagination. This presents as the individual having more expressive imagery, metaphorical thinking, fantastical thinking and animalistic thinking, which all may become obvious to others through the ways in which the individual tells stories, narrates their experiences and expresses themselves. (Nelson, K., 1989). ==== Intellectual overexcitability ==== Intellectually overexcited individuals have more mental activity than others, making their thinking patterns more theoretical. These individuals generally have a intense desire to learn and understand a range of topics or perhaps fewer niche ones. (Nelson, K., 1989). ==== Emotional overexcitability ==== Individuals who are emotionally overexcited experience intense emotional relationships, more so than the general population. These relationships are often formed with and by people and other living things, as well as places of interest. (Piechowski, M., 1979) === Dynamisms === [https://www.thirdfactor.org/subject-object-in-oneself/ Dynamisms] are processes of change, or the forces by which change is manifested. In relation to TPD, dynamisms serve to develop objectivity within an individual, relieve tensions which may not be conducive to creative processes and create conditions which allow the individual to develop their personality in ways which are psychically healthy. (Dąbrowski, K., 1964) Dąbrowski posits (Dąbrowski, K., 1964) that the overexcitability factors of Emotional, Intellectual and Imaginational are the ones which play the most significant role in forming the dynamisms that shape and direct the development of personality <blockquote>"Emotional, intellectual, and imaginational overexcitability play the significant role in the formation of developmental dynamisms that shape and direct personality development" (Dąbrowski, K., 1996)</blockquote> Developmental dynamisms which lack organization, or are spontaneous, do not generally contribute to the process of positive disintegration. Conversely, developmental dynamisms that are organized, and encourage understanding and reconceptualization, greatly contribute to the process of positive disintegration. (Dąbrowski, K., 1964). === Abilities and talents === Abilities and talents are specific to the individual. At low levels of personality development, individuals utilise their talents and abilities to support person-centred goals, such as to support their progression within social and workplace hierarchies. At higher levels of personality development, individuals no longer only use their abilities and talents egocentrically, rather implementing them into their own personal hierarchy of values, so that they may firstly express their vision of their ideal personality and worldview, and then secondly, achieve it. (Piechowski, M., 2002) === (Not so) secret third factor of personality development- drive/motivation === When considering the broader topic of motivation, the third factor of developmental potential really answers the question: How can TPD be applied to personal growth?. Dąbrowski outlines the third factor of DP to be a drive or motivation towards the growth and autonomy of the individual. As such, he posited that this third factor plays along with the second, as it '''requires''' that the individual apply their talents, abilities and creativity to the broad context of their autonomous expression. Due to this, the individual would then by '''motivated''' to achieve more and to begin to imagine and ideally achieve goals beyond their own expectations.(Dąbrowski, K., 1964). === Third factor vs free will === Whilst seemingly similar and interrelated, Dąbrowski argues that there is an important distinction to be made between the two. He posited that free will, as a concept, did not encapsulate motivation, as somebody may have free will, but not be motivated towards growth. His Third Factor refers to motivation specifically as a drive to become one's unadulterated and honest self. (Dąbrowski, K., 1964). The motivation of an individual to reach self-actualization may be (and often is) so intense that they may put themselves in harms way to do so. Whilst talking about motivation - especially in the context of the Theory of Positive Disintegration - it is crucial to ensure that one does not encourage others to seek out risk taking behaviours. When communicating the fact that circumstances which are hazardous or dangerous can lead to '''some''' individuals becoming closer to achieving their 'true self', one must highlight that this book chapter does not recommend that people go out of their way to endanger themselves. Some people feel that no cost is beyond the reward of 'being their real self', and as such, is not perfectly aligned with the concept of free will, because some people believe that their isn't really a choice here, that they must become themselves, no matter what. === Development potential - bottom line === Dąbrowski's Theory of Positive Disintegration says that individuals with a high enough DP most likely will undergo disintegration, and that high Developmental Potential is positively related to likelihood of disintegration of their personality. In fact, TPD considers the case of a high DP individual not undergoing personality disintegration as an outlier.(Dąbrowski, K., 1970) == Multi-level approach to understanding positive disintegration == Dąbrowski describes the continuity of personality development through a multilevel approach. His theory posits that DP actually contributes to the catalysing of a crisis. Overexcitability and the Third Factor (motivation/drive) combine to contribute to an individual seeking out experience which are anxiety and depression inducing. Dąbrowski referred to this phenomenon as [[wikipedia:Neurosis|psychoneurosis]]. This psychoneurosis (neurosis) contributes to disintegration. (Dąbrowski, K., 1964). === The levels of positive disintegration === Dąbrowski developed a multi-level system for describing positive disintegration. The levels are as follows: ==== Level 1: primary/primitive integration ==== Dąbrowski believed that people whose lives are largely guided by either biological impulse or social/environmental adherence, or both, are likely to live in a state of primary/primitive integration. He referred to these people as the 'average people', as they represent the majority of the general population. Dąbrowski posited that being at level of one was to be in a state contrary to a healthy mental state. He also stated that the average person has a '''fairly high''' degree of primary integration, and a psychopath would have a '''very high''' degree of primary integration. This level is characterized by selfishness, egocentrism and self fulfilment. (Nelson, K. C.,1989) Most people never break this level of integration down at all. Out of those who do, the majority return to this level after a brief period of disintegration (Nelson, K. C.,1989). Whilst this state is not generally conducive to a positive mental state, Dąbrowski found that those who return to this state after disintegration may have worth and value as this state is predictable and has innate structural stability, and when the individual possesses qualities of kindness and empathy may often provide support to people experiencing disintegration.(Nelson, K. C.,1989). ==== Level II: unilevel disintegration ==== This level is characterised by an initial crisis or crises. Often extreme, these crises are spontaneous, and unexpected. The individual is not prepared, nor taught to be, for these crises. Unilevel crises always, and only, exist on one level. There is no choice between better or worse. (Nelson, K. C.,1989) Often, these crises coincide with developmental crises such as puberty or menopause. This is because these crises are more likely to occur when the individual is experiencing difficulty coping with external events. This means that the crisis commonly occurs in conjunction with psychological distress. (Nelson, K. C.,1989) At this time, dynamisms begin to come into play. During Unilevel Disintegration, these dynamisms occur with a lack of self control and self-consciousness, due to this, these dynamisms may contribute to the individual being put in risk taking situations or dangerous circumstances. (Nelson, K. C.,1989) Unilevel crises present themselves in two distinct forms. The first is through ambitendencies, where the individual is presented with two options that they are equally attracted to and must decide on one. The second is ambivalences, where the individual has no preference between the two options. If the forces of development are intense enough, and/or the developmental potential of the individual is high enough, the individual will face an existential crisis. This is because their previously conceptions of reason does not account for their experience and there is no other possible explanation for the way that they are feeling. At this point, the individual experiences a heightened sense of existential despair, so much so that it usually becomes the predominant emotion of the individual at the time. (Nelson, K. C.,1989) In response to this, the individual must then tear down their prescribed values and form their own. During this time, we get phases of social rebellion, as social norms no longer make sense to the individual. This causes the individual to begin to assess other aspects of life and the existence of others and their lives, creating for themselves further crises. Dąbrowski does not suggest this be avoided. Dąbrowski encourages rebellion. He posit that these crises are representations of a strong potential for development of personality, as well as having strong potential for positive mental health consequences. (Nelson, K. C.,1989) Level II is a transitory period. Individuals who do not progress to level III will either regress back to level I, or never escape level II. A lack of escape from this level is seen through [https://www.who.int/news-room/fact-sheets/detail/suicide suicide] or [[wikipedia:Psychosis|psychosis]]. An unreasonable, and an rarely achievable amount of energy is required to progress to level III. When facing the transition (forward to level III, or backward to level I), an individual has to decide whether to follow their instincts (factor one of personality development), what they have been taught (factor two), or their heart — or dreams for their future (factor three). To progress to level III, the individual must transform their low level instincts, such as emotional reactions, into positive motivational forces, and resist what has been taught, instead following their inner sense of what is right.(Nelson, K. C.,1989) ==== Level III: spontaneous multilevel disintegration ==== At this level, the individual is faced with crises that transcend horizontal levels. Two alternatives do not exist on the same level, instead, one alternative is a lower choice (staying the same, or not becoming a better person, actuality) and one is a higher choice (imagined ideals). These crises require imaginational OE to navigate, as an individual with a genuine need to become their true selves would choose the higher alternative every time, knowing innately that it is the right one to chase. This means overcoming the ambivalences and ambitendencies of level II. (Nelson, K. C.,1989) If the individual's actual behaviour does not reach the level of their ideal self, the self-seeking individual will be driven (third factor) to reassess and rebuild their life. (Nelson, K. C.,1989) Level III is where the individual finds their '''drive''' and '''motivation''' for development. All future future events in life will henceforth be in relation to their ideal self, and it becomes unreasonable to be positioned in ways that favour a lower course of action, when a higher goal can be imagined (imaginational OE). (Nelson, K. C.,1989) ==== Level IV: directed multilevel disintegration ==== In this level, development is no longer enacted upon the individual involuntarily or spontaneously, rather the individual reviews life consciously, from the multilevel perspective. In this level, the third factor begins its full emergence as the individual guides their own life, affirming and rejecting aspects and qualities of their life and environment. Lower views and reactions get replaced by cautiously examined ideals. The individual's behaviour becomes less reactive and automatic, rather being deliberate and reflective of their higher, chosen ideals. Individuals within the highest levels of personality development place responsibility on themselves for protection of others, and for justice.(Nelson, K. C.,1989) ==== Level V: secondary integration ==== The fifth level is similar to the first level, in that the individual's personality is no longer in a state of disintegration. However, it varies from the first level, as the individual's behaviour is guided by decisions formed from a hierarchy of personal values. Very little inner conflict exists at this level, because the person's behaviour is based on their inner standard of how life is meant to be lived. (Nelson, K. C.,1989) People who are at the fifth level of personality development see problem solving as well as art as the most noble features of human life, and are often marked by their creative expression. This is likely due to how art is seen to capture the artists deep understanding of the subject, which generally tend to be suffering and sacrifice for artists at this level of personal development. (Nelson, K. C.,1989) == Key points == * '''TPD''' is a theory of personality development proposed by Kazimierz Dąbrowski, suggesting that psychological stress can lead to personal growth. * '''Core concepts:''' ** '''Positive disintegration:''' The process of breaking down existing personality structures to create a more integrated and authentic self.   ** '''Developmental potential (DP):''' The individual's capacity for growth and resilience.   ** '''Overexcitability:''' Increased sensitivity to stimuli in areas like psychomotor, sensual, imaginational, intellectual, and emotional. ** '''Dynamisms:''' Forces that shape personality development, including organized and spontaneous processes. ** '''Levels of positive disintegration:''' A multi-level approach to personality development, from primary integration to secondary integration. * '''Key stages of personality development:''' ** '''Primary/primitive integration:''' Initial state characterized by conformity and adherence to social norms.   ** '''Unilevel disintegration:''' Crisis-filled period of questioning and challenging existing beliefs. ** '''Spontaneous multilevel disintegration:''' A deeper level of questioning and self-reflection.   ** '''Directed multilevel disintegration:''' Conscious and deliberate development of personality.   ** '''Secondary integration:''' A final state of integration based on personal values and ideals. * '''TPD emphasizes:''' ** The importance of psychological stress for personal growth. ** The role of individual choice and autonomy in personality development. ** The connection between overexcitability and developmental potential.   ** The transformative power of crises and challenges. * '''Overall, TPD offers a unique perspective on personality development, suggesting that adversity can be a catalyst for positive change.''' The key points section of this book chapter utilises genAI for its summary. == Quiz == <quiz display="simple"> {Level II of personality development is characterized by multilevel crises: |type="()"} - True + False {Dąbrowski's Theory of Positive Disintegration posits that to develop personality past social adherence, one must face hardship and crisis: |type="()"} + True - False </quiz> ==Conclusion== TPD offers a valuable framework for understanding personal growth and development. By recognizing the role of disintegration and cultivating sensitivity, individuals can embark on a journey of self-discovery and self-actualization. TPD can be applied to personal growth, as the theory itself is one that focuses on how life events and crises impact decision making, and how decision making impacts personal growth. This is seen through the five levels of positive disintegration, where the linear path of disintegration includes changes at each level, which push the individual to grow rather than to decay. This theory is important, as it is a reminder that setbacks and crises do not make life meaningless. TPD posits that for people with a high development potential, these crises can actually be the catalyst for development and may ultimately be what the individual needs to become their true self. TPD ideates that individuals should seek out experience rather than waiting for it to happen. This theory encourages individuals to take control of their own growth on a personal level, rather than looking to change the world. TPD teaches that personal growth must be just that; personal. Whilst positive disintegration requires the same path to be taken to reach secondary integration, the decisions made and the length of time it takes will always be different, and as such, one individual can not intentionally push others towards their personal growth. The key takeaways for this chapter are as follows: # To embrace disintegration, as it is a natural process and an opportunity to break free from patterns and limitations. # To cultivate a sense of sensitivity in themselves, to recognise their strengths and sensitivities and use them for growth through self reflection and creativity. # To seek depth within their lives, explore their emotions, feelings and experiences and to challenge their beliefs and explore new perspectives. # To embrace challenges; to learn from setbacks and view them as opportunities for growth. Next time life throws you a curveball, try to recall this theory. Will you accept challenges and view them as an opportunity for growth, or avoid the crisis to hold on to primary integration? ==See also== * [[Motivation and emotion/Book/2022/Psychological trauma|Psychological Trauma]] (Book chapter, 2022) * [[wikipedia:Antifragility|Antifragility]] * [[wikipedia:Michael_Fordham#De-integration_and_re-integration|De-Integration and re-integration]] * [[wikipedia:Personal_development|Personal Development]] * [[wikipedia:Post-traumatic_growth|Post-Traumatic Growth]] * [[wikipedia:Personality_psychology|Personality Psychology]] * [[wikipedia:Kazimierz_Dąbrowski|Kazimierz Dabrowski]] * [[wikipedia:Impulsivity|Biological impulse]] ==References== {{Hanging indent|1= American Psychiatric Association. (2022). Diagnostic and statistical manual of mental disorders (5th ed.). Arlington, VA Dabrowski, K. (1964). Positive disintegration. Boston, MA: Little Brown. Dabrowski, K. , Kawczak, A. & Piechowski, M. (1970). Mental growth through positive Disintegration. London: Gryf Publication Ltd. Google AI. (2024) Gemini. [large language model] https://gemini.google.com/app He, W., Wong, W., & Chan, M. (2017). Overexcitabilities as important psychological attributes of creativity: A dabrowskian perspective. Thinking Skills and Creativity, 25(6), 27–35. https://doi.org/10.1016/j.tsc.2017.06.006 Mendaglio, S., & Tillier, W. (2006). Dabrowski's Theory of Positive Disintegration and Giftedness: Overexcitability Research Findings. Journal for the Education of the Gifted, 30(1), 68–87. https://doi.org/10.1177/016235320603000104 Nelson, K. C. (1989). Dabrowski's theory of positive disintegration. ''Advanced Development'', ''1'', 1-14. Piechowski, M. M. (1979). Developmental potential. "New voices in counseling the gifted. Piechowski, M. M. (2002). Experiencing in a Higher Key; Dabrowski's Theory of and for the Gifted. Schläppy M. L. (2019). Understanding Mental Health Through the Theory of Positive Disintegration: A Visual Aid. ''Frontiers in psychology'', ''10'', 1291. https://doi.org/10.3389/fpsyg.2019.01291 Third Factor (2024, October). Dabrowski's Dynamisms: Subject-Object in Oneself. Retrieved from https://www.thirdfactor.org/subject-object-in-oneself/ Thomasma, D.C., (2004). Morality as Impulse and Ethics as “Thinking” about Morality. INTERNATIONAL LIBRARY OF ETHICS, LAW, AND THE NEW MEDICINE, 309, 10. Tillier, W. (1998). The basic concepts of Dabrowski’s theory of positive disintegration. The Dabrowski Newsletter, 5, 1-5. Weckowicz, T. E. (1988). Kazimierz Dabrowski's Theory of Positive Disintegration and the American Humanistic Psychology. ''Counseling and Values, 32, 2.'' https://doi.org/10.1002/j.2161-007X.1988.tb00706.x Wikipedia (2023, September 29). Positive disintegration. Retrieved from https://en.wikipedia.org/wiki/Positive_disintegration Wikipedia (2024, September 29). Social learning theory. Retrieved from https://en.wikipedia.org/wiki/Social_learning_theory Wikipedia (2024, October 1). Stimming. Retrieved from https://en.wikipedia.org/wiki/Stimming }} ==External links== *[https://wikipedia.org/wiki/Positive_disintegration Positive Disintegration] *[https://wikipedia.org/wiki/Social_learning_theory Social Learning Theory] *[[wikipedia:Stimming|Self-Stimulatory Behaviours]] *[[wikipedia:Social_osmosis|Social Osmosis]] *[[wikipedia:Neurosis|Neurosis]] *[https://www.who.int/news-room/fact-sheets/detail/suicide Suicide] *[[wikipedia:Psychosis|Psychosis]] *[https://plato.stanford.edu/entries/altruism/ Altruism] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Personal development]] [[Category:Motivation and emotion/Book/Self]] ckez3yzmsodjmxr4d2k63afolvulmmx Talk:Motivation and emotion/Book/2024/Comprehensive action determination model 1 307040 2684060 2682777 2024-11-12T00:16:33Z Jtneill 10242 Draft feedback 2684060 wikitext text/x-wiki ==Initial suggestions== {{ping|HassanAlsamara}} Thanks for tackling this topic. Some initial suggestions: * Check out other related chapters and see how you can build on, link to, and integrate with that work: ** [[:Category:Motivation and emotion/Book/Behaviour]] ** [[:Category:Motivation and emotion/Book/Environment]] * Also [[Motivation and emotion/Book|search past book chapters for related topics]] * For the [[Motivation and emotion/Assessment/Topic|topic development]], consider: ** What psychological theory(ies) can help to understand and explain this topic? ** What is the main research in this area? * Let me know if I can do anything else to support the development of this chapter. Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:16, 11 August 2024 (UTC) <!-- Official topic development feedback --> {{METF/2024 |1= <!-- Title --> # The title and/or sub-title were not correctly worded and/or formatted (fixed) |2= <!-- Headings --> # See earlier comment about [[#heading casing|Heading casing]] # Insufficient development of headings to unpack the topic <!-- Alignment with focus questions --> # Reasonably good alignment between focus questions and heading structure, but consider closer alignment <!-- Other ---> # Check and correct capitalisation # Background info about motivation is not needed; instead, unpack the CADM and its application |3= <!-- Overview--> <!-- Scenario --> # Add a scenario or case study in a feature box (with an image) at the start of this section to help catch reader interest <!-- Description --> # Add a brief, evocative description of the problem/topic <!-- Focus questions --> # Reasonably good alignment between focus questions and heading structure, but consider closer alignment # Tailor the focus questions away from general questions about motivation to more specific unpacking of the sub-title |4= <!-- Key points--> # Promising development of key points for each section, with relevant citations # For sections which include sub-sections, include the key points for an overview paragraph prior to branching into the sub-headings # ''Avoid providing too much background information''. Aim to briefly summarise general concepts and provide internal links to relevant book chapters and/or Wikipedia pages for further information. Then focus most of the content on ''directly answering the core question(s)'' posed by the chapter sub-title. # Use APA style for citations (e.g., alphabetical order) # Use Australian spelling <!-- Theory and research --> # Strive for an integrated balance of the best psychological theory and research about this topic, with practical examples <!-- Conclusion --> # Conclusion (the most important section): ## Underway ## What might the take-home, practical messages be? (What are the answer(s) to the question(s) in the sub-title and/or focus questions?) |5= <!-- Figure --> # One or more figure(s) is/are presented and captioned # The relevance of one or more figures isn't clear <!-- Caption --> # The figure caption(s) could better explain how the image connects to key points being made in the main text <!-- Cite --> # Cite each figure at least once in the main text using APA style (e.g., see Figure 1) |6= <!-- Learning feature --> <!-- Interwiki links ---> # Include in-text [[m:Help:Interwiki linking|interwiki links]] for the first mention of key terms to relevant Wikipedia articles and/or to other relevant book chapters (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) <!-- Examples/case studies --> # Consider use of one or more scenarios/examples/case studies <!-- Quiz --> # Focus the quiz question(s) on the take-home messages for each focus question <!-- Tables --> # Also consider using one or more tables to summarise key information |7= <!-- References --> <!-- Overall --> # OK # Messy # Reeve is overused as a citation <!-- Systematic reviews --> # Are there any systematic reviews about this topic? <!-- Suggestions --> # Check and correct [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style]: ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] ## [https://apastyle.apa.org/instructional-aids/reference-guide.pdf doi formatting] ## make doi hyperlinks active (i.e., clickable) ## use dois where available instead of other links |8= <!-- Resources --> <!-- See also --> # See also ## Very good ## Link to the most relevant Wikipedia page(s) - emotion is too general ## Use alphabetical order <!-- External links --> # External links ## OK ## Move Wikipedia link to see also (much better than the emotion link) ## Other link is too general ## Only include links directly related to the sub-title |9= <!-- User page --> # Very good <!-- Description about self --> # Excellent description about self provided <!-- Links to profile(s) --> # Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks. <!-- Link to book chapter --> # A link to the book chapter is provided |10= <!-- Social contribution --> # Good – two out of three types of contributions made with with direct link(s) to evidence. The other type of contribution is making: ## posts about the unit or project on other platforms such as the {{Motivation and emotion/Canvas}} discussion forum or on [https://x.com X] using the {{Motivation and emotion/Hashtag}} }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:40, 26 August 2024 (UTC) {{MEMF/2024 |1= <!-- Overall comments ... --> <!-- Overall - Overall --> # Overall, this is a basic presentation |2= <!-- Overview comments ... --> <!-- Overview - Opening --> # The opening conveys the purpose of the presentation in a basic way # Incorrect date on opening slide <!-- Overview - Introduction --> # Create an engaging introduction to hook audience interest (e.g., through an example) <!-- Overview - Context --> # A basic context for the presentation is established <!-- Overview - Focus --> # Consider asking focus questions to help focus and discipline the presentation |3= <!-- Content comments ... --> # Comments about the book chapter may also apply to this section <!-- Content - Addresses topic --> # The presentation addresses the topic <!-- Content - Amount --> # An appropriate amount of content is presented — not too much or too little, but the balance could be improved (it is very theoretically dry) <!-- Content - Theory --> # The presentation makes good use of relevant psychological theory <!-- Content - Research --> # The presentation makes insufficient/no use of relevant psychological research <!-- Content - Citations --> # The presentation makes basic use of citations to support claims <!-- Content - Examples --> # The presentation makes insufficient use of examples <!-- Content - Practical advice --> # The presentation could be improved by providing practical advice |4= <!-- Conclusion comments ... --> <!-- Conclusion - Slide --> # Provide a conclusion which summarises the most relevant psychological theory and research about this topic, with take-home messages for each focus question |5= <!-- Audio comments ... --> <!-- Audio - Narration --> # The presentation makes very basic use of narrated audio <!-- Audio - Pacing --> # Audio communication is reasonably well-paced <!-- Audio - Voice --> # Basic [[w:Intonation (linguistics)|intonation]] <!-- Audio - Practice --> # The narration could benefit from further scripting and/or practice <!-- Audio - Recording quality --> # Audio recording quality was excellent <!-- Audio - Topic --> # The narrated [[#Content|content]] is reasonably well matched to the target topic |6= <!-- Video comments ... --> <!-- Video - Overall --> # Overall, visual display quality is basic <!-- Video - Video, Image, Text --> # The presentation makes basic use of text and image based slides # The presentation makes basic use of text-based slides <!-- Video - Text - Font --> # The font size is sufficiently large to make it easy to read <!-- Video - Text - Amount --> # The amount of text presented on one or more slides could be reduced to make it easier to read and listen at the same time <!-- Video - Images --> # The visual communication is supplemented in a basic way by relevant images and/or diagrams <!-- Video - Production --> # The presentation is basically produced using simple tools <!-- Video - Topic --> # The visual [[#Content|content]] is reasonably well matched to the target topic |7= <!-- Meta-data comments ... --> <!-- Meta-data - Title/sub-title --> # The (almost) correct title is used, but the sub-title (or a shortened version of it) is not used, as the name of the presentation. This would help to convey the purpose of the presentation and be consistent. <!-- Meta-data - Description --> # A brief written description of the presentation is provided. Expand. <!-- Meta-data - Links --> # Links to and from the book chapter are provided |8= <!-- Licensing comments ... --> <!-- Licensing - Images --> # Image sources and their copyright status are communicated # Provide clickable links to the image sources and license details (e.g., in the description) <!-- Licensing - Presentation --> # A copyright license for the presentation is clearly indicated }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 06:40, 10 November 2024 (UTC) == Heading casing == {| style="float: center; background:transparent;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:HassanAlsamara|Hi [[User:HassanAlsamara|HassanAlsamara]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:16, 12 November 2024 (UTC) |} ==Draft feedback== {{ping|HassanAlsamara}} From a very quick look at current draft: * Looks comprehensive (but this isn't based on reading, only a quick scan) * See comment above about heading capitalisation * Remove trailing colons from headings * Follow [https://apastyle.apa.org/style-grammar-guidelines/capitalization APA style for capitalisation] * Use ''focused'' focus questions (e.g., avoid general questions such as why is understanding motivation important) * Use APA style for citations (e.g., alphabetical order for multiple citations) * Use Australian spelling (internalized -> internalised) * The draft is over the maximum word count (e.g., reduce the section "What is motivation?") * Use APA style for references * Use 3rd person perspective rather than first person perspective (e.g., remove "we") * Some paragraphs overly long (aim for 3 to 5 sentences) Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 00:16, 12 November 2024 (UTC) qqklrwjho4dj9voikejjljng36n1sy5 Motivation and emotion/Book/2024/Generativity 0 307279 2684094 2676746 2024-11-12T01:58:15Z Rocxie 2969341 2684094 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). ====== '''Generativity and Self-Determination Theory''' ====== Generativity aligns closely with self-determination theory (SDT), which proposes that humans are motivated by the need for relatedness, competence, and autonomy. Generative actions, such as mentoring or community volunteering, fulfill these basic psychological needs by fostering connections with others (relatedness), offering meaningful contributions (competence), and often allowing individuals to act according to personal values (autonomy) (Ryan & Deci, 2000). <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however-it{{gr}} also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). ===== '''Link to Generativity in Social and Environmental Challenges''' ===== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In summary, generativity represents the human drive to leave a positive legacy. It encourages individuals to contribute to the world around them, fostering a sense of purpose and well-being. By engaging in generative actions, people can experience a stronger sense of belonging, improved mental health, and personal fulfillment. As research shows, whether through raising families, building communities, or advocating for social and environmental causes, generativity allows us to make a lasting impact. Looking ahead, future research could further examine how generativity is expressed in different cultures and how it impacts younger generations, particularly as they face unique challenges in a rapidly changing world. Investigating how digital platforms can facilitate generative actions, like online mentorship or activism, could also broaden our understanding of generativity in the modern age. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. ''The Journals of Gerontology: Series B, 69''(1), 55-64. https://doi.org/10.1093/geronb/gbt007 Erikson, E. H. (1950). Childhood and society. W. W. Norton & Company. Erikson, E. H. (1950). Generativity versus stagnation: An elaboration of Erikson's adult stage of human development. ''Journal of Adult Development, 10''(1), 53-65. Erikson, E. H., & Erikson, J. M. (1998). The life cycle completed (extended ed.). New York: W. W. Norton & Company. Epstein, R. (1999). Generativity theory. ''Encyclopedia of creativity, 1'', 759-766. Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] scs8j3jnq9c5ngnndispqab5cpxsc49 2684101 2684094 2024-11-12T02:02:47Z Rocxie 2969341 2684101 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). ====== '''Generativity and Self-Determination Theory''' ====== Generativity aligns closely with self-determination theory (SDT), which proposes that humans are motivated by the need for relatedness, competence, and autonomy. Generative actions, such as mentoring or community volunteering, fulfill these basic psychological needs by fostering connections with others (relatedness), offering meaningful contributions (competence), and often allowing individuals to act according to personal values (autonomy) (Ryan & Deci, 2000). <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however-it{{gr}} also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In summary, generativity represents the human drive to leave a positive legacy. It encourages individuals to contribute to the world around them, fostering a sense of purpose and well-being. By engaging in generative actions, people can experience a stronger sense of belonging, improved mental health, and personal fulfillment. As research shows, whether through raising families, building communities, or advocating for social and environmental causes, generativity allows us to make a lasting impact. Looking ahead, future research could further examine how generativity is expressed in different cultures and how it impacts younger generations, particularly as they face unique challenges in a rapidly changing world. Investigating how digital platforms can facilitate generative actions, like online mentorship or activism, could also broaden our understanding of generativity in the modern age. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. ''The Journals of Gerontology: Series B, 69''(1), 55-64. https://doi.org/10.1093/geronb/gbt007 Erikson, E. H. (1950). Childhood and society. W. W. Norton & Company. Erikson, E. H. (1950). Generativity versus stagnation: An elaboration of Erikson's adult stage of human development. ''Journal of Adult Development, 10''(1), 53-65. Erikson, E. H., & Erikson, J. M. (1998). The life cycle completed (extended ed.). New York: W. W. Norton & Company. Epstein, R. (1999). Generativity theory. ''Encyclopedia of creativity, 1'', 759-766. Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] q2ant1fvsykop3cfr3boctzmdt71wah 2684105 2684101 2024-11-12T02:15:41Z Rocxie 2969341 2684105 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). == '''Integrating Generativity with Other Theories''' == * '''Self-Determination Theory (SDT)''' Self-Determination Theory, developed by Ryan and Deci, posits that human motivation is driven by three core psychological needs: autonomy, competence, and relatedness (Ryan & Deci, 2000). Generativity aligns with these needs, particularly relatedness and competence. Generative actions, such as mentoring or community service, fulfill the need for relatedness by fostering deep connections with others. They also satisfy the need for competence, as individuals use their skills and knowledge in meaningful ways that benefit others. When people engage in generative behaviors, they experience a sense of accomplishment and purpose, strengthening their intrinsic motivation to continue contributing to their community and society. * '''Attachment Theory''' Bowlby’s Attachment Theory suggests that strong, secure attachments formed in early life influence relationships and behaviors in adulthood (Bowlby, 1969). Generativity can be viewed as an extension of secure attachment; individuals who have experienced strong, positive attachments often seek to provide the same security and support to others, particularly to younger generations. This drive to nurture and guide can be seen as an outgrowth of the attachment system, with adults aiming to create safe, supportive environments for those they care about. * '''Social Identity Theory''' Tajfel and Turner’s Social Identity Theory proposes that people derive a significant part of their self-concept from group memberships and social roles (Tajfel & Turner, 1979). Generativity often manifests as a desire to contribute positively to one’s social group, whether that group is defined by family, profession, culture, or even a global community. By engaging in generative acts—such as mentoring younger professionals or advocating for social causes—individuals strengthen their social identity and feel more connected to their group. Generativity thereby reinforces a positive self-image and enhances one's role within society. * '''Positive Psychology and Meaning in Life''' Positive psychology emphasizes the pursuit of a meaningful and fulfilling life. Viktor Frankl's concept of “meaning-making” aligns closely with generativity, as generative actions allow individuals to feel that they are part of something larger than themselves (Frankl, 1985). Research in positive psychology suggests that people who engage in generative behaviors often experience a greater sense of purpose and satisfaction (Seligman, 2002). This sense of meaning is crucial for mental well-being, as individuals who feel they are contributing to the future or to others’ well-being report higher levels of life satisfaction and personal fulfillment. * '''Theory of Moral Development''' Kohlberg’s stages of moral development describe how individuals’ moral reasoning evolves over time, from a focus on self-interest to a consideration of broader social welfare (Kohlberg, 1981). Generativity reflects higher stages of moral development, where individuals prioritize ethical responsibility and concern for future generations. Generative actions are often guided by principles of fairness, justice, and altruism, suggesting that individuals with strong generative drives may also exhibit advanced moral reasoning. * '''Terror Management Theory (TMT)''' Terror Management Theory posits that awareness of mortality drives people to seek meaning and legacy, which buffers existential anxiety (Greenberg et al., 1986). Generativity serves as a key response to this existential concern, as it allows people to invest in projects, relationships, and causes that will endure beyond their lifetime. By contributing to something lasting, individuals mitigate fears of death and secure a sense of symbolic immortality, finding comfort in the thought that their efforts will impact future generations. <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however-it{{gr}} also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In essence, generativity represents a profound human drive to leave a positive legacy, impacting not only our own lives but also the communities and generations that follow. Rooted in Erikson's stages of development, generativity encourages us to reach beyond ourselves, creating meaningful contributions through family, work, community involvement, and social causes. Research consistently demonstrates that engaging in generative actions promotes mental well-being, deepens social connections, and fosters resilience—qualities that become essential as societies face complex global challenges. Beyond personal fulfillment, generativity also has a ripple effect. When individuals commit to nurturing others, mentoring youth, or advocating for sustainable practices, they inspire similar behaviors in those around them. This cycle of positive influence strengthens communities and reinforces the importance of social responsibility. In a world increasingly defined by rapid change, generativity provides a stable foundation for fostering empathy, cooperation, and a shared commitment to future well-being. Reflecting on generativity invites us to ask important questions: ''What impact do I want to have?'' and ''How can I contribute to my community and future generations?'' By embracing generative actions, we actively shape not only our personal legacy but also the world we leave behind. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Bowlby, J. (1969). Attachment and loss: Vol. 1. Attachment. Basic Books. Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. ''The Journals of Gerontology: Series B, 69''(1), 55-64. https://doi.org/10.1093/geronb/gbt007 Erikson, E. H. (1950). Childhood and society. W. W. Norton & Company. Erikson, E. H. (1950). Generativity versus stagnation: An elaboration of Erikson's adult stage of human development. ''Journal of Adult Development, 10''(1), 53-65. Erikson, E. H., & Erikson, J. M. (1998). The life cycle completed (extended ed.). New York: W. W. Norton & Company. Epstein, R. (1999). Generativity theory. ''Encyclopedia of creativity, 1'', 759-766. Frankl, V. E. (1985). Man's search for meaning. Washington Square Press. Greenberg, J., Pyszczynski, T., & Solomon, S. (1986). The causes and consequences of a need for self-esteem: A terror management theory. In R. F. Baumeister (Ed.), Public self and private self (pp. 189–212). Springer-Verlag. Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 Kohlberg, L. (1981). The philosophy of moral development: Moral stages and the idea of justice. Harper & Row. McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Seligman, M. E. P. (2002). Authentic happiness: Using the new positive psychology to realize your potential for lasting fulfillment. Free Press. Tajfel, H., & Turner, J. C. (1979). An integrative theory of intergroup conflict. In W. G. Austin & S. Worchel (Eds.), The social psychology of intergroup relations (pp. 33–47). Brooks/Cole. Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] 5c2de02aapfy78pgpn1901l0idc7rzx 2684111 2684105 2024-11-12T02:34:41Z Rocxie 2969341 2684111 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). == '''Integrating Generativity with Other Theories''' == * '''Self-Determination Theory (SDT)''' Self-Determination Theory, developed by Ryan and Deci, posits that human motivation is driven by three core psychological needs: autonomy, competence, and relatedness (Ryan & Deci, 2000). Generativity aligns with these needs, particularly relatedness and competence. Generative actions, such as mentoring or community service, fulfill the need for relatedness by fostering deep connections with others. They also satisfy the need for competence, as individuals use their skills and knowledge in meaningful ways that benefit others. When people engage in generative behaviors, they experience a sense of accomplishment and purpose, strengthening their intrinsic motivation to continue contributing to their community and society. * '''Attachment Theory''' Bowlby’s Attachment Theory suggests that strong, secure attachments formed in early life influence relationships and behaviors in adulthood (Bowlby, 1969). Generativity can be viewed as an extension of secure attachment; individuals who have experienced strong, positive attachments often seek to provide the same security and support to others, particularly to younger generations. This drive to nurture and guide can be seen as an outgrowth of the attachment system, with adults aiming to create safe, supportive environments for those they care about. * '''Social Identity Theory''' Tajfel and Turner’s Social Identity Theory proposes that people derive a significant part of their self-concept from group memberships and social roles (Tajfel & Turner, 1979). Generativity often manifests as a desire to contribute positively to one’s social group, whether that group is defined by family, profession, culture, or even a global community. By engaging in generative acts—such as mentoring younger professionals or advocating for social causes—individuals strengthen their social identity and feel more connected to their group. Generativity thereby reinforces a positive self-image and enhances one's role within society. * '''Positive Psychology and Meaning in Life''' Positive psychology emphasizes the pursuit of a meaningful and fulfilling life. Viktor Frankl's concept of “meaning-making” aligns closely with generativity, as generative actions allow individuals to feel that they are part of something larger than themselves (Frankl, 1985). Research in positive psychology suggests that people who engage in generative behaviors often experience a greater sense of purpose and satisfaction (Seligman, 2002). This sense of meaning is crucial for mental well-being, as individuals who feel they are contributing to the future or to others’ well-being report higher levels of life satisfaction and personal fulfillment. * '''Theory of Moral Development''' Kohlberg’s stages of moral development describe how individuals’ moral reasoning evolves over time, from a focus on self-interest to a consideration of broader social welfare (Kohlberg, 1981). Generativity reflects higher stages of moral development, where individuals prioritize ethical responsibility and concern for future generations. Generative actions are often guided by principles of fairness, justice, and altruism, suggesting that individuals with strong generative drives may also exhibit advanced moral reasoning. * '''Terror Management Theory (TMT)''' Terror Management Theory posits that awareness of mortality drives people to seek meaning and legacy, which buffers existential anxiety (Greenberg et al., 1986). Generativity serves as a key response to this existential concern, as it allows people to invest in projects, relationships, and causes that will endure beyond their lifetime. By contributing to something lasting, individuals mitigate fears of death and secure a sense of symbolic immortality, finding comfort in the thought that their efforts will impact future generations. <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). A study by '''Steger, Frazier, Oishi, and Kaler (2006)''' explores the relationship between generativity and life satisfaction in adults. Their findings suggest that individuals who engage in generative behaviors experience higher levels of well-being, which further aligns with Erikson's assertion that generativity leads to fulfillment and purpose (Steger et al., 2006). Recent research has shown that generative behaviors are strongly linked to increased life satisfaction and psychological well-being, with studies like those by Steger et al. (2006) suggesting that generativity contributes to greater fulfillment and overall mental health. These findings support the idea that generativity is crucial for mental well-being across adulthood. Another longitudinal study by '''Grossmann and Gruenewald (2017)''' examined generativity at different stages of life, noting that while generativity peaks in middle adulthood, it remains significant in late adulthood as well. Their research provides insights into how older adults continue to engage in generative behaviors, often through community involvement, storytelling, and volunteerism. Grossmann and Gruenewald (2017) have emphasized that although generativity is most prominent during middle adulthood, it remains an important aspect of adult life well into late adulthood. Older adults often engage in generative behaviors through community service and passing on knowledge to younger generations, indicating that generativity is a lifelong developmental concern. {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. McAdams and Guo (2021) further expand on the cultural variations of generativity, showing how collectivist cultures emphasize family and community, while individualistic cultures may place more emphasis on personal achievement and career legacy. This cultural context is crucial in understanding the diverse ways in which generative behaviors are expressed across societies. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Schultz (2015) discusses how generativity motivates social activism, particularly in areas like human rights and environmental justice. These findings suggest that generative individuals feel a profound responsibility toward social and environmental change, contributing to broader societal progress. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. Matsuba and Pratt (2013) also highlight the growing importance of generativity in environmental advocacy. They found that individuals who are highly concerned with the well-being of future generations are more likely to engage in sustainable practices and support policies that address global challenges like climate change. Recent research by Van den Broeck et al. (2022) indicates that generative behaviors can act as a protective factor against mental health challenges, especially in older adults. By engaging in activities like mentoring or community service, individuals experience a sense of purpose and social connectedness, which can mitigate feelings of loneliness and depression in later life. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however-it{{gr}} also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In essence, generativity represents a profound human drive to leave a positive legacy, impacting not only our own lives but also the communities and generations that follow. Rooted in Erikson's stages of development, generativity encourages us to reach beyond ourselves, creating meaningful contributions through family, work, community involvement, and social causes. Research consistently demonstrates that engaging in generative actions promotes mental well-being, deepens social connections, and fosters resilience—qualities that become essential as societies face complex global challenges. Beyond personal fulfillment, generativity also has a ripple effect. When individuals commit to nurturing others, mentoring youth, or advocating for sustainable practices, they inspire similar behaviors in those around them. This cycle of positive influence strengthens communities and reinforces the importance of social responsibility. In a world increasingly defined by rapid change, generativity provides a stable foundation for fostering empathy, cooperation, and a shared commitment to future well-being. Reflecting on generativity invites us to ask important questions: ''What impact do I want to have?'' and ''How can I contribute to my community and future generations?'' By embracing generative actions, we actively shape not only our personal legacy but also the world we leave behind. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Bowlby, J. (1969). Attachment and loss: Vol. 1. Attachment. Basic Books. Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. ''The Journals of Gerontology: Series B, 69''(1), 55-64. https://doi.org/10.1093/geronb/gbt007 Erikson, E. H. (1950). Childhood and society. W. W. Norton & Company. Erikson, E. H. (1950). Generativity versus stagnation: An elaboration of Erikson's adult stage of human development. ''Journal of Adult Development, 10''(1), 53-65. Erikson, E. H., & Erikson, J. M. (1998). The life cycle completed (extended ed.). New York: W. W. Norton & Company. Epstein, R. (1999). Generativity theory. ''Encyclopedia of creativity, 1'', 759-766. Frankl, V. E. (1985). Man's search for meaning. Washington Square Press. Greenberg, J., Pyszczynski, T., & Solomon, S. (1986). The causes and consequences of a need for self-esteem: A terror management theory. In R. F. Baumeister (Ed.), Public self and private self (pp. 189–212). Springer-Verlag. Grossmann, I., & Gruenewald, T. L. (2017). Generativity across the life span: The importance of meaning and legacy. Psychology and Aging, 32(3), 370-380. https://doi.org/10.1037/pag0000172 Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 Kohlberg, L. (1981). The philosophy of moral development: Moral stages and the idea of justice. Harper & Row. Matsuba, M. K., & Pratt, M. W. (2013). The role of generativity in environmental advocacy. Environmental Psychology, 34(4), 81-89. https://doi.org/10.1016/j.jenvp.2013.07.004 McAdams, D. P., & Guo, G. (2021). Generativity and culture: The role of cultural beliefs and values in shaping generative behaviors. International Journal of Psychology, 56(3), 422-432. https://doi.org/10.1002/ijop.12738 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Schultz, P. W. (2015). The role of generativity in social activism: The case of climate change. Journal of Environmental Psychology, 43, 78-85. https://doi.org/10.1016/j.jenvp.2015.01.001 Seligman, M. E. P. (2002). Authentic happiness: Using the new positive psychology to realize your potential for lasting fulfillment. Free Press. Steger, M. F., Frazier, P., Oishi, S., & Kaler, M. (2006). The meaning in life questionnaire: Assessing the presence of and search for meaning in life. Journal of Counseling Psychology, 53(1), 80-93. https://doi.org/10.1037/0022-0167.53.1.80 Tajfel, H., & Turner, J. C. (1979). An integrative theory of intergroup conflict. In W. G. Austin & S. Worchel (Eds.), The social psychology of intergroup relations (pp. 33–47). Brooks/Cole. Van den Broeck, A., et al. (2022). Generativity and mental health in older adults: The protective role of meaningful engagement. Journal of Aging and Health, 34(5), 699-710. https://doi.org/10.1177/08982643221101547 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] qvootdk33vgfnvbikidos5x1xm8208b 2684116 2684111 2024-11-12T03:02:31Z Rocxie 2969341 2684116 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). == '''Integrating Generativity with Other Theories''' == * '''Self-Determination Theory (SDT)''' Self-Determination Theory, developed by Ryan and Deci, posits that human motivation is driven by three core psychological needs: autonomy, competence, and relatedness (Ryan & Deci, 2000). Generativity aligns with these needs, particularly relatedness and competence. Generative actions, such as mentoring or community service, fulfill the need for relatedness by fostering deep connections with others. They also satisfy the need for competence, as individuals use their skills and knowledge in meaningful ways that benefit others. When people engage in generative behaviors, they experience a sense of accomplishment and purpose, strengthening their intrinsic motivation to continue contributing to their community and society. * '''Attachment Theory''' Bowlby’s Attachment Theory suggests that strong, secure attachments formed in early life influence relationships and behaviors in adulthood (Bowlby, 1969). Generativity can be viewed as an extension of secure attachment; individuals who have experienced strong, positive attachments often seek to provide the same security and support to others, particularly to younger generations. This drive to nurture and guide can be seen as an outgrowth of the attachment system, with adults aiming to create safe, supportive environments for those they care about. * '''Social Identity Theory''' Tajfel and Turner’s Social Identity Theory proposes that people derive a significant part of their self-concept from group memberships and social roles (Tajfel & Turner, 1979). Generativity often manifests as a desire to contribute positively to one’s social group, whether that group is defined by family, profession, culture, or even a global community. By engaging in generative acts—such as mentoring younger professionals or advocating for social causes—individuals strengthen their social identity and feel more connected to their group. Generativity thereby reinforces a positive self-image and enhances one's role within society. * '''Positive Psychology and Meaning in Life''' Positive psychology emphasizes the pursuit of a meaningful and fulfilling life. Viktor Frankl's concept of “meaning-making” aligns closely with generativity, as generative actions allow individuals to feel that they are part of something larger than themselves (Frankl, 1985). Research in positive psychology suggests that people who engage in generative behaviors often experience a greater sense of purpose and satisfaction (Seligman, 2002). This sense of meaning is crucial for mental well-being, as individuals who feel they are contributing to the future or to others’ well-being report higher levels of life satisfaction and personal fulfillment. * '''Theory of Moral Development''' Kohlberg’s stages of moral development describe how individuals’ moral reasoning evolves over time, from a focus on self-interest to a consideration of broader social welfare (Kohlberg, 1981). Generativity reflects higher stages of moral development, where individuals prioritize ethical responsibility and concern for future generations. Generative actions are often guided by principles of fairness, justice, and altruism, suggesting that individuals with strong generative drives may also exhibit advanced moral reasoning. * '''Terror Management Theory (TMT)''' Terror Management Theory posits that awareness of mortality drives people to seek meaning and legacy, which buffers existential anxiety (Greenberg et al., 1986). Generativity serves as a key response to this existential concern, as it allows people to invest in projects, relationships, and causes that will endure beyond their lifetime. By contributing to something lasting, individuals mitigate fears of death and secure a sense of symbolic immortality, finding comfort in the thought that their efforts will impact future generations. <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). A study by '''Steger, Frazier, Oishi, and Kaler (2006)''' explores the relationship between generativity and life satisfaction in adults. Their findings suggest that individuals who engage in generative behaviors experience higher levels of well-being, which further aligns with Erikson's assertion that generativity leads to fulfillment and purpose (Steger et al., 2006). Recent research has shown that generative behaviors are strongly linked to increased life satisfaction and psychological well-being, with studies like those by Steger et al. (2006) suggesting that generativity contributes to greater fulfillment and overall mental health. These findings support the idea that generativity is crucial for mental well-being across adulthood. Another longitudinal study by '''Grossmann and Gruenewald (2017)''' examined generativity at different stages of life, noting that while generativity peaks in middle adulthood, it remains significant in late adulthood as well. Their research provides insights into how older adults continue to engage in generative behaviours, often through community involvement, storytelling, and volunteerism. Grossmann and Gruenewald (2017) have emphasized that although generativity is most prominent during middle adulthood, it remains an important aspect of adult life well into late adulthood. Older adults often engage in generative behaviors through community service and passing on knowledge to younger generations, indicating that generativity is a lifelong developmental concern. {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. McAdams and Guo (2021) further expand on the cultural variations of generativity, showing how collectivist cultures emphasize family and community, while individualistic cultures may place more emphasis on personal achievement and career legacy. This cultural context is crucial in understanding the diverse ways in which generative behaviors are expressed across societies. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Schultz (2015) discusses how generativity motivates social activism, particularly in areas like human rights and environmental justice. These findings suggest that generative individuals feel a profound responsibility toward social and environmental change, contributing to broader societal progress. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. Matsuba and Pratt (2013) also highlight the growing importance of generativity in environmental advocacy. They found that individuals who are highly concerned with the well-being of future generations are more likely to engage in sustainable practices and support policies that address global challenges like climate change. Recent research by Van den Broeck et al. (2022) indicates that generative behaviors can act as a protective factor against mental health challenges, especially in older adults. By engaging in activities like mentoring or community service, individuals experience a sense of purpose and social connectedness, which can mitigate feelings of loneliness and depression in later life. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however it also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In essence, generativity represents a profound human drive to leave a positive legacy, impacting not only our own lives but also the communities and generations that follow. Rooted in Erikson's stages of development, generativity encourages us to reach beyond ourselves, creating meaningful contributions through family, work, community involvement, and social causes. Research consistently demonstrates that engaging in generative actions promotes mental well-being, deepens social connections, and fosters resilience—qualities that become essential as societies face complex global challenges. Beyond personal fulfillment, generativity also has a ripple effect. When individuals commit to nurturing others, mentoring youth, or advocating for sustainable practices, they inspire similar behaviors in those around them. This cycle of positive influence strengthens communities and reinforces the importance of social responsibility. In a world increasingly defined by rapid change, generativity provides a stable foundation for fostering empathy, cooperation, and a shared commitment to future well-being. Reflecting on generativity invites us to ask important questions: ''What impact do I want to have?'' and ''How can I contribute to my community and future generations?'' By embracing generative actions, we actively shape not only our personal legacy but also the world we leave behind. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Bowlby, J. (1969). Attachment and loss: Vol. 1. Attachment. Basic Books. Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. 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K., & Pratt, M. W. (2013). The role of generativity in environmental advocacy. Environmental Psychology, 34(4), 81-89. https://doi.org/10.1016/j.jenvp.2013.07.004 McAdams, D. P., & Guo, G. (2021). Generativity and culture: The role of cultural beliefs and values in shaping generative behaviors. International Journal of Psychology, 56(3), 422-432. https://doi.org/10.1002/ijop.12738 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Schultz, P. W. (2015). The role of generativity in social activism: The case of climate change. Journal of Environmental Psychology, 43, 78-85. https://doi.org/10.1016/j.jenvp.2015.01.001 Seligman, M. E. P. (2002). Authentic happiness: Using the new positive psychology to realize your potential for lasting fulfillment. Free Press. Steger, M. F., Frazier, P., Oishi, S., & Kaler, M. (2006). The meaning in life questionnaire: Assessing the presence of and search for meaning in life. Journal of Counseling Psychology, 53(1), 80-93. https://doi.org/10.1037/0022-0167.53.1.80 Tajfel, H., & Turner, J. C. (1979). An integrative theory of intergroup conflict. In W. G. Austin & S. Worchel (Eds.), The social psychology of intergroup relations (pp. 33–47). Brooks/Cole. Van den Broeck, A., et al. (2022). Generativity and mental health in older adults: The protective role of meaningful engagement. Journal of Aging and Health, 34(5), 699-710. https://doi.org/10.1177/08982643221101547 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] di1glflz362r2hghsbdn0hmdwrtkxlw 2684117 2684116 2024-11-12T03:03:56Z Rocxie 2969341 2684117 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/HkL06LQ-8sg}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). == '''Integrating Generativity with Other Theories''' == * '''Self-Determination Theory (SDT)''' Self-Determination Theory, developed by Ryan and Deci, posits that human motivation is driven by three core psychological needs: autonomy, competence, and relatedness (Ryan & Deci, 2000). Generativity aligns with these needs, particularly relatedness and competence. Generative actions, such as mentoring or community service, fulfill the need for relatedness by fostering deep connections with others. They also satisfy the need for competence, as individuals use their skills and knowledge in meaningful ways that benefit others. When people engage in generative behaviors, they experience a sense of accomplishment and purpose, strengthening their intrinsic motivation to continue contributing to their community and society. * '''Attachment Theory''' Bowlby’s Attachment Theory suggests that strong, secure attachments formed in early life influence relationships and behaviors in adulthood (Bowlby, 1969). Generativity can be viewed as an extension of secure attachment; individuals who have experienced strong, positive attachments often seek to provide the same security and support to others, particularly to younger generations. This drive to nurture and guide can be seen as an outgrowth of the attachment system, with adults aiming to create safe, supportive environments for those they care about. * '''Social Identity Theory''' Tajfel and Turner’s Social Identity Theory proposes that people derive a significant part of their self-concept from group memberships and social roles (Tajfel & Turner, 1979). Generativity often manifests as a desire to contribute positively to one’s social group, whether that group is defined by family, profession, culture, or even a global community. By engaging in generative acts—such as mentoring younger professionals or advocating for social causes—individuals strengthen their social identity and feel more connected to their group. Generativity thereby reinforces a positive self-image and enhances one's role within society. * '''Positive Psychology and Meaning in Life''' Positive psychology emphasizes the pursuit of a meaningful and fulfilling life. Viktor Frankl's concept of “meaning-making” aligns closely with generativity, as generative actions allow individuals to feel that they are part of something larger than themselves (Frankl, 1985). Research in positive psychology suggests that people who engage in generative behaviors often experience a greater sense of purpose and satisfaction (Seligman, 2002). This sense of meaning is crucial for mental well-being, as individuals who feel they are contributing to the future or to others’ well-being report higher levels of life satisfaction and personal fulfillment. * '''Theory of Moral Development''' Kohlberg’s stages of moral development describe how individuals’ moral reasoning evolves over time, from a focus on self-interest to a consideration of broader social welfare (Kohlberg, 1981). Generativity reflects higher stages of moral development, where individuals prioritize ethical responsibility and concern for future generations. Generative actions are often guided by principles of fairness, justice, and altruism, suggesting that individuals with strong generative drives may also exhibit advanced moral reasoning. * '''Terror Management Theory (TMT)''' Terror Management Theory posits that awareness of mortality drives people to seek meaning and legacy, which buffers existential anxiety (Greenberg et al., 1986). Generativity serves as a key response to this existential concern, as it allows people to invest in projects, relationships, and causes that will endure beyond their lifetime. By contributing to something lasting, individuals mitigate fears of death and secure a sense of symbolic immortality, finding comfort in the thought that their efforts will impact future generations. <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). A study by '''Steger, Frazier, Oishi, and Kaler (2006)''' explores the relationship between generativity and life satisfaction in adults. Their findings suggest that individuals who engage in generative behaviors experience higher levels of well-being, which further aligns with Erikson's assertion that generativity leads to fulfillment and purpose (Steger et al., 2006). Recent research has shown that generative behaviours are strongly linked to increased life satisfaction and psychological well-being, with studies like those by Steger et al. (2006) suggesting that generativity contributes to greater fulfillment and overall mental health. These findings support the idea that generativity is crucial for mental well-being across adulthood. Another longitudinal study by '''Grossmann and Gruenewald (2017)''' examined generativity at different stages of life, noting that while generativity peaks in middle adulthood, it remains significant in late adulthood as well. Their research provides insights into how older adults continue to engage in generative behaviours, often through community involvement, storytelling, and volunteerism. Grossmann and Gruenewald (2017) have emphasized that although generativity is most prominent during middle adulthood, it remains an important aspect of adult life well into late adulthood. Older adults often engage in generative behaviors through community service and passing on knowledge to younger generations, indicating that generativity is a lifelong developmental concern. {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. McAdams and Guo (2021) further expand on the cultural variations of generativity, showing how collectivist cultures emphasize family and community, while individualistic cultures may place more emphasis on personal achievement and career legacy. This cultural context is crucial in understanding the diverse ways in which generative behaviors are expressed across societies. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Schultz (2015) discusses how generativity motivates social activism, particularly in areas like human rights and environmental justice. These findings suggest that generative individuals feel a profound responsibility toward social and environmental change, contributing to broader societal progress. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. Matsuba and Pratt (2013) also highlight the growing importance of generativity in environmental advocacy. They found that individuals who are highly concerned with the well-being of future generations are more likely to engage in sustainable practices and support policies that address global challenges like climate change. Recent research by Van den Broeck et al. (2022) indicates that generative behaviors can act as a protective factor against mental health challenges, especially in older adults. By engaging in activities like mentoring or community service, individuals experience a sense of purpose and social connectedness, which can mitigate feelings of loneliness and depression in later life. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however it also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In essence, generativity represents a profound human drive to leave a positive legacy, impacting not only our own lives but also the communities and generations that follow. Rooted in Erikson's stages of development, generativity encourages us to reach beyond ourselves, creating meaningful contributions through family, work, community involvement, and social causes. Research consistently demonstrates that engaging in generative actions promotes mental well-being, deepens social connections, and fosters resilience—qualities that become essential as societies face complex global challenges. Beyond personal fulfillment, generativity also has a ripple effect. When individuals commit to nurturing others, mentoring youth, or advocating for sustainable practices, they inspire similar behaviors in those around them. This cycle of positive influence strengthens communities and reinforces the importance of social responsibility. In a world increasingly defined by rapid change, generativity provides a stable foundation for fostering empathy, cooperation, and a shared commitment to future well-being. Reflecting on generativity invites us to ask important questions: ''What impact do I want to have?'' and ''How can I contribute to my community and future generations?'' By embracing generative actions, we actively shape not only our personal legacy but also the world we leave behind. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Bowlby, J. (1969). Attachment and loss: Vol. 1. Attachment. Basic Books. Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. 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Psychology and Aging, 32(3), 370-380. https://doi.org/10.1037/pag0000172 Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 Kohlberg, L. (1981). The philosophy of moral development: Moral stages and the idea of justice. Harper & Row. Matsuba, M. K., & Pratt, M. W. (2013). The role of generativity in environmental advocacy. Environmental Psychology, 34(4), 81-89. https://doi.org/10.1016/j.jenvp.2013.07.004 McAdams, D. P., & Guo, G. (2021). Generativity and culture: The role of cultural beliefs and values in shaping generative behaviors. International Journal of Psychology, 56(3), 422-432. https://doi.org/10.1002/ijop.12738 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Schultz, P. W. (2015). The role of generativity in social activism: The case of climate change. Journal of Environmental Psychology, 43, 78-85. https://doi.org/10.1016/j.jenvp.2015.01.001 Seligman, M. E. P. (2002). Authentic happiness: Using the new positive psychology to realize your potential for lasting fulfillment. Free Press. Steger, M. F., Frazier, P., Oishi, S., & Kaler, M. (2006). The meaning in life questionnaire: Assessing the presence of and search for meaning in life. Journal of Counseling Psychology, 53(1), 80-93. https://doi.org/10.1037/0022-0167.53.1.80 Tajfel, H., & Turner, J. C. (1979). An integrative theory of intergroup conflict. In W. G. Austin & S. Worchel (Eds.), The social psychology of intergroup relations (pp. 33–47). Brooks/Cole. Van den Broeck, A., et al. (2022). Generativity and mental health in older adults: The protective role of meaningful engagement. Journal of Aging and Health, 34(5), 699-710. https://doi.org/10.1177/08982643221101547 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] 534yqnlgyy3v4g8q1h2s8qo3if1x4q6 2684139 2684117 2024-11-12T03:53:46Z Rocxie 2969341 2684139 wikitext text/x-wiki {{title|Generativity:<br>What is generativity and how does it impact behaviour and life outcomes?}} {{MECR3|1=https://youtu.be/A2OFYQ8Y1BI}} __TOC__ ==Overview== {{RoundBoxTop|theme=3}} [[File:Erikson’s stages of psychosocial development.png|right|thumb|270px|'''Figure 1'''. A diagram illustrating Erikson’s stages of psychosocial development with a focus on generativity versus stagnation.]] ;Generativity in action Imagine a middle-aged teacher named Sarah, who has dedicated her life to nurturing her students. She finds great fulfillment in guiding them, not just academically but also in helping them grow as individuals. Her deep sense of responsibility towards her students drives her to constantly seek ways to improve their lives, both now and in the future. Sarah's story exemplifies generativity—a commitment to the well-being of the next generation and to leaving a positive legacy. Sarah, a 45-year-old high school teacher, has spent the last 20 years of her life dedicated to her students. Her goal has always been to inspire them to reach their full potential. She volunteers for after-school programs, mentors new teachers, and is involved in community outreach efforts aimed at supporting underprivileged children. Sarah's sense of purpose and fulfillment comes from her generative actions, which not only shape her identity but also have a lasting impact on her community. {{RoundBoxBottom}} [[wikipedia:Generativity|Generativity]] refers to the concern for establishing and guiding the next generation. This concept, introduced by [[wikipedia:Erikson's_stages_of_psychosocial_development|Erik Erikson]], plays a crucial role in adult development, particularly during middle adulthood. The chapter delves into the theoretical foundations of generativity, explores its [https://academic.oup.com/book/57273/chapter-abstract/459735243?redirectedFrom=fulltext cultural variations] {{ic|Use APA style citation and add to references}}, and discusses its significance across different life stages. The reader will gain an understanding of how generativity influences behavior and life outcomes, and the factors that encourage or hinder its development. {{RoundBoxTop}} '''Focus questions:''' * What is the relationship between generativity and life satisfaction? * How does generativity manifest across different cultures? * What factors influence the development or inhibition of generative behaviors? {{RoundBoxBottom}} == Theoretical foundations and developmental aspects of generativity == {{expand}} === What is generativity? === [[wikipedia:Generativity|Generativity]] is a developmental psychological concept designed by Erik Erikson within the scope of an eight-stage model that has to do with psychosocial development. It is the stage at which individuals take on the commitment to mentor, raise, and support the next generation through such means as [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood|parenting]], mentoring, teaching, and community service. Even though generativity is strong during middle adulthood, it actually can occur at any life stage (Erikson, 1950). People exhibiting [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative behaviours] generally demonstrate a sense of purpose and satisfaction because their contributions are being made toward the continuation and improvement of society (McAdams & de St. Aubin, 1992) ==== Erikson's theory of psychosocial development ==== Erikson defined generativity as the drive to contribute positively to future generations, placing it as a central challenge in middle adulthood. Failure to achieve generativity, he suggested, could lead to stagnation, where individuals feel unproductive and disconnected from the broader community (Erikson, 1963). Modern research has expanded this concept, revealing that generative actions contribute to self-esteem and life satisfaction across age groups (McAdams & de St. Aubin, 1992). For instance, studies show that individuals involved in mentorship programs report a higher sense of fulfillment and purpose (Peterson, 2006). According to Erikson, generativity forms the seventh stage of [[wikipedia:Erikson's_stages_of_psychosocial_development|psychosocial development]]; the preoccupation with individual identity has been overcome. In this stage, people aim at leaving a lasting legacy on the world. This might come through rearing children, guiding younger people, or, in fact, engaging in voluntary work within the community. Successfully resolving the process during this stage leads to a feeling of accomplishment while failure to do so will result in stagnation and self-absorption (Erikson, 1950). ===== Extensions and critiques of Erikson’s model ===== Although Erikson provided a starting point for the modern concept of generativity, subsequent work has furthered Erikson's original ideas. Other research has taken Erikson's age-specific timeline and demonstrated that generativity can occur during any stage of the life span, not just middle adulthood (McAdams, 1994). Others have noted that generativity is manifested differently across cultures, indicating that Erikson's stage model should be adapted to take into consideration cultural norms and values (Cheng, 2014). == '''Integrating Generativity with Other Theories''' == * '''Self-Determination Theory (SDT)''' Self-Determination Theory, developed by Ryan and Deci, posits that human motivation is driven by three core psychological needs: autonomy, competence, and relatedness (Ryan & Deci, 2000). Generativity aligns with these needs, particularly relatedness and competence. Generative actions, such as mentoring or community service, fulfill the need for relatedness by fostering deep connections with others. They also satisfy the need for competence, as individuals use their skills and knowledge in meaningful ways that benefit others. When people engage in generative behaviors, they experience a sense of accomplishment and purpose, strengthening their intrinsic motivation to continue contributing to their community and society. * '''Attachment Theory''' Bowlby’s Attachment Theory suggests that strong, secure attachments formed in early life influence relationships and behaviors in adulthood (Bowlby, 1969). Generativity can be viewed as an extension of secure attachment; individuals who have experienced strong, positive attachments often seek to provide the same security and support to others, particularly to younger generations. This drive to nurture and guide can be seen as an outgrowth of the attachment system, with adults aiming to create safe, supportive environments for those they care about. * '''Social Identity Theory''' Tajfel and Turner’s Social Identity Theory proposes that people derive a significant part of their self-concept from group memberships and social roles (Tajfel & Turner, 1979). Generativity often manifests as a desire to contribute positively to one’s social group, whether that group is defined by family, profession, culture, or even a global community. By engaging in generative acts—such as mentoring younger professionals or advocating for social causes—individuals strengthen their social identity and feel more connected to their group. Generativity thereby reinforces a positive self-image and enhances one's role within society. * '''Positive Psychology and Meaning in Life''' Positive psychology emphasizes the pursuit of a meaningful and fulfilling life. Viktor Frankl's concept of “meaning-making” aligns closely with generativity, as generative actions allow individuals to feel that they are part of something larger than themselves (Frankl, 1985). Research in positive psychology suggests that people who engage in generative behaviors often experience a greater sense of purpose and satisfaction (Seligman, 2002). This sense of meaning is crucial for mental well-being, as individuals who feel they are contributing to the future or to others’ well-being report higher levels of life satisfaction and personal fulfillment. * '''Theory of Moral Development''' Kohlberg’s stages of moral development describe how individuals’ moral reasoning evolves over time, from a focus on self-interest to a consideration of broader social welfare (Kohlberg, 1981). Generativity reflects higher stages of moral development, where individuals prioritize ethical responsibility and concern for future generations. Generative actions are often guided by principles of fairness, justice, and altruism, suggesting that individuals with strong generative drives may also exhibit advanced moral reasoning. * '''Terror Management Theory (TMT)''' Terror Management Theory posits that awareness of mortality drives people to seek meaning and legacy, which buffers existential anxiety (Greenberg et al., 1986). Generativity serves as a key response to this existential concern, as it allows people to invest in projects, relationships, and causes that will endure beyond their lifetime. By contributing to something lasting, individuals mitigate fears of death and secure a sense of symbolic immortality, finding comfort in the thought that their efforts will impact future generations. <quiz display=simple> {Which of the following is a corre{{sp}} characteristic of generativity in middle adulthood, according to Erikson's theory? |type="(-)"} - Accumulating wealth + Contributing to the next generation - Achieving personal career success - Avoiding societal resposibilities{{sp}} </quiz> == Generativity across the lifespan and cultural contexts == {{expand}} === Generativity in early, middle, and late adulthood === Generativity takes somewhat different forms across life stages. For instance, generativity during early adulthood can be an aspect of career choices and/or [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false mentoring] and service in the community. In this stage of life people are for the first time beginning to think about how their actions impact on others and society as a whole (McAdams, 1994). At the level of [[wikipedia:Erikson's_stages_of_psychosocial_development|middle adulthood]], generativity is higher, and most adults are concerned with rearing children, mentoring younger colleagues, or contributing to the community through various forms of service (Grossman & Gruenewald, 2017). In [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6392441/#:~:text=Generativity%20is%20an%20index%20of,47%E2%80%9350%20to%20rate%20generativity. late adulthood], generativity takes the form of sharing wisdom, life experiences, and knowledge with the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 younger generations] through stories, volunteering, or informal functions of mentoring ( McAdams & de St. Aubin, 1992). A study by '''Steger, Frazier, Oishi, and Kaler (2006)''' explores the relationship between generativity and life satisfaction in adults. Their findings suggest that individuals who engage in generative behaviors experience higher levels of well-being, which further aligns with Erikson's assertion that generativity leads to fulfillment and purpose (Steger et al., 2006). Recent research has shown that generative behaviours are strongly linked to increased life satisfaction and psychological well-being, with studies like those by Steger et al. (2006) suggesting that generativity contributes to greater fulfillment and overall mental health. These findings support the idea that generativity is crucial for mental well-being across adulthood. Another longitudinal study by '''Grossmann and Gruenewald (2017)''' examined generativity at different stages of life, noting that while generativity peaks in middle adulthood, it remains significant in late adulthood as well. Their research provides insights into how older adults continue to engage in generative behaviours, often through community involvement, storytelling, and volunteerism. Grossmann and Gruenewald (2017) have emphasized that although generativity is most prominent during middle adulthood, it remains an important aspect of adult life well into late adulthood. Older adults often engage in generative behaviors through community service and passing on knowledge to younger generations, indicating that generativity is a lifelong developmental concern. {{RoundBoxTop|theme=2}} [[File:Aspects of generativity.png|140px|thumb|'''Figure 2'''. A cultural comparison chart showing the expression of generativity in different societies.]] '''Case Study 1: Generativity in middle adulthood''' '''Background:''' Maria, a 45-year-old lawyer and mother of two, has been in her legal career for over 20 years. As she entered her mid-40s, Maria began to feel a growing desire to contribute to society in a more meaningful way beyond her professional achievements. '''Generative actions:''' Maria’s generativity manifests in two key areas: parenting and mentoring. As a mother, she focuses on raising her children with strong values, emphasizing education, community involvement, and empathy. She volunteers as a parent leader in her local school district, organizing events and supporting school programs. At work, Maria has also taken on a mentor role for younger colleagues. She dedicates time to offering guidance to interns and new hires, sharing her expertise in the field of law, and helping them navigate their career paths. Through this mentorship, Maria finds fulfillment in helping others succeed and feels a strong sense of responsibility toward shaping the next generation of lawyers. '''Outcome:''' By focusing on generativity, Maria experiences a profound sense of purpose. She feels connected to her community and is proud to be contributing to the future, both through her children and her professional legacy. This sense of purpose reduces feelings of stagnation, making her middle adulthood both productive and fulfilling. {{RoundBoxBottom}} ==== Cultural variations in generativity ==== The expression of generativity involves cultural norms and values. For instance, generativity in [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false collectivist cultures], where communal life is highly valued, may often take the front of [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false community involvement] and social responsibility (Cheng, 2014). On the contrary, generativity in an [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 individualist culture] may take the front of personal achievements and individual mentoring (McAdams, 1994) (McAdams & Guo, 2021). Again, this tends to depict cultural differences within generativity regarding cultural structure and belief systems. McAdams and Guo (2021) further expand on the cultural variations of generativity, showing how collectivist cultures emphasize family and community, while individualistic cultures may place more emphasis on personal achievement and career legacy. This cultural context is crucial in understanding the diverse ways in which generative behaviors are expressed across societies. Research has highlighted intriguing cultural variations in generative actions. In individualistic cultures, generativity may focus on individual achievement or personal legacy, while in collectivist societies, it often encompasses contributions to family and community well-being (Cheng, 2018). For example, in Japan, generativity is closely tied to community roles, with older adults often engaging in community gardening or teaching traditional skills to younger generations as a way of maintaining social ties and passing down cultural knowledge (Suzuki & Takahashi, 2015). ===== The role of generativity in social change ===== The role of generativity in [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 social change] beyond personal fulfillment, generativity makes a significant difference in societal change. It is easy to find generatively active persons who are involved in social movements or community projects that continue long afterwards and bring improvements to people. Schultz (2015) discusses how generativity motivates social activism, particularly in areas like human rights and environmental justice. These findings suggest that generative individuals feel a profound responsibility toward social and environmental change, contributing to broader societal progress. Focusing on the well-being of succeeding generations, generativity incorporates a sense of responsibility toward the shaping of a positive future in such forms as social activism, environmental projects, or community building projects (Grossman & Gruenewald, 2017). The concept of generativity is becoming increasingly relevant in addressing environmental issues. Recent studies reveal that individuals with high generative concerns are more likely to participate in sustainable practices and advocate for environmental protection (Matsuba & Pratt, 2013). For instance, environmentalists like Greta Thunberg often cite a generative sense of responsibility toward future generations as motivation for their activism. Matsuba and Pratt (2013) also highlight the growing importance of generativity in environmental advocacy. They found that individuals who are highly concerned with the well-being of future generations are more likely to engage in sustainable practices and support policies that address global challenges like climate change. Recent research by Van den Broeck et al. (2022) indicates that generative behaviors can act as a protective factor against mental health challenges, especially in older adults. By engaging in activities like mentoring or community service, individuals experience a sense of purpose and social connectedness, which can mitigate feelings of loneliness and depression in later life. '''Community Impact of Generative Actions''' Generative actions have the power to create positive change within communities. For example, programs like Big Brothers Big Sisters demonstrate how mentoring can transform lives. Volunteers who mentor young people often cite generative motives, like the desire to ‘give back’ and help the next generation succeed (Rhodes, 2008). These relationships foster resilience in both mentors and mentees, proving that generative actions can bridge generational gaps and strengthen community ties. '''Table 1.''' ''Generativity Across the Lifespan'' {| class="wikitable" style="margin: auto;" |- ! Life Stage!! Form of Generativity !! Example of Generative Behaviours !Key Outcome |- | '''Early Adulthood''' || Career and mentorship || Choosing professions that impact others, mentoring younger colleagues, community service |Developing a sense of contribution to society and shaping future generations. |- | '''Middle Adulthood''' || Parenting, community involvement, leadership roles || Raising children, mentoring, leading community initiatives |Feeling fulfilled by ensuring the welfare and growth of the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false next generation]. |- |'''Late Adulthood''' |Sharing wisdom, life experiences, legacy building |Volunteering, storytelling, guiding younger generations |Creating a legacy and achieving a sense of life satisfaction by passing down knowledge. |} == Challenges, measurement, and applications of generativity == {{expand}} === Measurement of generativity === Several tools have been developed to measure generativity. One of the most prominent was the [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Loyola Generativity Scale] issued by McAdams in 1994. This scale has two major features of generativity: [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 Generative concern] that is the interest in taking care of future generations and [https://psycnet.apa.org/doiLanding?doi=10.1037%2F0022-3514.62.6.1003 generative action]-actual behaviour that reflects concern. Indeed, research that has employed this scale has used it to show that generativity is linked to a myriad of positive life outcomes including heightened life satisfaction, [https://academic.oup.com/psychsocgerontology/article/72/1/162/2631969 psychological well-being], and purpose in life (Grossman & Gruenewald, 2017). ==== Applications of generativity in everyday life ==== The most obvious example of generative behaviour, parenting allows adults to raise and teach their children good citizenship. Parents who practice generative behaviours provide environments that foster their children's emotional, social, and intellectual growth (McAdams & de St. Aubin, 1992). Generativity is not confined to the family, however it also applies to workplace generativity and generativity in the broader community. Individuals may mentor younger colleagues, commit to other forms of community service, or otherwise engage in actions that are beneficial for society and make social continuity possible across generations (Grossman & Gruenewald, 2017). '''Case Studies of Notable Figures''' Examples of generativity are visible in figures like Jane Goodall, who dedicated her life to conservation and educating others about wildlife. Goodall’s work reflects a generative commitment to environmental stewardship and inspiring future conservationists. Her contributions illustrate how generativity can extend to global causes, reminding us of our responsibility to protect the planet for generations to come. ===== '''The Ripple Effect of Generative Role Models''' ===== Generative role models inspire others to contribute to society. Research shows that children who see their parents involved in volunteering or community work are more likely to participate in similar activities as they grow older (Colby & Damon, 1992). This ‘ripple effect’ means that each generative act can potentially lead to more positive contributions, fostering a culture of care and community involvement. ====== '''Link to Generativity in Social and Environmental Challenges''' ====== As society faces global challenges like climate change, generativity plays an essential role in motivating individuals to act for the greater good. Research shows that people with a strong generative drive are more likely to engage in activism and support policies that protect natural resources for future generations (Schultz, 2015). This highlights generativity’s role in social responsibility, encouraging us to look beyond ourselves and advocate for sustainable practices. ====== Challenges and barriers to generativity ====== There are a number of elements that oppress generative behaviours. Among the [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false psychological deterrents], depression and low self-esteem may result in inactivity toward generative behaviour. Further, [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833?login=false socioeconomically], poverty and reduced access to education are considered major hindrances to the generation cycle. The cultural deterrents include societal norms and values devaluing the different forms of generative actions (Grossman & Gruenewald, 2017; Cheng, 2014{{ic|Use alphabetical order}}). Overcoming these barriers is critical for enhancing generativity, and interventions such as therapy, community programs, and education facilitate overcoming these barriers and increased involvement in generative behaviours. {{RoundBoxTop|theme=4}} '''Case Study 2: Barriers to generativity''' '''Background:''' John, a 55-year-old factory worker, has struggled with financial insecurity for most of his adult life. Growing up in an economically disadvantaged neighborhood, John had limited access to education and career opportunities. He married young and spent much of his life working long hours to support his family, but his career never felt fulfilling. '''Challenges and barriers:''' John’s generativity is inhibited by several barriers: * '''Psychological factors:''' John suffers from depression due to his unfulfilled career ambitions. This mental health issue has caused him to feel disconnected from his community and his family, reducing his motivation to contribute meaningfully. * '''Socioeconomic challenges:''' The need to focus on making ends meet leaves John with little time or resources for generative activities. He often feels that he lacks the financial stability to engage in community work or mentoring. * '''Cultural barriers:''' In John’s community, there are few opportunities for engagement in generative roles. The absence of accessible mentorship programs or community service options in his area exacerbates the feeling of stagnation. '''Outcome:''' Due to these barriers, John finds it difficult to engage in generative behaviors. Without the support to overcome his mental health challenges and economic struggles, he feels stuck in a cycle of survival rather than personal growth. Addressing John’s barriers through interventions, such as mental health support or community programs, could help him overcome these challenges and unlock his generative potential. {{RoundBoxBottom}} == Test your knowledge == {{RoundBoxTop|theme=7}} Consider the following scenario: Sarah, a 50-year-old educator, is deeply involved in both her family life and her career. She mentors younger teachers, contributes to community programs, and spends time helping her children transition into adulthood. However, due to a recent personal financial crisis and the onset of depression, Sarah feels less motivated to continue her generative activities. Despite this, she remains committed to her professional and personal roles. Based on Sarah's situation, answer the following questions: {{RoundBoxBottom}} <quiz display= simple> What stage of Erikson’s psychosocial development theory is Sarah currently navigating? |type="(-)"} - Identity vs. Role Confusion - Intimacy vs. Isolation + Generativity vs. Stagnation - Integrity vs. Despair {Which of the following generative behaviors does Sarah exhibit in her daily life? |type="(-)"} - Focusing solely on career sucess{{sp}} + Mentoring younger colleagues - Isolating from the community - Prioritizing her financial success over others' well-being {What barriers to generativity is Sarah currently facing? |type="(-)"} - Possitive{{sp}} mental health and financial stability - Career advancement and strong community ties + Depression and financial difficulties - A supportive family and workplace environment {What might help Sarah overcome her barriers to generativity? |type="(-)"} - Ignoring her challenges and focusing on herself + Recieving{{sp}} mental health support and financial counseling - Withdrawing from her mentorship roles - Focusing solely on her personal career development {Based on the scenario, which cultural or societal factors could be impacting Sarah's generative actions? |type="(-)"} - Community support that promotes her involvement - Cultural norms that discourage community involvement - Societal emphasis on individual achievements over community contributions + Both Community support that promotes her involvement and Societal emphasis on individual achievements over community contributions </quiz> == Conclusion == In essence, generativity represents a profound human drive to leave a positive legacy, impacting not only our own lives but also the communities and generations that follow. Rooted in Erikson's stages of development, generativity encourages us to reach beyond ourselves, creating meaningful contributions through family, work, community involvement, and social causes. Research consistently demonstrates that engaging in generative actions promotes mental well-being, deepens social connections, and fosters resilience—qualities that become essential as societies face complex global challenges. Beyond personal fulfillment, generativity also has a ripple effect. When individuals commit to nurturing others, mentoring youth, or advocating for sustainable practices, they inspire similar behaviors in those around them. This cycle of positive influence strengthens communities and reinforces the importance of social responsibility. In a world increasingly defined by rapid change, generativity provides a stable foundation for fostering empathy, cooperation, and a shared commitment to future well-being. Reflecting on generativity invites us to ask important questions: ''What impact do I want to have?'' and ''How can I contribute to my community and future generations?'' By embracing generative actions, we actively shape not only our personal legacy but also the world we leave behind. ==See also== * Wikiversity: [[Developmental psychology/Chapter 13/Generativity: The Work of Adulthood]] * Wikiversity: [[Developmental psychology/Chapter 1/What is Developmental Psychology?|Developmental Psychology]] * Wikipedia: [[wikipedia:Generativity|Generativity]] * Wikipedia: [[wikipedia:Erikson's_stages_of_psychosocial_development|Erikson's stages of psychosocial development]] ==References== {{Hanging indent|1= Bowlby, J. (1969). Attachment and loss: Vol. 1. Attachment. Basic Books. Cheng, S. T. (2014). Generativity in later life: Perceived respect from younger generations as a determinant of goal disengagement and subjective well-being. ''The Journals of Gerontology: Series B, 69''(1), 55-64. https://doi.org/10.1093/geronb/gbt007 Erikson, E. H. (1950). Childhood and society. W. W. Norton & Company. Erikson, E. H. (1950). Generativity versus stagnation: An elaboration of Erikson's adult stage of human development. ''Journal of Adult Development, 10''(1), 53-65. Erikson, E. H., & Erikson, J. M. (1998). The life cycle completed (extended ed.). New York: W. W. Norton & Company. Epstein, R. (1999). Generativity theory. ''Encyclopedia of creativity, 1'', 759-766. Frankl, V. E. (1985). Man's search for meaning. Washington Square Press. Greenberg, J., Pyszczynski, T., & Solomon, S. (1986). The causes and consequences of a need for self-esteem: A terror management theory. In R. F. Baumeister (Ed.), Public self and private self (pp. 189–212). Springer-Verlag. Grossmann, I., & Gruenewald, T. L. (2017). Generativity across the life span: The importance of meaning and legacy. Psychology and Aging, 32(3), 370-380. https://doi.org/10.1037/pag0000172 Grossman, M. R., & Gruenewald, T. L. (2017). Caregiving and generativity in late midlife: Results from the Wisconsin Longitudinal Study. ''The Journals of Gerontology: Series B, 72''(4), 688-696. https://doi.org/10.1093/geronb/gbv068 Gruenewald, T. L., & Zhang, C. (2018). Generativity is an index of successful aging: evidence from a U.S. population sample. ''The Journals of Gerontology: Series B, Psychological Sciences and Social Sciences, 74''(1), 47-50. https://doi.org/10.1093/geronb/gby029 Hofer, J., Busch, H., Chasiotis, A., Kärtner, J., & Campos, D. (2014). The measurement of generativity across the adult lifespan: Psychometric properties of a German adaptation of the Loyola Generativity Scale. ''Journal of Adult Development, 21''(1), 23-36. https://doi.org/10.1007/s10804-013-9176-7 Kohlberg, L. (1981). The philosophy of moral development: Moral stages and the idea of justice. Harper & Row. Matsuba, M. K., & Pratt, M. W. (2013). The role of generativity in environmental advocacy. Environmental Psychology, 34(4), 81-89. https://doi.org/10.1016/j.jenvp.2013.07.004 McAdams, D. P., & Guo, G. (2021). Generativity and culture: The role of cultural beliefs and values in shaping generative behaviors. International Journal of Psychology, 56(3), 422-432. https://doi.org/10.1002/ijop.12738 McAdams, D. P., & de St. Aubin, E. (1992). A theory of generativity and its assessment through self-report, behavioral acts, and narrative themes in autobiography. ''Journal of Personality and Social Psychology, 62''(6), 1003–1015. https://doi.org/10.1037/0022-3514.62.6.1003 McAdams, D. P., & de St. Aubin, E. (1994). Generativity and adult development: How and why we care for the next generation. ''American Psychological Association.'' https://doi.org/10.1037/10160-000 McAdams, D. P., & Guo, J. (2021). Generativity in cultural context: A comparative study of Americans and Chinese. In Handbook of psychology and aging (pp. 459-473). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190233153.013.24 Newton, N. J., & Stewart, A. J. (2012). Personality development in adulthood: The role of generativity. ''Journal of Adult Development, 19''(3), 141-154. https://doi.org/10.1016/j.adolescence.2012.01.001 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Rothrauff, T. C., & Cooney, T. M. (2019). The links between generativity and well-being in later life: A longitudinal study. ''BMC Geriatrics, 19''(63). https://doi.org/10.1186/s12877-019-1100-5 Schoklitsch, A., & Baumann, U. (2012). Measuring generativity in older adults: The development of the Austrian adaptation of the Loyola Generativity Scale (LGS-A). ''International Psychogeriatrics, 24''(6), 973–983. https://doi.org/10.1017/S1041610212000035 Schoklitsch, A., & Baumann, U. (2012). Generativity and aging: A promising future research topic? ''Journal of aging studies, 26''(3), 262-272. https://doi.org/10.1016/j.jaging.2012.01.002 Schultz, P. W. (2015). The role of generativity in social activism: The case of climate change. Journal of Environmental Psychology, 43, 78-85. https://doi.org/10.1016/j.jenvp.2015.01.001 Seligman, M. E. P. (2002). Authentic happiness: Using the new positive psychology to realize your potential for lasting fulfillment. Free Press. Steger, M. F., Frazier, P., Oishi, S., & Kaler, M. (2006). The meaning in life questionnaire: Assessing the presence of and search for meaning in life. Journal of Counseling Psychology, 53(1), 80-93. https://doi.org/10.1037/0022-0167.53.1.80 Tajfel, H., & Turner, J. C. (1979). An integrative theory of intergroup conflict. In W. G. Austin & S. Worchel (Eds.), The social psychology of intergroup relations (pp. 33–47). Brooks/Cole. Van den Broeck, A., et al. (2022). Generativity and mental health in older adults: The protective role of meaningful engagement. Journal of Aging and Health, 34(5), 699-710. https://doi.org/10.1177/08982643221101547 Zacher, H., & Froidevaux, A. (2020). How does generativity enhance well-being in older adulthood? ''International Journal of Environmental Research and Public Health, 17''(6), 1745. https://doi.org/10.3390/ijerph17061745 Zittrain, J. L. (2006). The generative internet. ''Harvard Law Review, 119'', 1974-2040. }} ==External links== * ScienceDirect: [https://www.sciencedirect.com/science/article/abs/pii/S0890406512000035 Generativity and Aging; A promising future research topic?] * Encyclopedia of creativity pdf: [https://www.drrobertepstein.com/pdf/Epstein-Generativity_Theory-Encyclopedia_of_Creativity-1999.pdf Generativity theory] * Oxford University: [https://academic.oup.com/psychsocgerontology/article/64B/1/45/617833 Generativity in Later Life; Perceived Respect From Younger Generations as a Determinant of Goal Disengagement and Psychological Well-being] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Developmental]] [[Category:Motivation and emotion/Book/Motivation]] q4mo83ftq46ikxsqm7pqkjqofdzmf53 Motivation and emotion/Book/2024/Connection to country and well-being 0 307285 2684115 2680044 2024-11-12T02:50:56Z U3237101 2989643 /* Overview */ 2684115 wikitext text/x-wiki {{title|Connection to country and well-being:<br>What is the relationship between connection to country and well-being?}} {{MECR3|1=https://www.youtube.com/watch?v=5p3v_xLNJhM}} __TOC__ == Overview == {{robelbox|theme=9|title=Scenario}} <div style="{{Robelbox/pad}}"> [[File:Messier83 - Heic1403a.jpg|thumb|'''Figure 1.''' Stars in the galaxy]] Imagine a world without nature. No tall trees to provide shade on a sunny day, no beautiful beaches to stroll on, no green grass to lay on, no marine life, no sky full of stars to admire, no bushes to provide us with sweet fruits, sounds quite miserable right? Whether you are conscious of it or not, nature is an extremely significant part of the human experience. We are one with the land and this brings up the theme of [https://medium.com/gain-indpiration/the-interconnectedness-of-life-d2d0f97e790a interconnectedness]. The First Nations Australians relationship with the land is fundamental to how they live their daily lives, their social and emotional wellbeing, and their self-identity (TIMHWB, 2021). Despite the devastating period of colonization, discrimination, injustice, and displacement from their traditional land, they have been committed to protecting the land and passing their knowledge through each generation.</div> {{Robelbox/close}} This chapter explores the relationship between connection to Country and well-being, and what this connection to the land means to Aboriginal and Torres Strait Islanders. Additionally, this chapter shall discuss the holistic and psychological framework SEWB (Social and Emotional Wellbeing), key elements of this framework, and how these elements especially in relation to connection to Country affect Aboriginal and Torres Strait Islander peoples wellbeing. {{RoundBoxTop|theme=2}} '''Focus questions''' 1. Why is connection to Country foundational to Aboriginal and Torres Strait Islander mental health and well-being? 2. What are the differences between Indigenous frameworks of Social and Emotional Well-Being and traditional Western psychological models? 3. In what ways can the holistic framework (SEWB) provide an understanding about Indigenous perspectives of well-being? {{RoundBoxBottom}} == Connection to Country == [[File:Mustoja.jpg|thumb|315x315px|'''Figure 2:''' How do you feel when you look at this image? Do you feel any form of connection to nature?]] Connection to Country is more than just connection to the physical land. To First Nations Australians, the land is the giver of life and their mother, because it provides them with everything they need in abundance. It is a spiritual connection, and one cannot be separated from the other [https://www.workingwithindigenousaustralians.info/content/Culture_3_The_Land.html#:~:text=To%20them%20the%20land%20is,separate%20one%20from%20the%20other. (The Land, 2020)]{{f}} === What is Country? === * Country can be defined in many ways but these different definitions all have the same truth. According to the Aboriginal and Torres Strait Islanders, Country can be described as a living system which is closely linked to Aboriginal cultural practices.{{f}} * Country can also be seen as a multifaceted concept which involves a "''deep, intimate, holistic, complex, localized and reciprocal relationship and connection between Aboriginal and Torres Strait Islander (herein Aboriginal) peoples and elements of land, sea, waterways, sky, stars, and living and non-living entities''”(Yashadhana et.al., 2023). === What is connection to Country? === "''The land and the people are one, 'cause the land is also related. In our kinship system, as a custodian I am the child of that land''," says the Galpu Elder from Nyulunbuy in the Northern Territory, namely Dhangal Gurruwiwi.{{f}} * Connection to Country is as wide as spirituality, family, community, and culture (Gee et.al., 2014) which provides them with a sense of meaning and belonging, as well as identity which in turn has positive psychological consequences (Haslam et.al., 2009). ''"The land is the mother and we are of the land; we do not own the land rather the land owns us. The land is our food, our culture, our spirit and our identity"'' Dennis Foley, a Gai-mariagal and Wiradjuri man, and Fulbright scholar. * There are many ways in which First Nations people care for the land and which tend to be a community effort so as to promote ecological, spiritual, and human health long-term (Behndrent, 2020). === Why is it significant? === * Listening to the voices of the First Nations people with the intention of willing to learn helps us understand what their connection to Country means, and why it is so important to their self identity.{{ic|explain connection to topic}} * Aboriginal and Torres Strait Islanders have the responsibility to take care of both the physical and intangible aspects of Country, and each generation inherits this responsibility. This includes all flora, fauna, living beings, [[wikipedia:Storytelling|storytelling traditions]], language, and lore.{{ic|explain connection to topic}} * In a video that can be found on the [https://australianstogether.org.au/discover-and-learn/our-cultures/the-importance-of-land#video Australians Together] page, Dhangal Gurruwiwi goes on to explain the grief that comes with loss of the land. She says ''"A person dies of grief 'cause the soul has been torn, just like the earth moving equipment tears the land."''{{ic|explain connection to topic}} {{RoundBoxTop|theme=2}} ===Mindfulness practice=== ;Set an intention for your practise ;Pause for 1 minute and slow your breathing ;Consider these questions: <i>What does Country mean to you? Do you feel like you are one with the land/earth?</i> ;Now visualise your connection to country and different nature schemes ;Pause and reflect, how do you feel? what have you learned from this? {{RoundBoxBottom}} == Indigenous frameworks of well-being == [[File:Aboriginal Australian women and children, Maloga, N.S.W.jpg|thumb|340x340px|'''Figure 3:''' Aboriginal Australian women and children, Maloga, N.S.W|left]] * Healing for Aboriginal and Torres Strait Islanders involves healing of the collective, and that is why social and emotional well-being (SEWB) is important. (TIMHWB, 2021) * SEWB is a holistic framework that goes beyond Western concepts of mental health and recognizes that the well-being of Aboriginal and Torres Strait Islanders involves their relationships with the land (Country), their ancestors, families, bodies, and community. * The key elements of SEWB include: # Connection to Country and land # Connection to community # Connection to culture # Connection to spirituality, spirit, and ancestors # Connection to mind and emotions # Connection to family and kinship # Connection to body and behaviours * In order to feel connected to self, there has to be an understanding of self being intrinsically intertwined with community and family (TIMHW, 2021){{expand}} {{Robelbox|theme=8|title=Test your learning!|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {Which of the following is not considered a key element of SEWB? |type="()"} - Connection to Country - Connection to Spirit and Ancestors + Connection to wealth and financial success - Connection to culture and tradition {In SEWB, Connection to Country is important because it fosters a deep sense of identity, spirituality, and belonging. |type="()"} + True - False </quiz> </div> {{Robelbox/close}} == Self-determination theory in Connection to Country == [[Self-determination theory]] (SDT) places an emphasis on basic psychological needs which are: autonomy, competence and relatedness{{f}}. This theory is central to the provision of Aboriginal and Torres Strait Islander health services, due to the fact that connection to Country plays a big role in fulfilling their needs{{f}}. === What is self-determination? === The self-determination theory is a broad framework which has been used to understand human motivation, personality development, and wellness (Ryan, 2023)<ref>{{Cite web|url=https://selfdeterminationtheory.org/topics/application-basic-psychological-needs/|title=Basic Psychological Needs|language=en-US|access-date=2024-10-06}}</ref>. This theory contains six sub-theories which are used to explain different aspects of human motivation and well-being, one of them being the [https://selfdeterminationtheory.org/topics/application-basic-psychological-needs/ Basic Psychological Needs Theory (BPNT)] which shall be discussed further in relation to Connection to Country. === Basic Psychological Needs Theory (BPNT) === [[File:Self-Determination-Theory.png|center|thumb|455x455px|'''Figure 4:''' Self determination key elements]] The BPNT theory suggests that basic psychological needs act as essential ''nutrients'' which if satisfied, can aid in an individual's optimal psychological development, well-being, and self-motivation (Ryan, 2023)<ref>{{Cite web|url=https://selfdeterminationtheory.org/topics/application-basic-psychological-needs/|title=Basic Psychological Needs|language=en-US|access-date=2024-10-06}}</ref> Autonomy, competence and relatedness (see '''Figure 4''' for summarized definitions) play a key part in the well-being of an individual because they give one a sense of control, as well as a sense of belonging due to building a supportive community and building strong bonds. === Application of SDT in connection to Country === SDT is important and relevant in understanding Indigenous Australians motivation and emotional connection to the land and community and why it affects their identity and well-being significantly. [https://aigi.org.au/toolkit/self-determination-for-aboriginal-and-torres-strait-islander-peoples#:~:text=Autonomy%20is%20not%20just%20about,community%20matters Self-determination for Aboriginal and Torres Strait Islander peoples] is crucial because it gives them the power to make their own decisions about governance and what happens on their land and to their communities. Former Murdi Paaki chair Sam Jeffries says ''“Our mob believe that true self-determination is making the decisions about what you feel is important to you.”'' (Jeffries, 2012) {| class="wikitable" |+ !SDT !Application to connection to Country{{f}} |- |Autonomy |Having autonomy over decisions made to manage and care for Country and community is paramount. Often times, Indigenous Australians view their relationship with Country as mutually beneficial, therefore any disruptions caused (government intervention, land dispossession, colonization etc.) affect their well-being, self-identity, and cultural practices negatively. However, satisfaction of autonomy as a basic psychological need enables one to experience a sense of integrity (Vansteenskiste, n.d) |- |Competence |Having control over their own environment and their own lives means retaining the knowledge passed down from generation to generation about traditional cultural practices, which provides them with a sense of mastery and reinforces competence. These activities and this practice of cultural skills play a key role in improving their well-being as it also strengthens community. |- |Relatedness |The land is their giver and their mother. Connection to Country aids in fostering a relationship with their ancestors, their families, and future generations. This connection fulfills their sense of relatedness thereby improving their mental health and well-being. A disruption to this connection, as seen during the stolen generation, is psychological harmful hence negatively impacting their mental health quite heavily. |} {{robelbox|theme=12|title=Test yourself!|iconwidth=55px}} <div style="{{Robelbox/pad}}"> <quiz display="simple"> How will reconnecting with traditional cultural practices, the land, and community help satisfy relatedness as a need in SDT in the healing process? |type="()"} - Promotes individual goals - Reduces the need for community support + Fosters a sense of identity and belonging with community and the ancestors - None of the above </quiz> </div> {{RoundBoxBottom}} == Challenges == When considering improving the mental health and well-being of Indigenous Australians, Indigenous frameworks have to be considered. This is because Western perspectives and definitions of well-being differ from Indigenous perspectives. These frameworks need to be heavily studied and included so as to provide efficient support in their health services.{{vague}} === Challenges faced by Aboriginal and Torres Strait Islanders === {{ic|It might be more helpful to consider with this background/context earlier in the chapter}} Due to the effects of colonization, land dispossession, and racism all over the country for several years, Aboriginal and Torres Strait Islanders were forcefully displaced and relocated due to harsh government policies{{f}}. This means that they were moved to unfamiliar and more urban environments, which has restricted their access to Country (Yashadhana et.al., 2023) {{g}} thereby affecting their well-being and health in a myriad of ways. Evidence{{f}} showed that: * 79% of the Aboriginal people had a higher likelihood of developing mental and physical health issues * They have been incarcerated * They are at a higher level of experiencing socioeconomic disadvantages The denial that Aboriginal and Torres Strait Islanders were the rightful occupants of the land and had the right to retain possession of it while using it to their own discretion (due to the doctrine of ''terra nullius'') lead to the justification of colonization and several years of trauma (Langton, 2020) === Limitations in applying Western psychological theories === Applying Western psychological theories to Indigenous frameworks may pose a number of issues due to completely different worldviews. One of the most important things to be considered is the role that Country plays when revising Indigenous Australian well-being frameworks (Sangha et al., 2024){{expand}} * Differences in beliefs are bound to be a significant limitation. For example, Western vs Indigenous worldviews. {{g}} Majority of the existing psychological theories are rooted in Western research and there is a lack of research and representation of different worldviews and perspectives (Sangha et al., 2024). It cannot be a "one size fits all" situation because people's values and beliefs differ all over the world. * Secondly, ecological and spiritual connections may not apply significantly to Western ideas of healing. For Aboriginal and Torres Strait Islanders, connection to the land, spirit, ancestors is salient. Relationships with the land are deeply spiritual and involve Dreaming and ecological stewardship (Hume, 2002). However, Western psychological models rarely account for spiritual dimensions and other related beliefs which can be limiting in the research carried out. {{RoundBoxTop|theme=2}} '''Reflection''' {{ic|Use numbered list per Tutorial 2}} 1. What steps can be taken in order to incorporate Indigenous knowledge into contemporary and Western psychological practices and policies? 2. In what ways can recognizing the importance of community, Country, and culture lead to providing more effective and useful support for the mental health of Indigenous Australians? 3. Have your views on the importance of connection to Country/land changed after learning about Indigenous Australians perspectives? What has stood out to you? {{RoundBoxBottom}} == Conclusion == * There is a direct correlation{{f}} between connection to Country and wellbeing of the Aboriginal and Torres Strait Islanders, being that connection to the land has a significant effect on their wellbeing and the wellbeing of the community. * The Aboriginal people and Stolen Generation continue to experience discrimination, poor healthcare, lack of opportunities and good education systems among other issues due to racism.{{f}} * Connection to the land is vital for the First Nations people to thrive, as it is all{{f}} they know and it provides them with the space to connect with their ancestors and community in a sacred an spiritual way. * The well-being of Indigenous Australians is best{{f}} understood through the use of a holistic framework such as SEWB. * In order to develop beneficial policies and programs, well-being frameworks need{{f}} to evolve and include representation of all sorts of contemporary values and beliefs, including the role of nature. * Indigenous knowledge systems and Western psychological theories may be integrated, but this has to be done with careful consideration, as well as respect for a holistic approach and different cultural perspectives. {{ic|What is the relationship between CtC and WB? That's the topic.}} == See also == * [[Self-determination theory|Self determination theory]] (Wikiversity) * [[wikipedia:Indigenous_Australian_self-determination|Indigenous Australian self-determination]] (Wikipedia) == References == {{Hanging indent|1= Hume, L. (2002). Ancestral Power: The Dreaming, Consciousness and Aboriginal Australians. Melbourne University Press. Jeffries, S. (2023, December 4). MURDI PAAKI Self-determination. Retrieved from Reconcillliation AUS (youtube): https://www.youtube.com/watch?v=OvfTj9nbH6c&t=2s Kamaljit K. Sangha, Y. D. (2024). A comprehensive analysis of well-being frameworks applied in Australia and their suitability for Indigenous peoples. International Journal of Quantitative Studies on Health and Well-being. Langton, M. (2020). Understanding Sovereignity . Retrieved from Agreements Treaties and Negotiation Settlements : https://www.atns.net.au/understanding-sovereignty Ryan, R. M. (2023). The Oxford Handbook of Self-Determination Theory. Oxford University Press. Vansteenkiste, M. (n.d.). What are basic psychological needs in SDT? Retrieved from Basic Psychological Needs – selfdeterminationtheory.org. (n.d.). https://selfdeterminationtheory.org/topics/application-basic-psychological-needs/ Yang, Y., Cai, H., Yang, Z., Zhao, X., Li, M., Han, R., & Chen, S. X. (2022). Why does nature enhance psychological well-being? A Self-Determination account. ''Journal of Environmental Psychology'', ''83'', 101872. https://doi.org/10.1016/j.jenvp.2022.101872 Yashadhana, A., Fields, T., Liu, E., Serova, N., O’Leary, M., Kenning, G., Kuchelmeister, V., Lockhart, J., & De Leeuw, E. (2023). Therapeutic aspects of Connection to Country and cultural landscapes among Aboriginal peoples from the Stolen Generations living in urban NSW, Australia. ''Public Health Research & Practice'', ''33''(4). https://doi.org/10.17061/phrp3342332 }} == External links == * [https://experience.welcometocountry.com/blogs/learning/connection-to-country Connection to Country] (Welcome to Country) * [https://www.indigenoushpf.gov.au/measures/2-14-indigenous-people-with-access-to-their-tradit Indigenous people with access to their traditional lands] (Australian Institute of Health and Welfare) * [https://www.aboriginalheritagecouncil.vic.gov.au/taking-care-culture-discussion-paper/land-our-future-caring-country Land is our future: Caring for our Country] (Victorian Aboriginal Heritage Council) * [https://australianstogether.org.au/discover-and-learn/our-cultures/the-importance-of-land The importance of Land] (Australians Together) * [https://medium.com/gain-indpiration/the-interconnectedness-of-life-d2d0f97e790a The Interconnectedness of life] (Medium) [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Environment]] [[Category:Motivation and emotion/Book/Nature]] [[Category:Motivation and emotion/Book/Indigenous/Australian]] [[Category:Motivation and emotion/Book/Well-being]] 72havvqmgovp0nmbnkhnzys290nzk6g Talk:Motivation and emotion/Book/2024/Theory of positive disintegration and personal growth 1 307326 2684175 2683418 2024-11-12T10:10:00Z Jtneill 10242 Book chapter resubmission feedback 2684175 wikitext text/x-wiki <!-- Official topic development feedback --> {{METF/2024 |1= <!-- Title --> # The wording and/or capitalisation of the title is incorrect. Be consistent with the [[Motivation and emotion/Book/2024|book table of contents]]. # The wording and/or capitalisation of the sub-title is incorrect. Be consistent with the [[Motivation and emotion/Book/2024|book table of contents]]. |2= <!-- Headings --> # Under-developed – needs work (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 2]]) # Use more descriptive headings # Use sentence casing <!-- Alignment with focus questions --> # Adopt closer alignment between the sub-title, focus questions, and top-level headings <!-- Other ---> # Aim for 3 to 6 top-level headings between the Overview and Conclusion, with up to a similar number of sub-headings for large sections |3= <!-- Overview--> <!-- Scenario --> # Add a scenario or case study into a feature box (with an image) at the start of this section to help catch reader interest <!-- Description --> # Simplify/abbreviate introductory description - move detail into subsequent sections <!-- Focus questions --> # Present focus questions in a feature box at the end of this section |4= <!-- Key points--> |5= <!-- Figure --> # A relevant figure is presented # Caption could better explain how the image connects to key points being made in the main text |6= <!-- Learning feature --> <!-- Interwiki links ---> # Not developed # Include in-text [[m:Help:Interwiki linking|interwiki links]] for the first mention of key terms to relevant Wikipedia articles and/or to other relevant book chapters # Consider including more examples/case studies, quiz question(s), table(s) etc. |7= <!-- References --> <!-- Overall --> # OK # 4 out of minimum of 6 references # Are there any systematic reviews about this topic? # For [https://apastyle.apa.org/instructional-aids/reference-guide.pdf APA referencing style], check and correct: ## alphabetical order ## capitalisation ## [[Help:Wikitext quick reference|italicisation]] ## Do not include location of publisher ## Check and correct formatting of issue number ## page numbers should be separated by an en-dash (–) rather than a hyphen (-) |8= <!-- Resources --> # See also ## One of two links provided ## Use [[w:Letter case#Sentence casing|sentence casing]] ## Rename links so that they are more user friendly (see [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]]) ## Also link to relevant Wikipedia pages # External links ## Not developed |9= <!-- User page --> # Very good <!-- Description about self --> # Brief description about self provided – consider expanding <!-- Links to profile(s) --> # Consider linking to your [https://portfolio.canberra.edu.au/ eportfolio] page and/or any other professional online profile or resume such as [https://www.linkedin.com/ LinkedIn]. This is not required, but it can be useful to interlink your professional networks. <!-- Link to book chapter --> # Link provided to book chapter |10= <!-- Social contribution --> # None summarised on user page with direct link(s) to evidence – this was covered in [[Motivation and emotion/Tutorials/Physiological needs#Social contributions|Tutorial 03]]. Looking ahead to the book chapter submission, see how to earn marks for [[Motivation and emotion/Assessment/Chapter#socialcontribution|social contributions]]. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 03:10, 17 August 2024 (UTC) == Heading casing == {| style="float: center; background:transparent;" |- | [[File:Crystal Clear app ktip.svg|48px|left]] | {{#if:|Hi [[User:{{{1}}}|{{{1}}}]].|}} FYI, the recommended [[Wikiversity]] heading style uses [[w:Letter case#Sentence_case|sentence casing]]. For example:<br> <big><big>Self-determination theory</big></big> rather than <big><big>Self-Determination Theory</big></big> Here's an example chapter with correct heading casing: [[Motivation and emotion/Book/2019/Growth mindset development|Growth mindset development]] -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 22:08, 21 October 2024 (UTC) |} <!-- Official book chapter feedback --> {{MEBF/2024 |1= <!-- Overall comments... --> # Overall, this is an insufficient chapter # I suspect that some of this chapter is [[Motivation and emotion/Assessment/Using generative AI|genAI content]] which hasn't been acknowledged in the edit summaries. If so, it violates academic integrity. # The title and/or sub-title wording and casing were not correct (fixed) <!-- Overall – Citations --> # Insufficient use of primary, peer-reviewed sources as citations (e.g., see the {{fact}} tags) # Move non-peer reviewed links into the [[{{PAGENAME}}#External links|External links]] section <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FTheory_of_positive_disintegration_and_personal_growth&diff=2675071&oldid=2664719 these copyedits] |2= <!-- Overview comments... --> # Underdeveloped <!-- Overview – Case study --> # Engage reader via a case study or scenario in a feature box with a relevant image <!-- Overview – Explains problem --> # Explains the problem or phenomenon <!-- Overview – Focus questions --> # Provide focus questions in a feature box to help guide the reader |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic <!-- Theory – Builds on --> # Builds reasonably well on related chapters and/or Wikipedia articles <!-- Theory – Depth --> # Promising depth is provided about relevant theory(ies) <!-- Theory – Tables/Lists/Figures --> # Use tables, figures, and/or lists to help convey key theoretical information <!-- Theory – Citations --> # Insufficient use of academic, peer-reviewed citations (e.g., see the {{fact}} tags) <!-- Theory – Examples --> # Insufficient use of examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research # Insufficient use of academic, peer-reviewed citations (e.g., see the {{fact}} tags) <!-- Research – Critical thinking --> # Insufficient critical thinking about relevant research is evident # Critical thinking about research could be further evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## discussing the direction of relationships ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research # Many claims lack sufficient citation (e.g., see the {{fact}} tags) |5= <!-- Integration comments... --> # Insufficient integration between theory and research # The chapter places more emphasis on theory than on research; strive for an integrated balance # Where research is discussed, it is integrated with theory |6= <!-- Conclusion comments... --> # Basic summary and conclusion # Some points are summarised, but it would be better to address the focus questions and provide practical, take-home message(s) # The conclusion is confusing because it raises new ideas that weren't discussed earlier (e.g., self-compassion) |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## Overall, the quality of written expression is OK but there are several aspects which are below professional standard <!-- Written expression – Paragraphs --> ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. <!-- Written expression – Language --> ## Use 3rd person perspective (e.g., "it") rather than 1st (e.g., "we") or 2nd person (e.g., "you") perspective[https://www.grammarly.com/blog/first-second-and-third-person/] in the main text, although 1st or 2nd person perspective can work well for case studies or feature boxes ## Avoid directional referencing (e.g., "As previously mentioned"). Instead: ### it is, most often, not needed at all, or ### use [[w:Help#Section linking|section linking]] ## Embed direct quotes within sentences and paragraphs, rather than presenting them holus-bolus. ## "People" is often a better term than "individuals" <!-- Written expression – Layout --> # Layout ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion # Remove abbreviations from headings ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) <!-- Written expression – Grammar --> # Grammar ## The grammar for some sentences could be improved (e.g., see the {{gr}} tags) ## Check and correct use of possessive apostrophes (e.g., cats vs cat's vs cats')[https://grammar.yourdictionary.com/punctuation/apostrophe-rules.html] ## Check and correct use of [https://www.google.com.au/search?q=grammar+that+vs+who that vs. who] <!-- Written expression – Spelling --> # Spelling ## Use [https://www.abc.net.au/education/learn-english/australian-vs-american-spelling/11244196 Australian spelling] (e.g., hypothesize vs. hypothesise; behavior vs. behaviour) <!-- Written expression – Proofreading --> # Proofreading ## Remove unnecessary capitalisation (e.g., Psychologist -> psychologist) <!-- Written expression – APA style --> # APA style ## [https://apastyle.apa.org/style-grammar-guidelines/capitalization/diseases-disorders-therapies Use sentence casing for the names of disorders, therapies, theories, etc.] ## Use [[w:Serial comma|serial comma]]s[https://www.buzzfeed.com/adamdavis/the-oxford-comma-is-extremely-important-and-everyone-should]. [https://www.youtube.com/watch?v=gBx8ooDupXY Video] (1 min) ## Use double (not single) quotation marks "to introduce a word or phrase used ... as slang, or as an invented or coined expression" (APA 7th ed., 2020, p. 159) ## Direct quotes need page numbers – even better, communicate concepts in your own words <!-- Written expression – Figures --> ## Figures ### Briefly captioned; provide more detail to help connect the figure to the text ### Use this format for captions: ''Figure X''. Descriptive caption in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]] ### Each Figure is referred to at least once within the main text ### Refer to each Figure using APA style <!-- Written expression – Citations --> ## Citations use poor APA style (7th ed.) <!-- Written expression – References --> ## References use poor APA style: ### Very weak use of the best peer-reviewed psychological theory and research about this topic ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Check and correct use of italicisation ### Separate page numbers using an en-dash (–) rather than a hyphen (-) ### Move non-peer reviewed links into the [[{{PAGENAME}}#External links|External links]] section ### Move Wikipedia links into the See also section ### Acknowledge genAI use via edit summaries per using genAI guidelines |8= <!-- Learning features comments... --> # Insufficient use of learning features <!-- Learning features - Embedded links to Wikipedia --> # Reasonably good use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles. Adding more interwiki links for the first mention of key words and technical concepts would make the text even more interactive. See [[Motivation and emotion/Book/2020/Nutrition and anxiety|example]]. # Use [[m:Help:Interwiki linking|interwiki links]] (rather than external links) to Wikipedia articles, per [[Motivation and emotion/Tutorials/Wiki editing|Tutorial 02]] <!-- Learning features - Embedded links to Wikiversity --> # No use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Move links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section <!-- Learning features – Images etc. --> # Basic use of image(s) # No use of table(s) # Basic use of feature box(es) # No use of case studies or examples <!-- Learning features – Quizzes --> # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # Basic use of interwiki links in the "See also" section ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link <!-- Learning features – External links --> # Insufficient use of external links in the "External links" section ## Use [https://www.masterclass.com/articles/sentence-case-explained sentence casing] ## Use alphabetical order ## Include sources in [[w:Bracket#Parentheses|parentheses]] after the link ## Move Wikipedia links to the See also section |9= <!-- Social contribution comments... --> # No logged social contributions }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 22:08, 21 October 2024 (UTC) ===Resubmission feedback=== # Overall, this is an improved version, but is still insufficient mainly because it is over the maximum word count and lacks integration and relevant research ## [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FTheory_of_positive_disintegration_and_personal_growth&diff=2681783&oldid=2675071 The resubmission involved major revisions] ## The chapter is ~500 words over the maximum word count ## The structure is overly complex and needs more careful thinking/planning # Overview ## The opening scenario is difficult for an unfamiliar person to understand ## The Overview description of the problem is too long - abbreviate and move detail into subsequent sections ## There are no focus questions # Theory ## Much better use is made of citations ## However, there are still claims that lack sufficient citations # Research ## Some research is now incorporated # Integration ## Integration of theory and research is slightly improved # Style ## This has been improved to a basic level ## There is some basic acknowledgement of genAI use ## APA style is not used for citations (e.g., do not use initials; use et al. for three or more authors) ## More proofreading is needed to bring this to a professional standard # Learning features ## There is some improvement (but this is largely offset by being over the maximum word count e.g., external links not counted) # Social contributions ## None Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:09, 12 November 2024 (UTC) {{MEMF/2024 |1= <!-- Overall comments ... --> <!-- Overall - Overall --> # Overall, this is a basic presentation <!-- Overall - Time --> # The presentation is over the maximum time limit — content beyond 3 mins is ignored for marking and feedback purposes |2= <!-- Overview comments ... --> <!-- Overview - Opening --> # An opening slide with the correct title and incorrect sub-title is displayed. Also narrate or paraphrase the title and sub-title — this helps to clearly convey the purpose of the presentation. <!-- Overview - Introduction --> # Create an engaging introduction to hook audience interest (e.g., by introducing a case study or scenario) <!-- Overview - Context --> # A context for the presentation is established <!-- Overview - Focus --> # Consider asking focus questions that lead to take-away messages. This will help to focus and discipline the presentation. |3= <!-- Content comments ... --> # Comments about the book chapter may also apply to this section <!-- Content - Addresses topic --> # The presentation addresses the topic <!-- Content - Amount --> # There is too much content, in too much detail, presented within the allocated time frame. Zoom out and provide a higher-level presentation at a slower pace. It is best to cover a small amount of well-targetted content than a large amount of poorly selected content. <!-- Content - Theory --> # The presentation makes excellent use of relevant psychological theory <!-- Content - Research --> # The presentation makes no use of relevant psychological research <!-- Content - Citations --> # The presentation makes no use of citations to support claims <!-- Content - Examples --> # The presentation makes no use of examples #<!-- Content - Practical advice --> # The presentation provides practical advice <!-- Content - Easy to understand --> # The presentation provides easy to understand information |4= <!-- Conclusion comments ... --> <!-- Conclusion - Time --> # The Conclusion did not fit within the time limit |5= <!-- Audio comments ... --> <!-- Audio - Easy to follow --> # The audio is easy to follow <!-- Audio - Narration --> # The presentation makes reasonably good use of narrated audio <!-- Audio - Pacing --> # Audio communication is well paced <!-- Audio - Voice --> # Reasonably good [[w:Intonation (linguistics)|intonation]] <!-- Audio - Practice --> # The narration is reasonably well practiced and/or performed <!-- Audio - Recording quality --> # Audio recording quality was reasonably good <!-- Audio - Topic --> # The narrated [[#Content|content]] is well matched to the target topic but lacked synthesis of the best psychological research about this topic |6= <!-- Video comments ... --> <!-- Video - Overall --> # Overall, visual display quality is basic <!-- Video - Video, Image, Text --> # The presentation makes basic use of text-based slides <!-- Video - Font --> # The font size is sufficiently large to make it easy to read but could be increased on some slides <!-- Video - Images --> # The visual communication could be improved by including some relevant images and/or diagrams <!-- Video - Production --> # The presentation is basically produced using simple tools |7= <!-- Meta-data comments ... --> <!-- Meta-data - Title/sub-title --> # The video title does not match the chapter title and sub-title — this would help to clearly convey the purpose of the presentation and be more consistent <!-- Meta-data - Description --> # Provide a written description of the presentation to help potential viewers decide whether or not to watch <!-- Meta-data - Links --> # Links to and from the book chapter are provided |8= <!-- Licensing comments ... --> <!-- Licensing - Presentation --> # A copyright license for the presentation is not clearly indicated }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 11:17, 4 November 2024 (UTC) Resubmission comments: # Overview ## The opening slide is improved ## An (overly) long scenario is added at the beginning # Content ## This has been abbreviated ## No use of research # Conclusion ## A very basic verbal conclusion has been added # Audio ## No major changes # Video ## There is greater use of images # Meta-data ## There are some improvements # Licensing ## Basic improvements Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 06:33, 11 November 2024 (UTC) ox0acusdot8dhphjd6k26qmh3i9q9ym Motivation and emotion/Book/2024/Antisocial behaviour in children 0 307453 2684099 2648782 2024-11-12T02:02:26Z 27.96.194.184 /* Overview */ 2684099 wikitext text/x-wiki {{title|Antisocial behaviour in children:<br>What motivates antisocial behaviour in children? }} {{MECR3|1=}} __TOC__ ==Overview== {{robelbox|width=30|theme=4|title=}} <div style="{{Robelbox/pad}}"> . </div> {{Robelbox/close}} {{RoundBoxTop|theme=1}} '''Focus questions:''' * What are antisocial behaviours? * What are the antecedents for antisocial behaviours? * What motivates the development of antisocial behaviour in children? * What is the relationship between emotion and antisocial behaviour? {{RoundBoxBottom}} == Antisocial behaviour == Stockholm syndrome is complex adaptive response to traumatic and threatening situations[[File:[[File:Disruptive, impulse control, and conduct disorders.webm|<nowiki>thumb]</nowiki>''Figure 2. Video explaining Antisocial personality'']]Definition: * Origins: [[wikipedia:Norrmalmstorg_robbery|Norrmalmstorg robbery]]- Hyper link other cases i.e [[wikipedia:Patty_Hearst|Patty Hearst]], * Differentiation from disorder (why?) - comment, prior to DSM V consideration of inclusion under other stress related condition * Brief comment on need for language - title to change to reflect survival mechanism (discus later on) == Antecedents of antisocial behaviour == Topic sentence === Family === [[File:MPOTY_2012_domestic_violence_awareness.jpg|alt=|thumb|400x400px|''Figure 1.'' Emotive image capturing perspective of an individual being actively threatened]] Para one Para two Para three === Peer === Para one Para two Para three Para four === Emotions === Para one Para two Para three Para four Table 1. ''The Title of the table '' {| class="wikitable" style="margin: auto;" |- ! Likely to list emotions and definitions !! Heading |- | ''Terror (?)''||Explanation |- |''Gratitude (?)'' |Explanation |- |''Sympathy or Empathy (?)''||Explanation |- |''Fear (?)'' |Explanation |- | |Explanation |} === Test yourself === {{RoundBoxTop}}REVIEW QUIZ {{RoundBoxBottom}} Topic sentence ''(Brief): Survival'' === Sub heading one === Para one Para two Para three * {{Robelbox|width=30|theme={{{theme|4}}}|title=Case study}} <div style="{{Robelbox/pad}}"> insert a case study example that illustrates how positive affect/sympathy w. ones capture can be a mechanism of survival - i.e decrease threat level and increase provision of needs </div> {{Robelbox/close}} === Sub heading two === Para one == Emotional deficits == Topic sentence ''(Brief):'' === Test yourself === {{RoundBoxTop}}REVIEW HOW TO DO QUIZ {{RoundBoxBottom}} == Conclusion == == See also == * [[wikipedia:Traumatic_bonding|Trauma bonding]] (Wikipedia) * [[wikipedia:Attachment_theory|Attachment theories]] (Wikipedia) * [[Motivation and emotion/Book/2024/Stockholm syndrome motivation|Stockholm syndrome and motivation]] (Book Chapter, 2024) ==Reference== {{Hanging indent|1= Dieppe, C., Stanhope, B., & Rakhra, K. (2009). Children who harm themselves: development of a paediatric emergency department triage tool. Emergency Medicine Journal, 26(6), 418–420. https://doi.org/10.1136/emj.2008.062463 Fairchild, G., Hawes, D. J., Frick, P. J., Copeland, W. E., Odgers, C. L., Franke, B., Freitag, C. M., & De Brito, S. A. (2019). Conduct disorder. Nature Reviews. Disease Primers, 5(1), 43-. https://doi.org/10.1038/s41572-019-0095-y Jahic, I., Trulson, C. R., Caudill, J. W., Bonner, T., Slemaker, A., & DeLisi, M. (2021). Adverse Childhood Experiences and Forensic Typologies: Getting Specific about Trauma among Institutionalized Youth. International Journal of Environmental Research and Public Health, 18(21), 11307-. https://doi.org/10.3390/ijerph182111307 Klahr, A. M., Klump, K. L., & Burt, S. A. (2014). The Etiology of the Association Between Child Antisocial Behavior and Maternal Negativity Varies Across Aggressive and Non-Aggressive Rule-Breaking Forms of Antisocial Behavior. Journal of Abnormal Child Psychology, 42(8), 1299–1311. https://doi.org/10.1007/s10802-014-9886-5 McKeown, A. (2019). Is coercion ever beneficent? : Public health ethics in early intervention and prevention for mental health. Elsevier/Academic Press. McDonald, S. E., Cody, A. M., Booth, L. J., Peers, J. R., O’Connor Luce, C., Williams, J. H., & Ascione, F. R. (2018). Animal Cruelty among Children in Violent Households: Children’s Explanations of their Behavior. Journal of Family Violence, 33(7), 469–480. https://doi.org/10.1007/s10896-018-9970-7 Milone, A., Sesso, G., Milone, A., & Sesso, G. (2022). Disruptive Behavior Disorders Symptoms, Evaluation and Treatment. MDPI - Multidisciplinary Digital Publishing Institute. Nathanson, A., Music, G., & Sternberg, J. (Eds.). (2021). From trauma to harming others : therapeutic work with delinquent, violent and sexually harmful children and young people. Routledge. Persson, M., Sturup, J., Belfrage, H., & Kristiansson, M. (2018). Self-reported violent ideation and its link to interpersonal violence among offenders with mental disorders and general psychiatric patients. Psychiatry Research, 261, 197–203. https://doi.org/10.1016/j.psychres.2017.12.079 Robles-Haydar, C. A., Martínez-González, M. B., Flórez-Niño, Y. A., Ibáñez-Navarro, L. M., & Amar-Amar, J. J. (2021). Personal and Environmental Predictors of Aggression in Adolescence. Brain Sciences, 11(7), 933-. https://doi.org/10.3390/brainsci11070933 Ryan, R. M., & Deci, E. L. (2000). Intrinsic and Extrinsic Motivations: Classic Definitions and New Directions. Contemporary Educational Psychology, 25(1), 54–67. https://doi.org/10.1006/ceps.1999.1020 Stryker, R. (2013). Violent children and structural violence: Re-signaling ‘RAD Kids’ to inform the social work professions. Children and Youth Services Review, 35(8), 1182–1188. https://doi.org/10.1016/j.childyouth.2013.04.005 Sun, C.-F., Mansuri, Z., Trivedi, C., Vadukapuram, R., & Reddy, A. (2022). Homicidal ideation and psychiatric comorbidities in the inpatient adolescents aged 12–17. Frontiers in Psychiatry, 13, 933524–933524. https://doi.org/10.3389/fpsyt.2022.933524 Vaish, A., Carpenter, M., & Tomasello, M. (2016). The Early Emergence of Guilt-Motivated Prosocial Behavior. Child Development, 87(6), 1772–1782. https://doi.org/10.1111/cdev.12628 Van Damme, L., Colins, O. F., & Vanderplasschen, W. (2016). The Limited Prosocial Emotions Specifier for Conduct Disorder Among Detained Girls: A Multi-Informant Approach. Criminal Justice and Behavior, 43(6), 778–792. https://doi.org/10.1177/0093854815613104 Vaughn, M. G., Carbone, J., DeLisi, M., & Holzer, K. J. (2020). Homicidal Ideation among Children and Adolescents: Evidence from the 2012-2016 Nationwide Emergency Department Sample. The Journal of Pediatrics, 219, 216–222. https://doi.org/10.1016/j.jpeds.2019.12.045 }} == External links == * [https://www.youtube.com/watch?v=F-6VkeBv3G0 What is Stockholm syndrome] (Youtube) * [[google:lifeline&oq=lifeline&aqs=chrome..69i57j69i64j69i59j0i67i512i650j0i512l2j0i402i512i650j0i512.3492j0j7&sourceid=chrome&ie=UTF-8|Lifeline]] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Cognitive]] [[Category:Motivation and emotion/Book/Social psychology]] 27sq9olqpjd3uvpn18uhovumzy6v31g Industrial and organizational psychology 0 307498 2683979 2679486 2024-11-11T20:51:27Z Atcovi 276019 /* Content */ mod12 2683979 wikitext text/x-wiki {{underconstruction}} [[File:Society for Industrial and Organizational Psychology Office.jpg|thumb|320x320px|The office of the [[w:Society_for_Industrial_and_Organizational_Psychology|Society for Industrial and Organizational Psychology]] (''SIOP'') in Bowling Green, Ohio.]] '''Industrial and organizational psychology''' (abbreviated as ''I/O psych'') relates to the psychology of work. It intersects with related disciplines of psychology such as [[motivation]] and [[social psychology]]. This speciality aims to investigate the actions, behavior, and attitudes of humans in the workforce - usually addressing work-related issues, such as recruitment, satisfaction in work life, work structure, and the overall well-being of workers in an organization. An I/O psychologist would apply their knowledge in psychology to assisting and aiding human and organizational issues in the workforce. For example, an I/O psychologist may assist in recruiting the best candidate for a job position, investigate factors into poor work-life quality, and/or developing rubrics for assessing employee performances. ==Content== * [[/Module 1]] * [[/Module 2]] * [[/Module 3]] * [[/Module 4]] * [[/Module 5]] * [[/Module 7]] * [[/Module 8]] * [[/Module 9]] * [[/Module 10]] * [[/Module 11]] * [[/Module 12]] == See also == * [[w:Industrial and organizational psychology|Industrial and organizational psychology]] (Wikipedia) * [https://www.siop.org/ Society for Industrial and Organizational Psychology] (official website) - provides history of I/O psych, membership info, newsletter, job openings, graduate training programs in I/O psych, and a list of SIOP publications. [[Category:Atcovi's Work]] [[Category:Organizational psychology]] kbporujwcmjg2i7mj6amgjdecfnnr5i User:Jaredscribe/2024 US Presidential Debate 2 307868 2683989 2651554 2024-11-11T21:10:43Z Jaredscribe 2906761 2683989 wikitext text/x-wiki {{delete|user's own subpage. no intention to develop this}} = 2024 presidential campaign == {{Main|Kamala Harris 2024 presidential campaign}} On July 21, 2024, incumbent president and presumptive Democratic nominee Joe Biden [[Withdrawal of Joe Biden from the 2024 United States presidential election|suspended]] his [[Joe Biden 2024 presidential campaign|campaign for reelection in 2024]] and endorsed Harris for president.<ref>{{Cite news |last1=Samuels |first1=Brett |last2=Gangitano |first2=Alex |date=July 21, 2024 |title=Biden Endorses Harris as Democratic Nominee After Ending His Candidacy |url=https://thehill.com/homenews/campaign/4784460-joe-biden-endorses-kamala-harris/ |url-status=live |archive-url=https://web.archive.org/web/20240723214700/https://thehill.com/homenews/campaign/4784460-joe-biden-endorses-kamala-harris/ |archive-date=23 July 2024 |work=[[The Hill (newspaper)|The Hill]] |access-date=24 July 2024}}</ref> Harris was also endorsed by [[Jimmy Carter]], [[Bill Clinton|Bill]] and [[Hillary Clinton]], [[Barack Obama|Barack]] and [[Michelle Obama]], the [[Congressional Black Caucus]], and [[List of Kamala Harris 2024 presidential campaign endorsements|many others]].<ref>{{Cite news |last1=Gamio |first1=Lazaro |last2=Keefe |first2=John |last3=Kim |first3=June |last4=McFadden |first4=Alyce |last5=Park |first5=Andrew |last6=Yourish |first6=Karen |date=July 22, 2024 |title=Many Elected Democrats Quickly Endorsed Kamala Harris. See Who Did. |url=https://www.nytimes.com/interactive/2024/07/22/us/politics/kamala-harris-democrats-endorsement-list.html |access-date=July 22, 2024 |newspaper=The New York Times |issn=0362-4331 |archive-date=July 22, 2024 |archive-url=https://web.archive.org/web/20240722072026/https://www.nytimes.com/interactive/2024/07/22/us/politics/kamala-harris-democrats-endorsement-list.html |url-status=live }}</ref><ref>{{Cite news |title=The Democrats who have endorsed Kamala Harris to replace Biden as nominee |first1=Hayden |last1=Godfrey |first2= Adrián |last2=Blanco |first3=Kati |last3=Perry |first4=Hannah |last4=Dormido |first5=Eric |last5=Lau |url=https://www.washingtonpost.com/politics/interactive/2024/kamala-harris-endorsements/ |date=21 July 2024 |access-date=August 5, 2024 |newspaper=The Washington Post}}</ref><ref>{{Cite web |last1=Davis |first1=Ebony |date=July 26, 2024 |title=Barack and Michelle Obama endorse Kamala Harris for president |url=https://www.cnn.com/2024/07/26/politics/barack-michelle-obama-kamala-harris-endorsement/index.html |access-date=August 5, 2024 |publisher=CNN |archive-date=August 5, 2024 |archive-url=https://web.archive.org/web/20240805160641/https://www.cnn.com/2024/07/26/politics/barack-michelle-obama-kamala-harris-endorsement/index.html |url-status=live }}</ref><ref>{{Cite news |last1=Bluestein |first1=Greg |date=August 3, 2024 |title=Jimmy Carters next goal is voting for Kamala Harris for president |url=https://www.ajc.com/politics/jimmy-carters-next-goal-is-voting-for-kamala-harris/UKCLDIUSSJC6JM4NP7HGOEDCNY/ |access-date=August 3, 2024 |work=[[The Atlanta Journal-Constitution]] |archive-date=August 3, 2024 |archive-url=https://web.archive.org/web/20240803125750/https://www.ajc.com/politics/jimmy-carters-next-goal-is-voting-for-kamala-harris/UKCLDIUSSJC6JM4NP7HGOEDCNY/ |url-status=live }}</ref> In the first 24 hours of her candidacy, her campaign raised $81&nbsp;million in small-dollar donations, the highest single-day total of any presidential candidate in history.<ref>{{Cite news |last1=Samuels |first1=Brett |date=July 22, 2024 |title=Harris breaks 24-hour fundraising record after Biden drops out |url=https://thehill.com/homenews/campaign/4786610-harris-breaks-fundraising-record/ |url-status=live |archive-url=https://web.archive.org/web/20240722220814/https://thehill.com/homenews/campaign/4786610-harris-breaks-fundraising-record/ |archive-date=July 22, 2024 |access-date=July 22, 2024 |newspaper=[[The Hill (newspaper)|The Hill]]}}</ref> If elected, Harris would be the first female and first Asian-American president of the United States, and the second African-American president, after Obama.<ref>{{Cite news |date=July 21, 2024 |title=Harris could become the first female president after years of breaking racial and gender barriers |first1=Chris |last1=Megerian |url=https://apnews.com/article/kamala-harris-president-democrat-biden-96df4c46fab767269056511037776b15 |access-date=August 6, 2024 |publisher=Associated Press |archive-date=August 7, 2024 |archive-url=https://web.archive.org/web/20240807074158/https://apnews.com/article/kamala-harris-president-democrat-biden-96df4c46fab767269056511037776b15 |url-status=live }}</ref> By August 5, Harris had officially secured the nomination via a virtual roll call of delegates.<ref name="KHnom">{{Cite web|last=Kim|first=Seung Min|title=Kamala Harris is now Democratic presidential nominee, will face off against Donald Trump this fall|url=https://apnews.com/article/harris-democratic-presidential-nomination-eb43b6b346cc644b2d195315cb2bfb20|publisher=Associated Press|date=August 5, 2024|access-date=August 5, 2024|archive-date=August 8, 2024|archive-url=https://web.archive.org/web/20240808041440/https://apnews.com/article/harris-democratic-presidential-nomination-eb43b6b346cc644b2d195315cb2bfb20|url-status=live}}</ref><ref>{{Cite news |last=Nehamas |first=Nicholas |date=August 6, 2024 |title=Harris Officially Secures Democratic Party's Nomination for President |url=https://www.nytimes.com/2024/08/06/us/politics/kamala-harris-president-campaign-2024.html |access-date=August 6, 2024 |newspaper=The New York Times |issn=0362-4331 |archive-date=August 6, 2024 |archive-url=https://web.archive.org/web/20240806062412/https://www.nytimes.com/2024/08/06/us/politics/kamala-harris-president-campaign-2024.html |url-status=live }}</ref><ref name="HarrisClinches2020">{{cite web|url=https://www.bloomberg.com/news/articles/2024-07-23/harris-crosses-delegate-threshold-in-sign-nomination-is-hers|title=Harris Has Enough Delegates to Clinch Nomination for President |first1=Gregory |last1=Korte |first2=Jordan |last2=Fabian|date=July 22, 2024|access-date=July 22, 2024|publisher=[[Bloomberg News]]|archive-date=July 23, 2024|archive-url=https://web.archive.org/web/20240723020348/https://www.bloomberg.com/news/articles/2024-07-23/harris-crosses-delegate-threshold-in-sign-nomination-is-hers?srnd=homepage-uk|url-status=live}}</ref> The next day, she announced Minnesota Governor [[Tim Walz]] as [[2024 Democratic Party vice presidential candidate selection|her vice presidential running mate]].<ref>{{Cite web|last1=Parnes|first1=Amie|last2=Samuels|first2=Brett|last3=Conradis|first3=Brandon|date=August 6, 2024|title=Harris picks Walz for vice president|url=https://thehill.com/homenews/campaign/4789021-kamala-harris-vp-tim-walz-minnesota/|access-date=August 6, 2024|newspaper=The Hill|archive-date=August 6, 2024|archive-url=https://web.archive.org/web/20240806130648/https://thehill.com/homenews/campaign/4789021-kamala-harris-vp-tim-walz-minnesota/|url-status=live}}</ref> On August 22, 2024, the fourth day of the [[Democratic National Convention]], Harris officially accepted the Democratic nomination for president.<ref>{{Cite web |title=12 highlights from the 2024 Democratic National Convention |url=https://www.cbsnews.com/news/dnc-highlights-2024/ |access-date=August 23, 2024 |publisher=CBS News date=August 23 2024}}</ref> 49hkmswzs37d1cx6760lcygneiqjqaw Social Victorians/Diamond Jubilee Garden Party 0 307962 2684068 2682726 2024-11-12T00:40:14Z Scogdill 1331941 2684068 wikitext text/x-wiki =Event= On Monday 28 June 1897, Queen Victoria hosted a garden party at Buckingham Palace, inviting between 5,000 and 6,000 people. This party was the final official event of the London Diamond Jubilee celebrations. The Queen released to the press the names of people invited, which means the newspapers could print some or all of this list. The very long article in the London ''Morning Post'', for example, prints what may be the comprehensive list of those invited, although two columns are illegible in some places. The original newspaper account seems to have been published by the ''Court Circular'', and then the popular newspapers reprinted pieces of that story, many adding contextualizing paragraphs of their own. Some of these later reports are quite long, perhaps 5 or more full columns. Sometimes the newspapers included short descriptions of the women's dresses, suggesting that for the list of people invited, the source was the ''Court Circular'', but the parts of the stories devoted to context, history or fashion might have been written by a reporter present at the event. ==Logistics== * 28 June 1897, Monday, in the gardens at Buckingham Palace, hosted by Queen Victoria. * Between 5,000 and 6,000 guests were invited. * Many visitors from the empire who were in town for the Jubilee celebrations were invited to this garden party. * The weather was fine, having improved since the day before. * The garden party was held in the grounds around Buckingham Palace, and the Palace itself was open and available for guests to visit:<blockquote>Great preparations had been made in the splendid grounds adjoining the Royal Palace for the party, the whole scene presenting a fascinating appearance. The beautifully-kept grounds were partially covered with tents and marquees for the convenience of the many guests, and the lovely lake was really in the hands of the Queen’s bargemen, who had charge of the many boats which had been placed on the extensive ornamental waters for the use of guests. There was also plenty of music, several regimental bands being in attendance, while for those who wished to become acquainted with the valuable pictures and works art which are to be found at the Royal residence, all the State and reception rooms of the Palace were thrown open.<ref name=":2">“The Queen’s Garden Party. Brilliant Scene at Buckingham Palace.” ''Globe'' 29 June 1897, Tuesday: 6 [of 8], Col. 3a–c [of 5]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0001652/18970629/050/0006. Print p. 6.</ref> (6, Col. 3a)</blockquote> *The streets around the entrances to Buckingham Palace were lined with spectators beginning hours before the Queen was to arrive:<blockquote>Although the Garden Party was not timed to commence until after five o’clock, the Mall from Marlborough House to Buckingham Palace was well lined by two o’clock, and an hour afterwards large crowds, for the most part composed of ladies, had taken up their positions. This was also the case along Constitution-hill, where the assembly which had gathered to witness the Queen’s arrival at the Palace from Windsor nad [sic] to a large extent remained. The heat was somewhat oppressive, but the trees along the Mall and the Green Park afforded welcome shelter. Many ladies had evidently come prepared for a long wait, as they had provided themselves with the now familiar camp stool, which is always prominent on these occasions. On the other hand, the police were waging war against the men who frequent such places with stools and forms, and as soon as any of them put in an appearance they were quickly pounced upon by the officers, who at once proceeded to destroy the intended stands before the eyes of the helpless owners. Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote> ==Related Events== This garden party was the culminating event of the official celebrations for Queen Victoria's Diamond Jubilee, and more specific events led up to it: # Trip from Windsor to Paddington Station Queen Victoria and a large retinue traveled by train from Windsor to Paddington Station the day before, preceded on an earlier train by "the royal equipages sent from Buckingham Palace for the use of the Queen and her suite," which were<blockquote>First came the splendied semi-state landau in which the Queen made her now famous journey on June 22d. It was preceded by scarlet-coated outriders, and horsed by four magnificent bays driven by postilions in navy blue and white uniforms. Two similar carriages followed, and these were in turn succeeded by a number of pair-horse clarences for the conveyance of the household and suite, and several breaks and ‘buses for luggage. A captain's escort, furnished by the 2d Life Guards, and commanded by Captain Ellison, clattered along in rear of the carriages, and took up a position opposite the spot where, by prior arrangement, Her Majesty’s saloon was to be brought to a standstill. These magnificent troops, riding their great black horses, and with the sunlight dancing upon their nodding plumes, and reflected by their burnished helmets, cuirasses, and trappings, made a very fine show indeed. The escort did not carry the colour, as it did on the 21st, nor was it accompanied by the regimental trumpets.<ref name=":0">"Jubilee Festivities. The Queen Again in London. Interesting Functions. A Visit to Kensington. The Garden Party." ''North British Daily Mail'' 29 June 1897, Tuesday: 5 [of 8], Col. 3a–7b [of 9]. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0002683/18970629/083/0005. Print p. 5.</ref>{{rp|5, Col. 3b}}</blockquote> # Reception at Paddington # Visit to Kensington # Kensington to Buckingham Palace # The Garden Party # Return to Windsor by Way of Paddington === Foreign Admirals === On 29 June 1897, the day after the garden party, the ''North British Daily Mail'' reports that, after the Queen's garden party, the foreign admirals would return to Spithead for a tour around the dockyard and luncheon:<blockquote>THE FLEET AT SPITHEAD<p> The fleet at Spithead was again illuminated last night, the railway companies having duplicated the ordinary train service to bring visitors down. The Koenig Wilhelm was to have sailed on Sunday evening, but her departure has been deferred, and last night her officers gave a private dinner party aboard for the anniversary of the Queen’s Coronation. All the commissioned ships in the harbour were dressed at noon. A royal salute was fired. The [Col. 6c–7a] foreign admirals will return from their visit to London on the occasion of the Queen’s garden party to be conducted round the dockyard to-day, and they will be entertained to luncheon.<ref name=":0" />{{rp|5, Col. 6c–7a}}</blockquote> === Colonial Premiers === The day of the garden party the colonial premiers attended a meeting with Secretary of State for the Colonies, [[Social Victorians/People/Chamberlain|Joseph Chamberlain]]:<blockquote>THE COLONIAL PREMIERS The whole of the Colonial Premiers went to the Colonial Office yesterday for further conference with Mr Chamberlain, who received them in his private room, attended by Mr F. H. Wilson, legal assistant, Mr Reid and the Hon. T. Cochrane, M.P., assistant private secretaries. The conference lasted hours, and was of a strictly private and confidential character, the matters discussed involving several points of high State policy. Premiers will be entertained at Warwick Castle by the Earl and Countess of Warwick on July 15th. On the same occasion the Attorney General of Queensland will present a loving cup from Warwick, in Queensland, to the old county town of Warwick, from which it takes its name. He will be accompanied by the Colonial troopers.<ref name=":0" />{{rp|5, Col. 7a}}</blockquote> For these visitors to London during the Diamond Jubilee, the next major social event was on 15 July, at Warwick Castle, hosted by [[Social Victorians/People/Warwick|Daisy, Countess of Warwick and Francis, 5th Earl of Warwick]], although perhaps some attended the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]]. == Who Was Present == In the absence of a copy of the report about the garden party in the ''Court Circular'', the newspaper account with the fullest list of names is from the ''Morning Post'', although people further down the list can be impossible to identify, and two full columns are damaged (Col. 7 on p. 4 and Col. 1 on p. 5).<ref name=":1">“The Queen’s Garden Party.” ''Morning Post'' 29 June 1897, Tuesday: 4 [of 12], Cols. 1a–7c [of 7] and 5, Col. 1a–c. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/BL/0000174/18970629/032/0004 and https://www.britishnewspaperarchive.co.uk/viewer/bl/0000174/18970629/032/0005.</ref> Whenever possible, then, what is here has been amended with other newspaper reports that have names to help decipher the illegible ones in the ''Morning Post'' account. The names in the Morning Post are grouped, mostly by rank and name. === People of Color at This Event === One purpose of a closer look at this event is to get a more precise list of names of people of color from the various countries in the empire, who were not recognized and thus not named in newspaper descriptions of other events. For example, the [[Social Victorians/1897 Fancy Dress Ball|Duchess of Devonshire's 2 July 1897 fancy-dress ball]] was said to include a number of South Asian dignitaries, but because the Duchess did not release to the newspapers the names of those who were invited, those dignitaries went mostly unnamed in the newspaper reports, if their presence was noted at all. Besides the South Asian guests invited to this garden party, some South Asian visitors to London were spectators as well:<blockquote>Among the sightseers were several of the Indian visitors in gorgeous coloured coats, tight-fitting trousers, and turbans, as well as some of the Australian and New Zealand troops.<ref name=":2" /> (6, Col. 3a)</blockquote>In a section on what people — mostly women — wore, the reporter for the ''Daily News'' said,<blockquote>Suffice to say, the modistes had done their best, and that their achievements excited general admiration. Here and there, however, was an Eastern beauty whose golden lace drapery, loosely enveloping a figure that owed nothing to the corset, challenged comparison, we will not say with what success, with the European model. In the almost entire absence of uniforms or Court dress, the costumes of the East Indian notables lent colour to the assemblage, while their pearls and diamonds, the wealth of Ormuz and of Ind, were not allowed to pass unobserved.<ref name=":3" /> (5, Col. 6b)</blockquote> === People Invited === # Queen Victoria, with escort and attendants ## Captain's Escort of the 2nd Life Guards ## The Duchess of Buccleuch, Mistress of the Robes ## The Dowager Lady Churchill, Lady in Waiting ## The Hon. Harriet Phipps, Woman of the Bedchamber ## Maids of Honour in Waiting ### The Hon. Mary Hughes ### The Hon. Aline Majendie ## the Earl of Kintore, Lord in Waiting ## Captain Drummond, Groom in Waiting ## Equerries in Waiting ### Major-General Sir John M'Neill, V.C. ### Lieutenant Colonel Davidson, M.V O. [sic] #Grand Duke and Grand Duchess Serge of Russia #Princess Henry of Battenberg, with attendants ##Miss Minnie Cochrane ##Colonel John Clerk, C.S.I., C.V.O. #Her Imperial Majesty the Empress Frederic, attended by ##the Dowager Lady Ampthill ##Lord Harris ##Colonel S. Waller ##Princess Hatzfeldt Trachenberg ##Count Seckendorff ##Baron and Baroness Reischach #Their Royal Highnesses the Prince and Princess of Wales, with attendants ##Lady Suffield, Lady in Waiting ##Miss Knollys, Woman of the Bedchamber ##Lord Colville of Culross, K.T., G.C.V.O., Chamberlain to the Princess of Wales ##The Earl of Gosford, K.P., Lord in Waiting ##General Sir D. Probyn, G.C.V.O., K.C.B., K.C.S.I., V.C, Comptroller ##Sir Francis Knollys, K.C.M.G., C.B., Groom in Waiting ##Major-General Stanley Clarke, C.M.G., Equerry in Waiting #Princess Victoria of Wales #Their Royal Highnesses Prince and Princess Charles of Denmark #Their Royal Highnesses the Grand Duke and Grand Duchess of Mecklenburg-Strelitz, attended by ##Lady Caroline Cust ##Mr. Hugo Erskine Wemyss ##Count Reventlow Criminil ##Baron von der Wense #Their Royal Highnesses Prince and Princess Christian, attended by ##Baroness von und zu Egloffstein ##Colonel the Hon. Charles Eliot #Her Highness Princess Victoria #His Highness Prince Christian Victor #His Highness Prince Albert of Schleswig-Holstein #Her Royal Highness Princess Louise Marchioness of Lorne and the Marquis of Lorne, attended by ##Lady Sophia Macnamara ##[[Social Victorians/People/Arthur Collins|Colonel Arthur Collins]], M.V.O. #Their Royal Highnesses Prince and Princess Henry of Prussia, attended by ##Admiral of the Fleet Sir Edmund Commerell ##Baron and Baroness Seckendorff ##Count Hahn ##Captain Muller #Their Royal Highnesses the Duke and Duchess of Saxe-Coburg and Gotha, attended by ##The Hon. Mrs. Monson ##His Excellency Herr von Schön ##Captain the Hon. D. J. Mouson [sic, s/b Monson?], M.V.O. ##Mr. A. D. J. Monson ##Captain von Ruxleben #Princess Beatrice of Saxe-Coburg and Gotha #The Hereditary Prince of Saxe-Coburg and Gotha #Their Royal Highnesses the Duke and Duchess of Connaught and Strathearn, attended by ##Colonel and the Hon. Mrs. A. Egerton #Her Royal Highness the Duchess of Albany, attended by ##Sir Robert and Lady Collins ##Miss Potts #Her Royal Highness Princess Frederica of Hanover and Baron von Pawel Raminingen, attended by ##Mr. and Mrs. Charles Wood #His Royal Highness the Duke of Cambridge, attended by ##Colonel A. C. FitzGeorge, C.B. #Her Royal Highness the Duchess of Teck and his Highness the Duke of Teck, attended by ##Lady Katherine Coke ##The Hon. A. Nelson Hood #Her Royal Highness Princess Louise Duchess of Fife and the Duke of Fife #His Highness the Prince and her Royal Highness Princess Frederic Charles of Hesse, attended by ##The Hon. A. Hay ##Fraulein von Tasmund ##Baron von Kotwitz #Their Highnesses Prince and Princess Aribert of Anhalt, attended by ##Miss Deverell ##Major Evan Martin #Her Royal Highness the Hereditary Princess of Saxe-Meiningen and her Serene Highness Princess Feodore of Saxe-Meiningen, attended by ##The Hon. Aubrey FitzClarence ##Miss von Dreskan ##Baron von Roeder #His Serene Highness the Prince of Schaumburg-Lippe #Their Highnesses Prince and Princess Edward of Saxe-Weimar #Her Serene Highness Princess Victor of Hohenlohe #Countess Gleichen (x2) #Their Serene Highnesses Prince and Princess Adolphus of Teck #The Prince Francis and Prince Alexander of Teck #His Highness Prince Augustus Leopold of Saxe-Coburg #Their Serene Highnesses Prince and Princess Blucher von Wahlstatt #Their Serene Highnesses Prince and Princess Joachim Murat #Their Serene Highnesses [[Social Victorians/People/Pless|Prince and Princess Hans Henry Pless]] #Prince and Princess Loewenstein #Their Serene Highnesses the Duke and Duchess of Arenberg #Prince Victor Duleep Singh #Prince Frederick Duleep Singh #Princess Duleep Singh (x2) #ARGENTINE REPUBLIC — M. Florencio Dominguez and M. Carlos Dominguez #BADEN — Herr yon Brauer, Mr. Brook Taylor, and Baron Bohlen Halbach #BAVARIA — His Royal Highness the Prince Rupert, General Sir L. Gardiner, K.C.V.O., C.B., Major Fairholme, Lieutenant-Colonel Emile von le Bret Nucourt, and Captain Othon von Stettin #BELGIUM — His Serene Highness the Prince Charles de Ligne, Princess de Ligne, Madlle. de Ligne, Mr. C. lnnes Ker, Count de Jonghe d'Ardoye, and the Marquis d’Asshe #BOLIVIA — M. Caso, Mr. Conway Seymour, M. Pedro Suarez, Madame Suarez, and M. Adolfo Bolivian #BRAZIL — M. [[Social Victorians/People/Souza Correa|de Souza Correa]] [Corréa?] #BULGARIA — Their Royal Highnesses the Prince and Princess of Bulgaria, Colonel J. R. Slade, C.B., Madame Petrow Tchomakoff, Count Robert de Bourboulon, Lieutenant-Colonel Marcoff, Major Petrew, Captain Stoïanow, and Mr. Martin Furth #CENTRAL AMERICA (Greater Republic) — M. Medina and Miss Medina #CHILI — M. Ramon Subercasseaux and Mr. Raglan Somerset #CHINA — His Excellency Chang Yen Hoon, Colonel Mark Bell, V.C,. Mr. Liang, Mr. Jui, and Mr. Koo #COREA — His Excellency Min Young Hwan, Major A. Cavendish, Mr. Min Young Chan, Mr. Min Shangho, and Mr. von Rautenfeld #COSTA RICA — Senor Don Demetrio Iglesias, Mr. C. Alban Young, Dona Eudoxia Castro, Señorita Maria Iglesias, Don Ricardo Fernandez Guardia, and Dona Christina Castro Keith #DENMARK — His Royal Highness the Prince Waldemar, Major-General Arthur Ellis, C.S.I., M. Charles Rothe, and Captain Evers #EGYPT — Prince Mohammed Ali Pasha, Colonel Larking, Tigrane Pasha, Colonel Aziz Bey, Mr. George Smart, Said Zoulfikar Bey #ECUADOR — M. Navares, Colonel Concha #FRANCE — General Davoust, Duc d'Auerstadt, Duchesse d'Auerstadt, and Madlle. Davoust, Colonel Brabazon, Colonel Dawson, General Hagron, M. Crozier, Colonel Humbert, and Captain Riviers de Mauny #GERMANY — His Royal Highness the Prince Albert of Prussia, Prince Regent of Brunswick, Major-General Sir C. du Piat, K.C.B., Colonel Grierson, Lieutenant-General von Plessen, Colonel von Arnim, Captain Fischel, Count von der Schulenberg (Hofmarschall), Major Freiherr von Stein, Dr. Schreibe, Captain von Unzer #GREECE — M. Rangabi, Mr. R. D. Norton #GUATEMALA — Dr. Cruz, Madlles. Cruz (2), Señor Estrada #HAWAIIAN ISLANDS — Mr. S. M. Damon, Captain the Hon. H. Napier, Major Curtis P. Jaukea #HESSE — Their Royal Highnesses the Grand Duke and Grand Duchess of Hesse, Colonel the Hon. H. Byng, C.B., Baroness de Grancy, Baron Riedesel zu Eisenbach, Baron de Genadius Grancy #ITALY — Their Royal Highnesses the Crown Prince and Princess, the Earl of Clarendon, Colonel Needham, Countess Giulia Trigona, Lieutenant-General Terzaghi, Major Cavaliere Viganoni, Captain Cavaliere Merli Miglietti, Count Romnaldo Trigona, Cavaliere F. Comotto #JAPAN — His Imperial Highness the Prince Arisugawa, Mr. R. F. Synge, Captain Beaumont, R.N., Marquis Ito, Mr. S. Saito, Marquis Kido, Captain Funaki, Lieutenant-Colonel Murata, Lieutenant Kato, Mr. Nabeshima #LIBERIA — Mr. H. Hayman #LUXEMBURG — His Royal Highness the Hereditary Grand Duke of Luxemburg, Colonel H. D. Browne, Baron Ritter yon Grünstein #MECKLENBURG-SCHWERIN — His Excellency Herr D. yon Vietinghoff, Mr. Eyre A. Crowe #MEXICO — Don Antonio Mier y Celis, Mr. Arnold Royle, C.B., Don Francisco R. Gallardo, Don Eustagino dc Escaudon, and Captain Don Ponfirio Diaz #MONTENEGRO — His Highness the Prince Danilo, Major the Hon. C Harbord, Colonel Djurcovitch, and Captain Pejanovitch #NETHERLANDS — Count van Lynden, Countess van Lynden, Mr. Horace West, and Count W. de Bylandt #PARAGUAY — M. E. Machain and Madame Machain #PERSIA — His Imperial Highness the Prince Amir Khan, General Sir Thomas Gordon, K.C.I.E., C.B., C.S.I.[,] Mr. Harry Churchill, General Karim Khan, Mirza Ahmad Khan, Mirza Ohaness Khan, Mirza Mohamad Ali Khan #PERU — Senor Canevaro, Duchesse de Zoagli Canevaro, Dr. Don A. N. Puente, Don Alfredo Elster, and Don Carlos von der Heyde #PORTUGAL — His Royal Highness the Duke of Oporto, Major the Hon. H. C Legge, M.V.O., Colonel Duval Telles, Captain Moreira de Sà, Major d'Albuquerque, and Lieutenant Jose de Melie[?] #ROME — Right Rev. Monsignore Sambucetti, [[Social Victorians/People/Stonor|Hon. Harry Stonor]], Right Rev. Monsignore Belmont, the Right Rev. Monsignore de Vaz, Marchesi and Marchesa Muccioli, of the Noble Guard #ROUMANIA — General Pancovici, Colonel G. P. Georgescu #RUSSIA — Their Imperial Highnesses the Grand Duke Serge and Grand Duchess Feodrowna, the Grand Duke Cyril, Lord Churchill, Lieutenant-Colonel Waters, Countess Olsouffiew, Princess Youssoupoff, Princess Lobanoff de Rostow, General Stépanoff, Colonel Gadon, and Prince Youssoupoff, Colonel Clements, Mr. Alexander Gordon Ross, and Sub-Lieutenant N. Coubé (A.D.C. to Grand Duke Cyril) #SAXE-COBURG — His Royal Highness the Prince Philip of Saxe-Coburg, Captain Walter Campbell, and Herr von Schön #SAXE-WEIMAR — His Highness the Prince Hermann of Saxe-Weimar, Mr. Frederick Campbell, and Count Zeppelin #SAXONY — His Royal Highness the Prince Frederick Augustus, Duke of Saxony, Colonel Howard, Freiherr yon Reitzenstern, First Lieutenant von Metzsch, and Baron von Oppell #SERVIA — M. Mijatovich and Madame Mijatovich #SIAM — His Royal Highness the Crown Prince and the Prince Mahit of Siam, Colonel E. H. Sartorius, V.C., Lieutenant-Colonel Rajavallabha, Lieutenant-Colonel C. Vernon Hume, Colonel Indaraty, Surgeon-Major Yarr #SPAIN — Duke of Sotomayor, Captain the Hon. A. Greville, Señor José Caro, Señor Alfonso Merry del Val, and Señor Benitez al Villar #SWEDEN AND NORWAY — His Royal Highness the Prince Eugène of Sweden and Norway, Captain G. L. Holford, Count G. Gyldenstolpe, Captain Roeder, Captain Baron Cederstrom #TURKEY — Munir Pasha, Major Surtees, Brigadier-General Nassir Pasha, Captain Enver Bey, Colonel Gordon Ponsonby #UNITED STATES — His Excellency the Hon. Whitelaw Reid, Mrs. Whitelaw Reid, Colonel Hallam Parr, Major-General Nelson A. Miles, Mrs. Nelson Miles, Rear-Admiral Joseph N. Miller, Captain M. P. Maus, Mr. Ogden Mills, Mrs. Ogden Mills, Mr. G. Creighton Webb, Mr. Erskine Hewett, Commander W. H. Emory, Lieutenant Philip Andrews, Lieutenant T. S. Rogers #URUGUAY — Dr. Alberto Nin, Madlle. Nin, Don Alfonso Saenz de Zumaran, Don Luis Posadas, Colonel C. Robido #WURTEMBURG— His Royal Highness the Duke Albert of Wurtemburg, Colonel C. Swaine, Lieutenant-General von Bilfinger, First Lieutenant Count von Degenfeld- Schonburg; five officers of the Queen's German Regiment: Major C. R. Burn (in attendance), Lieutenant-Colonel von Falkenhayn, Major von Arnim, First Lieutenant Baron von Moeller-Lilienstern, First Lieutenant von Gerlach, Second Lieutenant von Studnitz #"Native Princes, and gentlemen and ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##His Highness the Raja of Kaparthala ##His Highness the Thakur Sahib of Morvi, K.C.I.E. ##His Highness the Thakur Sahib of Gondal, C.I., and her Highness the Maharani of Gondal, C.I. ##Colonel Maharaj Dhiraz ##Sir Pratab Singh, K.C.S.I. ##Thakur Hari Singh[,?] ##Kunwar Dhokal Singh ##Rajah Ajit Singh of Khetri, attended by ##Rajkumar Unmaid Singh of Shahpura, attended by ###Colonel Trevor (in attendance upon the Rajah Ajit Singh of Khetri and the Rajkumar Unmaid Singh of Shahpura) ##Bijey Singh ##Sir Jamaetjee Jejeebhoy, Bart., C.S.I., Miss Jejeebhoy, Mr. Jejeebhoy ##Mr. and Mrs. Powrala ##Major J. G. Turner and Mrs. Turner ##Mr. A. R. Wood and Mrs. Wood #The "officers of the Imperial Service Troops, with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Captain Mir Hashim Ali Khan Hyderabad-Resaldar ##Major Sunayat Singh, Kashmir ##Commandant Abdul Ganny, Gwalior ##Commandant Gooind, Rao Matkar, Indore ##Commandant Mirza Kurim Beg, Bhopal ##Rai Bahadur Dhunpat Rai, Jeypore ##Commandant Nand Singh, Patiala ##Commandant Rai Bahadur Thakur Dip Sing, Bikanir ##Commandant Chatru Singh, Bhartpur ##Resaldar Abdul Majid Khan, Babawalpur ##Commandant Daud Khan, Ulwar ##Commandant Nazir Khan, Rampur ##Risalda-Major Didar Singh, Sindi ##Risaldar-Major Kishan Singh, Nabha ##Risaldar Hara Singh, Karpurthala ##Risaldar Dhan Singhi, Bhavnagar ##Colonel H. Melliss, C.S.I., and Mrs. Melliss ##Major F. H. R. Drummond and Mrs. Drummond ##Captain F. Angelo ##Lieutenant H. Coape-Smith ##Captain G. F. Chenevix-Trench #The "officers of Native Cavalry Corps with British officers and ladies"<ref name=":1" /> (4, Col. 2b) ##Risaldar-Major Baha-ud-din-Khan ##Sardar Bahadur, A.D.C. to Viceroy ##Risaldar-Major Sayyid Abdul Aziz ##Risaldar-Major Khan Bahadur ##Risaldar-Major Izzat Khan ##Risaldar-Major Hukam Singh ##Risaldar-Major Sher Singh ##Risaldar-Major Husain Khan ##Risaldar-Major Mangal Singh ##Risaldar-Major Kesar Singh ##Risaldar- Major Faiz Khan ##Risaldar-Major Muhammad Umar Khan ##Risaldar-Major Ali Mahomed Khan ##Risaldar-Major Mihrab Ali Khan ##Risaldar Kaddam Khan ##Risaldar Jahanzir Khan ##Risaldar Nadir Khan ##Risaldar Mir Haidar Shah Khan ##Risaldar Makbul Khan ##Risaldar Net Ram ##Ressaidar Gurdatt Singh ##Subadar Muhammed Beg Junadar ##Abdul Karin Khan ##Lieutenant-Colonel J. C. H. Gordon and Mrs. Gordon ##Major A. Phayre and Mrs. Phayre ##Captain C. F. Campbell ##Captain P. Melville, in attendance on his Highness Thakur Sahib of Morvi ##Captain M'Cartney Filgate, in attendance on their Highnesses the Thakur Sahib and Maharani of Gondal ##Mr. Nowroz ##M. Parveez ##Sir M. Mansherjee Bhownaggree, M.P. ##Mr. Percy Armytage and Mrs. Armytage ##Mr. Frank Cook, C.I.E., and Mrs. Frank Cook #The "commanding officers of Colonial contingents, with the ladies accompanying them"<ref name=":1" /> (4, Col. 2b) ##Colonel the Hon. M. and Mrs. Aylmer, Canada ##Colonel and Mrs. Lassetter, New South Wales ##Major Reay, Victoria ##Colonel Pitt, New Zealand ##Major and Miss King, Queensland ##Lieutenant and Mrs. Phillips, Cape of Good Hope ##Lieutenant-Colonel Rowell, South Australia ##Major Strickland, Western Australia ##Captain Shepstone, Natal ##Major and Miss Reeves, Ceylon ##Mr. Badeley, Hong Kong ##Colonel Walker, C.M.G., and Mrs. Walker, Straits Settlements ##Captain Lucie Smith, Jamaica ##Lieutenant-Colonel E. B. M'lnnis, C.M.G., and Mrs. M'lnnis, British Guiana ##Major Rooks, Trinidad ##Captain Bernard, Malta ##Captain Kershaw, Cyprus ##Captain and Mrs. Middlemist, Gold Coast ##Inspector Hook, Lagos ##Captain Blakeney, Sierra Leone ##Lieutenant Festing, Royal Niger Company ##Captain Flint, British North Borneo Company ##The Hon. M. Gifford, Rhodesian Horse ##The following British officers attached: Lieutenant-Colonel Boulton, Lieutenant-Colonel Prior, Lieutenant-Colonel Tucker, Lieutenant-Colonel Domville, Lieutenant-Colonel Gibson, and Lieutenant-Colonel Tyrwhitt #The "gentlemen representing the various races in the Island of Ceylon"<ref name=":1" /> (4, Col. 2c) ##Maha Mudaliyar don Solomon Dias Bandaranaihe ##The Hon. Alexander Dealius Sonewiratne ##M. E. Rowland Goonoratne ##M. Charles de Soysa Dessanayaka ##Panabokko Jikiri Banda ##Nugawela Kuia Banda ##Kobbokeduwe Loku Banda ##M. E. S. W. Senathi rajah [sic] and Mrs. Senathi ##M. J. H. de Saram and Miss de Saram ##M. P. Ramanathan ##M. Saunders and Miss Saunders #The "members of the Corps Diplomatique and other foreigners of distinction"<ref name=":1" /> (4, Col. 2c) ##The Russian Ambassador, Madame de Staal, Madlle. de Staal, Madame de Stoeckl, Princess de San Donato, Madame Yermoloff, Madlle. Yermoloff, the Councillor, three Secretaries, and four Attachés of Embassy ##The German Ambassador, Countess Paul Hatzfeldt-Wildenburg, her Serene Highness Princess Hans Hohenlohe-Oehringen, Baroness yon Eckardtstein, the Councillor, two Secretaries, three Attachés of Embassy, and the Director of the Chancery ##The Austro-Hungarian Ambassador, Countess Deym, Countess Isabella Deym, Countess Clary Aldringen, Baroness Ferstel, the Councillor, two Secretaries, and four Attachés of Embassy ##The French Ambassador, Baroness de Courcel[,] Madlle. de Courcel, Madame Geoffray, the Minister Plenipotentiary, five Secretaries, and three Attachés of Embassy ##The Italian Ambassador, Princess Ruspoli, three Secretaries, and three Attachés of Embassy ##The Spanish Ambassador, Countess de Casa Valencia; Mesdlles. de Alcala Galiano (2), Marquise de Guiria, Donna de Zea Bermudez, Countess de Morella, Donna de Ia Camara y Livermore, three Secretaries, and four Attachés of Embassy ##The Turkish Ambassador, Madame Antbopoulos, the Councillor, and two Secretaries of Embassy ##The United States Ambassador, Mrs. Hay, Miss Hay, Mrs. Henry White, Mrs. Carter, Mrs. Colwell, two Secretaries, one Attaché of Embassy, and the Private Secretary to the Ambassador ##The Argentine Minister, Madame Dominguez, Mesdlles. Dominguez (3), and the Secretary of Legation ##The Persian Minister, and one Secretary of Legation ##The Danish Minister, Madame de Bille, Madame Gosch, and the Secretary of Legation ##The Siamese Minister, Mrs. Verney, Miss Verney, Mrs. Loftus, the Councillor, the Secretary, the Attaché, and the Interpreter to the Legation ##The Liberian Minister ##The Roumanian Minister and the Councillor of the Legation ##The Netherlands Minister, Baroness de Goltstein d'Oldenaller, Baroness Schimmelpenninck van der Oye, and the Councillor of Legation ##The Belgian Minister, the Councillor, and two Secretaries of Legation ##The Mexican Minister, Madame Yturbe, Madame Romero, Madame Farias, Madame Garcia, two Secretaries and three Attachés of Legation ##The Japanese Minister, Madame Kato, two Secretaries, and three Atachés [sic] of Legation ##The Minister for Sweden and Norway, Countess Lewenhaupt, and the Attaché of Legation ##The Chinese Minister, Lady Macartney, the English Secretary, three Secretaries, and four Attachés of Legation ##The Portuguese Minister, Madlle. de Quilinan, three Secretaries, and one Attaché of Legation ##The Swiss Minister, Madame Bourcart, Madame de Salis, the Secretary, and the Attaché of Legation ##The Haytian Chargé d’Affaires ##The Chargé d’Affaires of Greece, Madame Metaxas, and the Attaché ##The Chargé d’Affaires of Chile and Madame Bascunan ##Two Secretaries and one Attaché of the Brazilian Legation ##Count E. van Rosen ##Mr. Hippolyte de Aranjo ##Vice-Admiral Montt ##Mr. Pinto, Mrs. Pinto ##Mr. and Mrs. Scaramanga ##Vicomte de Galard ##Dr. Arnold, and Madlle. von Rappoport ##Mrs. John Meiggs, Miss Meiggs ##Miss Margaret Butler ##Mrs. Henry Morgan ##Hon. Chauncey Depew ##Mr. and Mrs. James Taylor ##Mr. and Mrs. Charles Marshall ##Mr. and Mrs. Edmund Bayliss ##Mrs. Colgate ##Miss Furniss ##Miss Wells ##Miss Harris ##Hon. Levi P. Morton, Mrs. Morton, and the Misses Morton ##The Bishop of Illinois and Mrs. Leonard, Miss Leonard ##The Bishop of Albany and Mrs. Doane ##The Bishop of New York and Mrs. Potter ##the Bishop of Minnesota and Mrs. Whipple ##Mr. and Mrs. Walter Burns ##Mrs. Douglas Grant ##Miss Scott ##Mrs. Grace, Miss Margarita Grace ##Mrs. Wentworth ##Miss van Wart ##M. Valentin de Courcel ##Madame la Marquise de Talleyrand Perigord ##Comte Boson de Perigord ##Vicomte d'Espenilles ##Madame and Madlle. Thierry Delanoue ##Madlle. de la Cherè ##M. Cellerier ##M. and Madame Delawarre ##Madame Evelina Fenzi ##Count A. Zannini ##M. and Madame Jules Cottran ##Chevalier E. Mazzuechi ##Signor A. Tedeschi ##Signor A. Mariotti ##Captain Lucian von Ziegler ##Chevalier Lieutenant von Barry ##Baron Georg Rothschild ##Privy Councillor Count Berchtold ##Baron G. E. Levi, Baroness Levi ##Commander E. Philipson, Mrs. E. Philipson ##The Duke and Duchess of San Germano Calabritto ##The Marquis of San Vito ##Donna Lidia Serramezzana ##Donna Margherita Chigi ##Marchioness Vitelleschi ##Chevalier Elia ##Count de Franqueville ##Count Urbain Chevrau ##M. Marcel Fonquier ##M. Baudon de Mony, Madame Baudon de Mony ##Duchess de Rohan ##Marquis de Lastorgrie, Marchioness de Lastorgrie ##Count de Boisgelin, Countess L. de Boisgelin ##M. Stern, Madame Stern, Madlle. Stern ##Count Charles du Luart ##General de Saucy ##M. E. Seydoux ##Count Jean de Madre ##M. de Monbrison ##Baron de la Chevrelière ##Count de la Villestreux, Countess de la Villestreux ##Count Urbain de Maille, Countess Urbain de Maille ##General Faveret de Kerbrich ##Monsieur de la Haye Jousselin ##Baronne Faveret de Kerbrich ##Colonel Matton ##M. Ferinier Didet ##Madame Ferinier Didet ##Donna Isabella Colonna, Donna Victoria Colonna ##Pom-k-Soh ##Madame Reyntiens ##Marquis de Fuente Hermosa ##Herr Rudolf Swobody ##M. Lauritz Tuxen ##Duchesse de Baiten ##M. de Marcoarti ##Comte de Heeren, Madlle. de Heeren ##Monsieur M. de Mauny Talvande ##Senor Don Nicolas Campero ##Lieutenant Charny ##Lieutenant Sanders ##Madame and Madlle. de Mouni ##Comtesse de Montsoulmin #"Foreign Admirals and Commanding Officers and Staffs"<ref name=":1" /> (4, Col. 3a / Col. 3b) ##Austrian Admiral Baron von Spaun, Commander von Ziegler, Lieutenant Retter yon Barry, Lieutenant Mitchell, R.N. (attached) ##Danish Admiral H. H. Koch, Captain Waudel, Lieutenant Middelboc, Lieutenant Majendie, R.N. (attached) ##French Admiral C. F. E. De Courthille, Captain Germinet, Commander Poidlone, Lieutenant Perdriel, Sub-Lieutenant de Caqueray, Lieutenant Phillimore, R.N. (attached) ##Italian Admiral C. E. Morin, Commander Count Prasca, Lieutenant Lunghetti, Lieutenant Count Morano, Lieutenant Henderson. R.N. (attached) ##German Admiral his Royal Highness Prince Henry of Prussia, Captain Muller, Lieutenant von Spee, Sub-Lieutenant Wittman, Lieutenant Garforth, R.N. (attached) ##Japanese Admiral H.I.H. Prince Arizugawa, Captain Miura, Commander Tsuda, Lieutenant Stewart, R.N. (attached) ##Netherlands Admiral F. K. Englebrecht, Captain de Groot, Lieutenant Baron von Hardenbrock, Lieutenant Woolcombe, R.N. (attached) ##Norwegian Rear-Admiral von Krogh, Captain Muller, Lieutenant Petersen, Lieutenant Kerr Pearse, R.N. (attached) ##Portuguese Captain Barreto de Vascomellos, Captain de Cartillo, Lieutenant Trye, R.N. (attached) ##Russian Admiral Nicholas Skrydloff, Captain Domojiroff, Lieutenant Stetsenkoff, Lieutenant Twisleton Wykeham Fiennes, R.N. (attached) ##Spanish Admiral Don Segismundo Bermijo y Merelo, Captain Don Antonio Eulate y Fery, Lieutenant Don Juan Romero, Lieutenant Don Antonio Romero, Lieutenant Fair, R.N. (attached) ##Swedish Admiral A. F. H. Klintberg, Captain Ingelman, Commander Flack, Lieutenant Alton, R.N. (attached) ##United States Admiral J. N. Miller, Lieutenaut Richmond (attached) ##Captain de Mar E. Guerra ##Captain R. S. D. Cumins #The Lord Lieutenant of Ireland and Countess Cadogan #The Right Hon. the Speaker and Mrs. Gully, Miss Gully, and Miss Shelly Gully #Cardinal Vaughan #Right Hon. the Lord Mayor and Lady Mayoress, and Misses Faudel Phillips (2) #The Gold Stick in Waiting, Silver Stick in Waiting, Silver Stick Adjutant in Waiting #Officer Commanding 1st Life Guards and five officers #Officer Commanding 2nd Life Guards and four officers #Officer Commanding Royal Horse Guards and four officers #Officer Commanding 2nd Dragoons and three officers #Field Officer in Brigade Waiting, Adjutant in Brigade Waiting #Commanding Officer Grenadier Guards #Commanding Officer Coldstream Guards #Commanding Officer Scots Guards, a Regimental Adjutant #Commanding Officer 1st, 2nd, and 3rd Battalions Grenadier Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions Coldstream Guards and three officers of each Battalion #Commanding Officer 1st and 2nd Battalions of Scots Guards and three officers of each Battalion #Commanding Officer Woolwich District and six officers #Commanding Officer R.H.A. Home District and two officers #Commanding Officer R.E. and four officers #Commanding Officer 2nd Battalion Lincolnshire Regiment and three officers #Commanding Officer Royal Marines (Chatham) and four officers #Commanding Officer Royal Marines (Portsmouth) and two officers #Four officers of the Honourable Corps of the Gentlemen at Arms #Archbishops — Canterbury, York, Armagh, Ontario, Rupertsland #Dukes and Duchesses ##The Duke and Duchess of [[Social Victorians/People/Argyll|Argyll]] ##The Duke and Duchess of [[Social Victorians/People/Abercorn|Abercorn]] ##The Duchess of De Baileu ##The Duke and Duchess of [[Social Victorians/People/Buccleuch|Buccleuch]] ##The Duchess of [[Social Victorians/People/Cleveland|Cleveland]] ##The Duke and Duchess of [[Social Victorians/People/Devonshire|Devonshire]] ##The Duchess of [[Social Victorians/People/Douglas-Hamilton Duke of Hamilton|Hamilton]] ##The Duke and Duchess of [[Social Victorians/People/Leeds|Leeds]] ##The Duke and Duchess of [[Social Victorians/People/Marlborough|Marlborough]] ##The Duke and Duchess of [[Social Victorians/People/Manchester|Manchester]] ##The Duke and Duchess of [[Social Victorians/People/Montrose|Montrose]] ##The Duke and Duchess of [[Social Victorians/People/Newcastle|Newcastle]] ##The Duke of [[Social Victorians/People/Norfolk|Norfolk]] ##The Duke of [[Social Victorians/People/Northumberland|Northumberland]] ##The Duke and Duchess of [[Social Victorians/People/Portland|Portland]] ##The Duke of [[Social Victorians/People/Richmond and Gordon|Richmond and Gordon]] ##The Duke and Duchess of [[Social Victorians/People/Roxburghe|Roxburghe]] ##The Duke and Duchess of [[Social Victorians/People/Somerset|Somerset]] ##The Duke and Duchess of [[Social Victorians/People/Sutherland|Sutherland]] ##The Duke and Duchess of St. Albans ##The Duke and Duchess of Wellington ##The Duchess of [[Social Victorians/People/Westminster|Westminster]] #Marquises and Marchionesses ##The Marquis of Abergavenny ##The Marchioness of Ailesbury ##The Marquis and Marchioness of Ailsa ##The Marquis of Anglesey ##The Marquis and Marchioness of [[Social Victorians/People/Breadalbane|Breadalbane]] ##The Marchioness of [[Social Victorians/People/Marlborough#Marchioness of Blandford|Blandford]] ##The Marquis and Marchioness of Bristol ##The Marquis of [[Social Victorians/People/Camden|Camden]] ##The Marquis and Marchioness of Conyngham ##Dowager [Marchioness of] Conyngham ##The Marchioness of Cassar de Sai[n] ##The Marquis and Marchioness of Cholmondeley ##The Marquis of D'Auerstadt ##The Marquis and Marchioness [[Social Victorians/People/Stonor|D'Hautpoul]] ##The Marquis and Marchioness of Downshire ##Dowager [Marchioness of] Downshire ##The Marquis and Marchioness of [[Social Victorians/People/Hamilton Temple Blackwood|Dufferin and Ava]] ##The Marquis and Marchioness of [[Social Victorians/People/Exeter|Exeter]] ##The Marquis and Marchioness of Granby ##The Marchioness of [[Social Victorians/People/Florence Rawdon-Hastings Chetwynd|Hastings]] ##The Marquis and Marchioness of [[Social Victorians/People/Bective|Headfort]] ##The Marquis and Marchioness of Hertford ##The Marquis and Marchioness of Huntly ##The Marquis and Marchioness of [[Social Victorians/People/Abercorn#James Hamilton, Marquess of Hamilton|Hamilton]] ##The Marquis and Marchioness of [[Social Victorians/People/Lansdowne|Lansdowne]] ##The Marquis and Marchioness of Lothian ##Dowager (Marchioness of) [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Londonderry|Londonderry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ormonde|Ormonde]] ##The Marchioness of [[Social Victorians/People/Queensberry|Queensberry]] ##The Marquis and Marchioness of [[Social Victorians/People/Ripon|Ripon]] ##The Marquis and Marchioness of [[Social Victorians/People/Salisbury|Salisbury]] ##The Marquis and Marchioness of [[Social Victorians/People/Tweeddale|Tweeddale]] ##Dowager (Marchioness of) [[Social Victorians/People/Tweeddale|Tweeddale]] ##John Stewart-Murray, [[Social Victorians/People/Atholl|Marquess of Tullibardine]] ##Lawrence, [[Social Victorians/People/Zetland|Marquess of Zetland]] and Lilian, [[Social Victorians/People/Zetland|Marchioness of Zetland]] #Earls and Countesses ##Countess of Aberdeen and Dowager Countess of Aberdeen ##Earl and Countess of Albemarle and Dowager Countess of Albemarle ##Earl and Countess of Ancaster ##Earl and Countess of Amherst ##Earl of Ava ##Earl and Countess of Antrim ##Earl and Countess of Aylesford ##Earl and Countess of Annesley ##Earl and Countess of Airlie ##Earl and Countess of Arran ##Earl of Aberdeen ##Earl and Countess of Bandon ##Countess of Bantry ##Earl and Countess of Beauchamp ##Earl and Countess of Bathurst and Dowager Countess of Bathurst ##Countess of Bective ##Earl and Countess of Belmore ##Earl of Bradford ##Countess of Bremer ##Earl and Countess of Brownlow ##Earl and Countess of Buckinghamshire ##Earl of Burford ##Earl and Countess of Cairns ##Earl and Countess of Caledon ##Earl of Camperdown ##Earl of Cardigan ##Earl and Countess of Carnarvon and Dowager Countess of Carnarvon ##Earl of Carnwath ##Earl and Countess of Carrington ##Earl and Countess of Carysfort ##Earl and Countess of Castlestuart ##Earl and Countess of Cathcart ##Earl and Countess of Cavan ##Earl and Countess of Chesterfield ##Earl and Countess of Chichester ##Dowager Countess of Clancarty ##Countess of Clanwilliam ##Earl and Countess of Compton ##Countess of Cottenham ##Earl of Courtown ##Earl and Countess of Cowper ##Earl and Countess of Cranbrook ##Earl and Countess of Craven and Dowager Countess of Craven ##Earl and Countess of Crawford ##Earl of Crewe ##Earl and Countess of Cork and Orrery ##Earl and Countess of Coventry ##Countess of Cromartie and Dowager Countess of Cromartie ##Earl and Countess of Dalkeith ##Earl and Countess of Dartmouth ##Earl and Countess of De Grey ##Dowager Countess of De La Warr ##Earl and Countess of Denbigh ##Earl and Countess of Derby ##Earl and Countess of Donoughmore ##Earl and Countess of Drogheda ##Earl of Ducie ##Earl and Countess of Dudley and Dowager Countess of Dudley ##Earl and Countess of Dundonald ##Earl and Countess of Dunmore ##Earl and Countess of Dunraven ##Earl of Durham ##Earl and Countess of Eglinton and Winton ##Earl of Eldon ##Earl and Countess of Ellesinere ##Earl and Countess of Enniskillen ##Earl and Countess of Erne ##Earl and Countess of Errol ##Earl and Countess of Essex and Dowager Countess of Erroll ##Earl of Euston ##Earl and Countess of Feversham ##Earl and Countess of Fingall ##Earl of Fortescue ##Earl and Countess of Gainsborough ##Earl and Countess of Galloway ##Earl and Countess of Glasgow ##Countess of Gosford ##Earl and Countess of Granard ##Countess of Granville ##Earl and Countess of Grey ##Countess of Grosvenor ##Countess of Guilford ##Earl and Countess of Harewood and Dowager Countess of Harewood ##Earl and Countess of Harrington ##Earl and Countess of Hopetoun ##Earl and Countess of Huntingdon ##Earl and Countess of Harrowby ##Countess of Hohenau ##Countess of Howe ##Earl and Countess of Iddesleigh ##Earl and Countess of Jersey ##Earl and Countess of Kenmare ##Earl of Kerry ##Earl and Countess of Kilmorey ##Earl of Kimberley ##Earl and Countess of Kingston ##Earl of Kinnoull ##Josephine, Countess Kinsky ##Earl and Countess of Kintore ##Countess of Leitrim ##Earl and Countess of Lanesborough ##Countess of Lathom ##Earl and Countess of Lauderdale ##Countess of Leicester ##Earl and Countess of Leven and Melville ##Earl and Countess of Lichfield ##Earl and Countess of Limerick ##Earl and Countess of Lindsay ##Earl and Countess of Lisburne ##Earl and Countess of Listowel ##Earl and Countess of Londesborough ##Earl and Countess of Longford ##Earl and Countess of Lonsdale and Dowager Countess of Lonsdale ##Earl and Countess of Loudoun ##Earl and Countess of Lovelace ##Earl and Countess of Lucan ##Countess of Lytton ##Countess of Macclesfield ##Earl and Countess of Malmesbury and Dowager Countess of Malmesbury ##Earl and Countess of Mar ##Earl and Countess of Mar and Kellie and Dowager Countess of Mar and Kellie ##Earl and Countess of Mayo and Dowager Countess of Mayo ##Countess of Meath ##Countess of Metaxas ##Earl and Countess of Mexborough ##Earl and Countess of Minto ##Earl of De Montalt ##Earl and Countess of Morley ##Earl and Countess of Morton and Dowager Countess of Morton ##Earl of Nelson ##Earl and Countess of Norbury ##Earl of Northbrook ##Earl and Countess of Northesk and Dowager Countess of Northesk ##Earl and Countess of Onslow ##Earl of Orford ##Countess of Oxford ##Earl and Countess of Pembroke ##Countess of Percy ##Earl and Countess of Portarlington ##Earl and Countess of Portsmouth ##Earl and Countess of Powis ##Earl and Countess of Radnor ##Earl and Countess of Ravensworth ##Earl and Countess of Roden ##Earl and Countess of Romney ##Lawrence, [[Social Victorians/People/Zetland|Earl of Ronaldshay]] ##Earl of Rosebery ##Earl and Countess of Rosse ##Earl and Countess of Rosslyn and Dowager Countess of Rosslyn ##Earl of Sandwich ##Earl of Scarbrough ##Earl and Countess of Selborne ##Countess of Selkirk ##Countess of Shaftesbury ##Dowager Countess of Shrewsbury and Talbot ##Earl and Countess of Spencer ##Earl and Countess of Stamford ##Earl and Countess of Stanhope ##Earl and Countess of St. Germans ##Earl of Stradbroke ##Earl of Strafford ##Earl and Countess of Suffolk and Berkshire ##Earl and Countess of Temple (of Stowe) ##Earl and Countess of Verulam ##Earl and Countess of Waldegrave ##Earl and Countess of Warwick ##Earl and Countess of Westmeath ##Earl and Countess of Wharncliffe ##Elizabeth, Dowager Countess of Wilton and Isabella, Dowager Countess of Wilton ##Earl and Countess of Winchilsea and Nottingham ##Earl and Countess of Winterton ##Earl and Countess of Yarborough and Dowager Countess of Yarborough #Viscounts<ref name=":1" /> (4, Col. 3c / Col. 4a) and Viscountesses ##Viscount and Viscountess of Boyne ##Viscountess of Cantelupe ##Viscount and Viscountess of Castlerosse ##Viscount and Viscountess of Chelsea ##Viscount and Viscountess of Chetwynd ##Viscountess of Chewton ##Viscount and Viscountess of Clifden ##Viscount and Viscountess of Cobham ##Viscount and Viscountess of Coke ##Viscount of Corry ##Viscount and Viscountess of Cranborne ##Viscount of Crichton ##Viscount and Viscountess of Cross ##Viscount of Curzon ##Viscount and Viscountess of Dalrymple ##Viscount and Viscountess of Deerhurst ##Viscount and Viscountess of De Vesci ##Viscount and Viscountess of Dillon ##Viscount of Doneraile ##Viscount and Viscountess of Duncannon ##Viscount of Dungarvan ##Viscount and Viscountess of Ebrington ##Viscount and Viscountess of Emlyn ##Viscount of Encombe ##Viscount and Viscountess of Exmouth ##Viscount and Viscountess of Falkland ##Viscount and Viscountess of Falmouth ##Viscount of Fitz Harris ##Viscount and Viscountess of Folkestone ##Viscount and Viscountess of Frankfort de Montmorency ##Viscount and Viscountess of Gage ##Viscount and Viscountess of Galway ##Viscount and Viscountess of Garnock ##Viscount and Viscountess of Gough ##Viscount of Gort ##Viscount and Viscountess of Halifax ##Viscount and Viscountess of Hardinge ##Viscount of Harrington ##Viscount and Viscountess of Hood ##Viscount and Viscountess of Kilcoursie ##Viscount and Viscountess of Knutsford ##Viscount and Viscountess of Lifford ##Viscount of Llandaff ##Viscount and Viscountess of Maitland ##Viscount and Viscountess of Marsham ##Viscount and Viscountess of Massereene and Ferrard ##Viscount and Viscountess of Melville ##Viscount and Viscountess of Midleton ##Viscount and Viscountess of Milton ##Viscount and Viscountess of Monck ##Viscount and Viscountess of Morpeth ##Dowager Viscountess of Mountmorres ##Viscount and Viscountess of Newark ##Viscount and Viscountess of Newport ##Viscount and Viscountess of Oxenbridge ##Viscount of Parker ##Viscount of Peel ##Viscount and Viscountess of Portman ##Viscount and Viscountess of Powerscourt ##Viscount and Viscountess of Raincliffe ##Viscountess of Sherbrooke ##Viscount of Sidmouth ##Viscount of St. Cyres ##Viscount of Southwell ##Viscount of Suirdale ##Viscount and Viscountess of Templetown ##Viscountess of Torrington ##Viscount and Viscountess of Trafalgar ##Viscount and Viscountess of Valentia ##Viscount of Valletort ##Viscount of Villiers ##Viscountess of Wolseley # #Bishops — Auckland, Barry, Bath and Wells, British Colombia, Chichester, Durham, Ely, Exeter, Gloucester and Bristol, Gibraltar, Hereford, London, Lichfield, Lincoln, Manchester, Newcastle, Norwich, Oxford, Peterborough, Rochester, Ripon, Stepney, Southwark, St. Albans, Salisbury, Sodor and Man, Southwell, Sydney, Sierra Leone, Worcester, Winchester, Wellington #Baronesses — Burdett-Coutts, Macdonald #Lords and Ladies<ref name=":1" /> (4, Col. 4b / Col. 5a) — ##Lord and Lady Abercromby ##Lord and Lady Aberdare ##Lord Aberdour ##Lady Abinger ##Lady Alexandra Acheson ##Lady Adam ##Lady Adderley ##Lord and Lady Addington ##Lady Adye ##Lady Agnew ##Lady Alderson ##Lord and Lady Alington ##Lady Alison ##Lady Mildred Allsopp ##Lord and Lady Amherst of Hackney ##Lady Heathcoat Amory ##Lord and Lady Ampthill ##Lady Agnes Anderson ##Lady Bertha Anson ##Lady Arbuthnot ##Lady Alice Archer Houblon ##Lord Ardee ##Lord and Lady Ardilaun ##Lady Armstrong ##Lady Arnold ##Lady Arnott ##Lord and Lady Ashbourne ##Lord and Lady Ashburton and Dowager Ashburton ##Lord and Lady Ashcombe ##Lady Alice Ashley ##Lady Edith Ashley ##Lady Ashmead-Bartlett ##Lord and Lady Ashton ##Lord and Lady Ashtown ##Lady Florence Astley ##Lady Gertrude Astley-Corbett ##Lady Austin ##Lord Bagot ##Lady Bailey ##Lady Blanche Baillie ##Lady Baird ##Lady Baker ##Lord Balcarres ##Lord and Lady Balfour of Burleigh, Lady Nina Balfour and Lady Betty Balfour ##Lord Balvaird ##Lord Bangor ##Dowager Lady Barclay ##Lord and Lady Barnard ##Lady Florence Barnardiston ##Lady Constance Barne ##Lady Barran ##Lady Barrington ##Lord and Lady Basing ##Lord and Lady Bateman ##Lady Evelyn Bathurst ##Lord and Lady Battersea ##Lady Steuart Bayley ##Lady Violet Beauchamp ##Lord Osborne Beauclerk and Lady Beauclerk (2) ##Lady A. Beaumont ##Lady Bedford ##Lord and Lady Belhaven and Stenton and Dowager Belhaven and Stenton ##Lord and Lady Bellew and Dowager Bellew ##Lord and Lady Belper ##Lady Charles Beresford ##Lady William Beresford (Lilian Duchess of Marlborough) ##Lady Bergne ##Lord and Lady Bertie and Lady Elizabeth Bertie ##Lady Biddulph, Lady Elizabeth Biddulph and Lady Wilfreda Biddulph ##Lady Bigge ##Lord and Lady Bingham ##Lord and Lady Binning ##Lord Blackwood, Lord Basil Blackwood. Lady Hermione Blackwood and Lord Terence Blackwood ##Lady Bloomfield ##Lady Blythswood ##Lord and Lady Bolton ##Lady Maud Bootle-Wilbraham, Lady Bertha Bootle-Wilbraham and Lady Edith Bootle-Wilbraham ##Lord Borthwick ##Lady Margaret Boscawen ##Lord and Lady Boston ##Lady Boughey ##Lady Albreda Bourke and Lady Florence Bourke ##Lady Bowen ##Lady Bower ##Lady Muriel Boyle and Lady Boyle (2) ##Lady Mary Brabazon ##Lady Brackenbury ##Lady Braddon ##Lady Bramwell ##Lady Bramston ##Lord Brassey, Lady Idina Brassey and Lady Violet Brassey ##Lord and Lady Braye ##Lady Mary Bridgeman ##Lady Eleanor Brodie ##Lady Hilda Brodrick ##Lady De Capel Brooke and Dowager Brooke ##Lady Cunliffe Brooks ##Lord and Lady Brougham and Vaux ##Lord and Lady Ulick Browne, Lady Browne and Lady Crichton Browne ##Lady Brownlow ##Lord and Lady F. Brudenell-Bruce ##Lady Brunner ##Dowager Buchanan-Riddeil ##Lady Audrey Buller ##Lady Burdett ##Lord and Lady Burghclere ##Lord Burghley ##Lady Agnes Burne ##Lady Burrell ##Lord and Lady Burton ##Lady Butler and Lady Butler (2) ##Lord and Lady Arthur Butter ##Lady Buxton and Lady Victoria Buxton ##Lady Susan Byng ##Charles Cavendish-Bentinck, Henry Cavendish-Bentinck, William Cavendish-Bentinck, Calthorpe, Archibald Campbell, George Campbell, Camoys, Carbery, Carew. Courtenay, Coleridge, Connemara, Castletown, Carnegie, Castlemaine, Eustace Cecil, Hugh Cecil, John Cecil, Edward Cecil, Churston, Edward Spencer-Churchill, Chesham, Cheylesmore, Clonbrock, Alwyne Compton, Cottesloe, Crawshaw, Cloncurry, Clifford of Chudleigh, Colchester, Clinton, Colville of Culross, Cardross, Fitzwarine Chichester, Robert Cecil, W. Cecil, Crofton, De Manley, Davey, De Freyne, Dunleath, Dunglass, De Saumarez, De Ramsey, Digby, Dynevor, Dunsandle and Clanconal, De L’Isle and Dudley, Deramore, Dunally, Elphinstone, Egerton of Tatton, Elcho, Esher, Elibank, Ebury, Erskine, Farrer, Henry Fitz-Gerald, F. FitzRoy, Foley, Forester, Glenesk, R. S. Gower, Glamis, Greenock, Arthur Grosvenor, Gerard, Walter Gordon-Lennox, Algernon Gordon-Lennox, Garioch, Halsbury, Hatherton, Hawkesbury, E. Hamilton, F. Hamilton, Harlech, Hastings, Heneage, Henley, Henniker, Herschell, Herries, Hillingdon, Hindlip, Hotham, Hothfield, Hobhouse, Arthur Hill, Howard of Glossop, Hyde, Francis Hervey, Inverurie, Iveagh, Inchiquin, James of Hereford, Kelvin, Kenyon, Kilmarnock, Kinnaird, Kensington, Lurgan, Lawrence, Lovat, Llangattock, Loch, Leigh, Leconfield, Lingen, Lister, Montagu of Beaulieu, Charles Montagu, Cecil Manners, Edward Manners, Morris, Macnaghten, Muncaster, Mowbray and Stourton, Mostyn, Moreton, Monkswell, Moncreiff, Macdonald, Monteagle, Manners, Medway, Middleton, Napier of Magdala, Henry Nevill, Newton, Newtown-Butler, Norreys, North, Norton, Napier and Ettrick, O'Neill, Penrhyn, Playfair, George Pratt, Poltimore, Berkeley Paget, Pirbright, Pearson, Rathdonnell, Rendel, Rendlesham, Ribblesdale, Revelstoke, Rossmore, Russell of Killowen, Rothschild, Raglan, Ruthven, Rodney, Rayleigh, Reay, Rowton, Robartes, Romilly, Rookwood, George Scott, Henry Scott, Herbert Scott, Seaton, Saltoun, Southampton, Sherborne, Sinclair, Stalbridge, Skelmersdale, St. Levan, Shand, Stanmore, Stavordale, Savile, Stanley, St. Oswald, Swansea, Stratheden and Campbell, Settrington, Suffield, Tollemache, Templemore, Tweedmouth, Trevor, Tredegar, Thring, Tewkesbury, Tennyson, Teynham, E. Talbot, Herbert Vane-Tempest, Henry Vane-Tempest, Ventry, Watson, Willoughby de Broke, Wrottesley, Windsor, Welby, Wimborne, Wolverton, Westbury, Wenlock, Wandsworth, Warksworth, Willoughby de Eresby, and Zouche #Ladies — Clements (2), Mabel Coke, Ottoline Cavendish-Bentinck, Culme-Seymour, Gwendolen Cecil, Robert Cecil, Cromer, Cunliffe, Churchill, Isabel Clayton, Chetwode, Helen Craven, Cooper, Cowell, Cardon, Chelmsford, Dowager Carbery, Fitzwarine Chichester, Colomb, Henry Cholmondeley, Cardross, Coddington, Alfred Spencer-Churchill, Castletown, Carnegie, Frederick Cavendish, Castlemaine, Florence Cecil, Eustace Cecil, Edward Cecil, John Cecil, Randolph Churchill, Cholmeley. Chesham, Clinton, Clonbrock, Alwyne Compton, Conyers, Crawshaw, Cochrane, Colchester, Churston, Cottesloe, E. Clarke, Clifford of Chudleigh, Gertrude Cochrane, William Cecil, Commerell, Collins, Myra Cavendish. C. Cameron, Colvile, Carew, Carbutt, Carmichael, Jane Seymour Combe, Mary Crosse, Evelyn Cotterell[,] Adela Cochrane, Margaret Cameron, Calthorpe, A. Campbell, Eva Cathcart, R. Cathcart, Evelyn Cavendish, Harriet Cavendish, Courtenay, Colebrooke, Coleridge, Blanche Conyngham, Louisa Cecil, Alwyne Compton, Cole (2), Evelyn Crichton, Mary Cuffe, Crossley, Connemara, Dowager Congleton, Emma Crichton, Elizabeth Cust, Dowager Churchill, Couch, Chitty, Coventry (2), Georgiana Curzon, Chamberlain, Marshal Clarke, Campbell-Bannerman, Henry Cavendish-Bentinck, Spencer Churchill (2), Carbery, Colville, George Campbell, Camoys, Archibald Campbell, Constance Combe, Muriel Close, Evelyn Cobbold, Colville of Culross, Francis Cecil-Dallas, Mildred Denison, Alice Dundas, De Winton, Margaret Douglas, Dorchester, Dunally, De Trafford, Florence Duncombe, De Ross, De Ramsey, De L’Isle and Dudley, Elinor Denison, Mary Dashwood, Victoria Dawnay, Evelyn Dawnay, Adelaide Dawnay, H. Douglas-Hamilton, Ulrica Duncombe, Eva Dugdale, Digby, De Saumarez, Davey, Dowell, Edith Drummond, Dorington, Dunn, Dunleath, Decies, De Freyne, Duckworth, Du Cane, Des Voeux, Durand, Ida Dalzell, Dering, Drummond, Agnes De Trafford, Caroline Duncombe, Edith Douglas, Erskine (2), Grey-Egerton, Ernestine Edgcumbe, Egerton (2), Engleheart, Elcho, Ellenborough, Esher, Edwards, J. B. Edwards, Evans, Horatia Erskine, Evelyn Ewart, Elphinstone, Ellis, Ebury, Elibank, Erskine, Evelyn Eyre, Edmonstone, Blanche Edwards, Egerton of Tatton, Mary Ewart, Winifred Cary-Elwes, Beatrix Fitzmaurice, Ffolkes, Forester, Forwood, Mary Foley, Fowler, Finlay, Dorothea Fitz-Clarence, Louisa Feilding, B. Fitz Gerald, Fremantle, FitzWygram, Foster, Helen Munro Ferguson, Angela Forbes, Mary Fitzwilliam, M. FitzGerald, Fulton, Flower, Anne Fane, Fairbairn, Gertrude Foljambe, Edith Franklin, Forbes (2), Susan Fortescue, Fisher, Farrer, Fayrer, Farquhar, Augusta Fane, Fairfax, Maria Fitz-Clarence, H. Fitz-Gerald, F. Fitz-Roy, C. Fitz-Roy, Fergusson, Fletcher, Flower, Forrest, Freemantle, Dowager Helen Forbes, Frere, Dorothy Fitzclarence, Gardiner, Katharine Gathorne-Hardy, Gore Langton (2), Helen Grimston, Mary Carr Glyn, Jane Grey-Trefusis, D'Arcy Godolphin-Osborne, Frances Gresley, Charlotte Graham-Toler, Grant-Duff, Seymour Fitz-Gerald, Victoria Grey, Griffin, Graham, Gillford, Green, Susan Gilmour, Galton, Garvagh, Glamis, Glenesk, Glyn, Evelyn Goschen, Margaret Graham, Lynedoch Gardiner, Grosvenor (2), Arthur Grosvenor, Grenfell, Grant, Gipps, Grey, Gull, Gilbey, Gerard, Margaret Ormsby Gore, Constance Gore, Helen Graham, Florence Grant, Gordon, Halsbury, Beatrice Hare, Eleanor Howard, Agnes Howard, Alice Havelock-Allan, Beatrix Herbert, Alexandra Hamilton, Howard (2), Maria Hood, Mary Hope, Hely-Hutchinson (2), Seager Hunt, Howard of Glossop, Clement Hill, Hart, Augustus Hervey, Basil Hall, Fermor Hesketh, Hooker, Blanche Haygarth, Hunter, Hartopp, Baillie Hamilton (2), C. Hamilton, Beatrix Douglas Home, Constance Harris, Mabel Howard, Hayter, Florentia Hughes, Halle, E. Hamilton, Haldon, F. Douglas Hamilton, Victoria Hamilton, Cicely Hardy, Hatherton, Hawke, Hawkesbury, Heneage, Henley, Herschell, Herries, Hillingdon, Norah Hodgson, Hibbert, Mary Holland, Harcourt, Hothfield, Mary Hozier, Hylton, George Hamilton, Haliburton, Rachel Howard, Hobhouse, Arthur Hill, Harris, John Hay, Hotham, Hoskins, Hood of Avalon, Harrison, Hay, Holdich, Dixon-Hartland, Hanson, Harriet Harrison, Stock Hill, Hindlip, Houldsworth, Howarth, Emily Hart-Dyke, Hervey-Bathurst, Hastings, Lucy Hicks-Beach, Hardy, Herbert (2), Hemming, Iveagh, Inchiquin, Margaret Jenkins, Alice Jolliffe, Jeune, Jenner, Jenkins, Joicey, Dowager Jessel, Jephson, Hill Johnes, Jackson, Burn Jones, Jessell, Caroline Lister Kaye, Kemball, Beatrice Kemp, Kennaway, King, Kitson, Lister Kaye, Edith King-Tenison, Florence King King, Kennard, Kerr (2), Innes-Ker (2), Mabel Kenyon-Slaney, Aline Kennedy, Beatrice Lister Kaye, Kelvin, Kinnaird, Keith-Falconer (2), Emily Kingscote, Kennett-Barrington, Mary Stuart Keppel, Isabella Keane, Leconfield, Constance Leslie, Isabel Larnach, Leigh, Henry Gordon-Lennox, Walter Gordon-Lennox, Algernon Gordon-Lennox, Lister, Margaret Littleton, Llangattock, Loch, Lockwood, Louise Loder, Lovat, Mary Loyd, Lubbock, Lawrence, Dowager Lurgan, Doreen Long, Lyttelton, Lyall, Emily Lytton, Loraine, Lyons, Drury Lowe, Lysons, Lawson, Lindley, Elliott Lees, Adela Larking, Albertha Lopes, Lyell, Harriet Lindsay, Laking, Frances Lambart, Victoria Lambton, Gwendolen Little, Lurgan, Llewelyn, Catherine Loftus, Jane Lindsay, Lewis, Lucy Drury Lowe, Longley, Jane Lindsay, Caroline Gordon-Lennox, Mary Lygon, Lilian Liddell, Leese, Susan Leslie-Melville, Katharine Le Poer Trench, Mary Lascelles, Ellen Lambart, Lowry-Corry (2), Lees, Legard, Lingen, Edith Montgomerie, Blundell Maple, H. Maxwell, Georgiana Mure, Macgregor, Martin, Victoria Manners, Hilda M'Neile, Maxwell, Miller, Middleton, Monckton, Charlotte Montgomery, Maclean, Medway, Magheramorne, Mappin, Milner, Cecil Scott Montagu, S. Montagu, Nora Maitland, Mary Milbanke, Meysey-Thompson, Monkswell, Evelyn Mason, Maude (2), Monson, Mackenzie, Markham, Louisa Magenis, Macpherson-Grant, MacCormac, MacDonald, Mackenzie, Margaret Crichton-Maitland, Manners, M'lver, Middleton, Dowager Magheramorne, Margaret Majendie, Maxwell, Monteagle, Moncreiffe, Moreton, Morgan, Blanche Morris, Mary Morrison, Mostyn, Mowbray and Stourton, Dowager Mowbray and Stourton, Mowbray, Muncaster, Anne Murray, Scott Moncrieff, MacGregor, Macnaghten, Morris, M'Clintock, Mackworth, Evelyn M'Donnell, Sophia Montgomerie, More-Molyneux, Meade (2), Murray (2), Heron-Maxwell, Georgiana Mure, Martin, Marriott, Maxwell, Caroline Madden, Helen MacGregor, Clementina Mitford, Agneta Montagu, Methuen, Madden, Moseley, Marjoribanks, Augusta Noel, Naylor-Leyland, Elizabeth Nugent, Napier and Ettrick, Napier of Magdala, Henry Nevill, Dowager Napier of Magdala, Newton, Newtown-Butler, Norreys, North, Northcote, Norman, Northcote (2), Nelson, Agnes Noel, Muriel North, Nicolson, O'Brien, Olpherts, O'Hagan, Gwendoline O'Shee. O'Neil, O'Brien, Katherine Pakenham, Evelyn Parker, Percy (2), Pontifex, Pearson, Playfair, Poltimore, Dickson-Poynder, Dowager Lady Peyton, Princep [sic] Alice Packe, Berkeley Paget, Paget of Cranmore, Palmer, Peel, Georgiana Peel, Palgrave, Powell, Priestley, Poynter, Pearson, Constance Childe-Pemberton, Sophia Palmer, Chichele Plowden, William Phipps, Penhryn, Pirbright, Baden-Powell, Perceval, George Pratt, Probyn, Phillimore, Muriel Parsons, Pollock, Anna Chandos-Pole, Parratt, Alice Portal, Petre, Powell, Alfred Paget, Maude Parry, Mary Pepys, Eva Wyndham-Quin, Wyndham-Quin (2), Reid, Dowager Rayleigh, Reay, Rayleigh, Rathmore, Dowager Raglan, Rodney, Robartes, Victoria Russell, Arthur Russell, Robinson, Ribblesdale, Roberts of Kandahar, Jane Repton, Rookwood, Rossmore, Rothschild, Russell of Killowen, G. Russell, Raglan, Jane Ryan, Alexander Russell, W. H. Russell, Ramsay, Ruthven, O. Roberts, Rathdonnell, Rendel, Laura Ridding, Roxburgh, Stafford, Swinnerton Dyer, Catherine Somerset, Geraldine Somerset, Stevenson, Helen Stewart, Constance Shaw-Lefevre, Sophie Scott, D. Smith, Stratheden and Campbell, Swansea, Mary Stewart, Henry Somerset, Savory, Shute, Smyth, William Seymour, Mark Stewart, Samuelson, Alice Stanley, Stansfield, Stephenson, Stewart, Stone, Sutherland, St. Oswald, Evelyn Sutton, Settrington, Savile, Albert Seymour, Simeon, Charles Scott, Saltoun, Seaton, Seymour, Southampton, Shaw, Kay-Shuttleworth, Sherborne, Octavia Shaw-Stewart, Alice Shaw-Stewart, Esther Smith, Barbara Smith, Sinclair, Skelmersdale, Edith St. Aubyn, St. Levan, Houston Stewart, Shand, Smith, Simmons, Stewart, S. Samuel, Dowager Southampton, Salmon, Shippard, Simpson of Windsor, Margaret Spicer, Sprigg, Mary Shelley, Stewart of Grantully, Marie Savile, Mary Sackville, Mary Stuart-Richardson, Edward Spencer-Churchill, Charlotte Stopford, Seymour (2), Blanche Smith, Isabel Stewart, Isobel Stanley, Louisa Scott, Susan Sutton, Stanhope (2), Sybil Smith, Euan Smith, Scott (2), Kathleen Swinnerton-Pilkington, St. Leonards, Mary Saurin, Tatton Sykes, Tyler, Thursby, E. Talbot, Emma Talbot, Tennyson, E. Thornton, Thring, Ulrica Thynne, Mary Trefusis, Trevelyan, Tuson, Henrietta Turnor, Tennant, Jane Taylor, Tweedmouth, Templemore, Tenterden, Trevelyan, Turner, Teynham, Trevor, Agnes Townshend, Tollemache, Troubridge, Taylour (2), Vivian, Ventry, Jane Van Koughnet, Howard Vincent, Helen Vincent, Vincent, Jane Vivian, Emily Van De Weyer, Villiers (2), Edith Villiers, Wilson, Willshire, Wood, Hugh Wyndham, Leucha Warner, Woods, Warrender, Wantage, Clementine Walsh, Dowager Westbury, Sarah Gordon Wilson, F. F. Walker, Rose Weigall, Elizabeth Williamson, Arthur Wellesley, Willes, Willis, White, Westbury, Whitehead, Winnington, Isabella Whitbread, Julia Wombwell, Wenlock, Cecilia Webb, Williams-Wynn, Walrond, Watson, Mary Waldegrave, Wimborne, Windsor, Wolverton, Mary Wood, James Walker, Whiteway, Windeyer, Willoughby (2), Constance Wodehouse, Barbara Yeatman, Lilian Yorke #Right Honourables — H. H. Asquith, E. Ashley, A. H. Dyke Acland, J. Atkinson, J. B. Balfour, Sir G. Bowen, G. W. Balfour, Sir Hicks-Beach, A. J. Balfour, James Bryce, Sir H. Campbell-Bannerman. A. H. Smith-Barry, E. Carson, H. Chaplin, Sir J. Chitty, Jesse Collings, Sir R. Couch, G. N. Curzon, J. Chamberlain, L. Courtney, Sir M. Grant-Duff, A. Akers-Douglas, Sir W. Hart Dyke, Sir H. Elliot, F. Foljambe, Sir H. Fowler, Sir A. B. Forwood, Sir J. Fergusson, Herbert Gladstone, Sir J. Gorst, G. J. Goschen, W. E. Gladstone, Sir G. Grey, C. H. Hemphill, Charles Seale-Hayne, R. W. Hanbury, Lord George Hamilton, Staveley Hill, Sir J. T. Hibbert, Sir W. Harcourt, lon Hamilton, Sir Arthur Hayter, Sir F. Jeune, W. L. Jackson, Sir John Kennaway, G. Shaw-Lefevre, W. Lidderdale, Sir Massey Lopes, James Lowther, Sir J. Lubbock, Sir H. Lopes, Walter Long, Sir N. Lindley, J. W. Mellor, Sir G. O. Morgan, John Morley, Arnold Morley, Sir J. Mowbray, A. J. Mundella, J. H. Macdonald, F. Max Müller, Sir W. Marriott, Graham Murray (the Lord Advocate), Sir E. Monson, Sir P. O'Brien, Sir A. Otway, Sir F. Peel, Sir R. Paget of Cranmore, W. J. Pirrie, J. P. Robertson, Sir. J. Rigby, C. T. Ritchie, Sir S. H. Strong, Sir B. Saunderson, Sir J. Stansfeld, Sir A. Smith, C. R. Spencer, Sir C. Kay-Shuttleworth, Sir R. Temple, Sir R. Thompson, Sir E. Thornton, Lord Henry Thynne, Sir G. O. Trevelyan, C. P. Villiers, Sir Algernon West, Sir C. L. Wyke, C. B. Stuart-Wortley, S. J. Way #Honourables<ref name=":1" /> (4, Col. 5a / Col. 5b) — H. Allsopp, George Allsopp, O. Borthwick, T. J. Byrnes, Sir E. C. Braddon, T. Brassey, Henry Bourke, Charles Bourke, J. Boscawen, C. E. Bingham, Charles Brand, Terence Bourke, Ivo Bligh, Reginald Brett, W. St. John Brodrick, Algernon Bourke, Arthur Brand, Albert Bingham, Allen B. Bathurst, John Baring, Eric Barrington, Coplestone Bampfylde, G. H. Campbell, K. Campbell, T. H. Cochrane, George Colville, R. Chetwynd, Arthur Chichester, Hamilton Cuffe, Henry Coventry, Henry Cubitt, Hugh Campbell, Osbert Craven, Arthur Cadogan, Montagu Curzon, W. Cavendish, John Dawnay, Conrad Dillon, Hubert V. Duncombe, R. C. Devereux. Hew Dalrymple, Eustace Dawnay, W. Dawnay, A. Hay Drummond, C. T. Dundas, Cecil Duncombe, W. Dundas, H. Escombe, F. Egerton, Tatton Egerton, Herbert Eaton, Arthur Elliot, R. Fitzwilliam, Everard Fielding, Sir John Forrest, W. H. Fitzwilliam, Sir C. Fremantle, Ailwyn Fellowes, Sir Malcolm Fraser, Sir S. Ponsonby Fane, N. Fitzgerald, George Ormsby Gore, Robert Grosvenor, Algernon Grosvenor, Ronald Greville, Louis Greville, Sidney Greville, F. Leveson-Gower, Geoffrey Browne Guthrie, A. E. Gathorne-Hardy, C. Hardinge, A. Hardinge, C. G. Hay, Evelyn Hubbard, Lionel Holland, Grosvenor Hood, A. Holland Hibbert, Sydney Holland, Robert Herbert, Sir Robert Herbert, G. Jolliffe, Sydney H. Jolliffe, G. Keppel, Derek Keppel, C. C. Kingston, Reginald Lister, F. W. Lambton, Atholl Liddell, Henry Littleton, Wilfrid Laurier, R. l’Estrange, Charles Laurence, Herbert Laurence, F. D. Leigh, E. Chandos Leigh, G. W. Leslie, William Lowther, L. Lowther, T. W. Legh, Alfred Lyttelton, C. Hanbury Lennox, Schomberg M'Donnell, Archibald Marjoribanks, R. Moreton, Charles Mills, W. Massey-Mainwaring, John Scott Montagu, Sir H. S. Northcote, Sir Hugh Nelson, R. Nevill, R. Terence O'Neill, C. B. Parsons, Cecil Parker, Horace C. Plunkett, E. W. B. Portman, Albert Petre, R. Parker, E. S. Douglas-Pennant, F. Parker, Sydney Peel, H. Orde Powlett, Thomas Playford, Ashley Ponsonby, F. Roberts, J. M. Rolls, the Master of Ruthven, Gustavus Hamilton-Russell, C. Ramsay, G. H. Reid, W. Rowley, A. Russell, W. Rothschild, Sir J. Gordon Sprigg, Lyulph Stanley, Sir Donald Smith, Randolph Stewart, R. J. Seddon, J. Maxwell Scott, FitzRoy Stewart, Sir Saul Samuel, Granville Somerset, Arthur Somerset. W. F. D. Smith, A. Saumarez, F. C. Stanley, George Stanley, R. Somerset, Edward Thesiger, George Hill-Trevor, Sir D. Tennant, R. Marsham-Townshend, Charles Trevor, Marcus Hill-Trevor, Charles Grey Trefusis, Rev. L. Tyrwhitt, Alfred Talbot, Frederick Thesiger, Sir G. Turner, S. R. Thayer, F. Villiers, R. Greville-Verney, F. Bootle-Wilbraham, Robert Ward, Armine Wodehouse, Arthur Walsh, F. Wood, Percy Wyndham, Sir W. Whiteway, Tatton Willoughby, Alex. G. Yorke #Honourable Ladies<ref name=":1" /> (4, Col. 5b / Col. 5c) — Mrs. Allsopp, Mrs. Alexander, Mrs. Anstruther, Mrs. Armytage, Mrs. Acland, Vere Annesley, Susan Baring, Lady Birkbeck, Mrs. Baillie of Dochfour, Mrs. Balfour, Mrs. Bampfylde, Mrs. Hamar Bass, Mrs. Bagot, Mrs. Barrington, Misses Bateman-Hanbury (2), Mrs. Bingham, Mary Byng, Mrs. A. Brassey, Mrs. A. Bourke, Mrs. E. R. Bourke, Mrs. T. C. Bruce, Mrs. Stapleton Bretherton, Mrs. Benyon, Diana Sclater-Booth, Mrs. F. Bridgeman, Mrs. Britten, Misses Bruce (2), Mrs. Barlow, Mrs. Brett, Mrs. Bligh, Misses M'Clintock Bunbury (2), Mrs. T. Bourke, Mrs. Brand, Mrs. T. Brand, Emmeline Brownlow, Lady Biddulph, Mrs. Bingham, Mrs. H. Bourke, Mrs. Bagot, Mrs. Barker, Misses Bridgeman (2), Lilian Baring, Albinia Brodrick, Beresford, Mrs. A. Cadogan, Mrs. H. Corry, Caroline Courtenay, Lady Cunningham, Mrs. Candy, Mrs. W. Cavendish, Mrs. C. Cadogan. Ethel Cadogan, Audrey Coleridge, Mrs. H. Campbell, Darea Curzon, Mrs. Ronald Campbell, Misses Campbell (2), Mrs. Gough-Calthorpe, Rachel (Gough) Calthorpe, Misses Gough Calthorpe (2), Mrs. Otway Cuffe, Mrs. Carpenter, Mrs. Curzon, Emily Cathcart, Misses Cross, Mrs. P. Crutchley, Mrs. Carington, Mrs. Cavendish, Mrs. J. B. Campbell, Mrs. Corbett, Mrs. A. Chichester, Eleonora Chetwynd, Mrs. R. Chetwynd, Mrs. Clowes, Mrs. Cubitt, Mildred Campbell, Hilda Chichester, Mrs. C. Duncombe, Mrs. C. T. Dundas, Mrs. W. Dundas, Mrs. Hay Drummond, Mrs. Dawnay (2), Mrs. C. Dillon, Mrs. Digby, Mrs. John Dundas, Frances Drummond, Mrs. R. C. Devereux, Mrs. M. Drummond, Misses de Montmorency (2), Edith Dillon, Lady Du Cane, Misses Douglas-Pennant (2), Mrs. H. Dennison, Lady Grey Egerton, Mrs. T. Egerton, Mrs. Arthur Elliot, Mrs. Evans, Mrs. H. Eaton, Lady Elliot, Mrs. A. F. Egerton, Lilian Elphinstone, Mrs. Ellis. Mrs. Escombe, Mrs. Eliot, Muriel Erskine, Mrs. Lionel Fortescue, Mary Fremantle, Mary Forester, Mrs. Charles Keith-Fraser, Mrs. C. Keith-Falconer, Mrs. A. Fellowes, Mrs. W. H. Forster, Mrs. W. Farquhar, Mrs. Fitzgerald, Mrs. Ferguson of Pitfour, Mrs. F. G. FitzGerald, Lady FitzGerald, Misses Fraser (2), Mrs. N. Fitzgerald, Mrs. A. Greville, Mrs. Alaric Grant, Mrs. Gye, Maud Grosvenor, Evelyn Giffard, Violet Gibson, Mrs. L. Greville, Mrs. R. Greville, Lady Godley, Mrs. A. Grosvenor, Mrs. A. H. F. Greville, Elizabeth Grosvenor, Mrs. Henry Gladstone, Lady Hamilton Gordon, Nevil Gordon, Misses Guest (2), Mrs. Gough, Mrs. North Dalrymple-Hamilton, Mrs. Halford, Mrs. Assheton Harbord, Misses Hawke (2), Misses Heneage (2), Alice Hubbard, Mrs. Herbert, Helen Henniker, Mrs. R. Herbert, Misses Hamilton (2), Mrs. A. Holland Hibbert, Dorothy Hood, Lady Acland-Hood, Mrs. Henniker, Mrs. Curzon Howe, Mrs. C. Harbord, Mrs. C. Hardinge, Fanny Hood of Avalon, Lady Higginson, Mrs. E. Hubbard, Mary Hughes, Judith Harbord, Mrs. A. Haig, Mrs. Hill, Mrs. Hobart Hampden, Bridget Harbord, Nina Gathorne-Hardy, Mrs. Harbord, Mrs. Meynell Ingram, Lady Johnston, Mrs. Jolliffe, Mrs. Keppel, Mrs. William Keppel, Lady Knollys, Mrs. Alfred Ker, Constance Kerr, Mrs. Kingscote, Mrs. A. Lyttelton, Misses Lyttelton (2), Mrs. Legge, Mrs. Lumley, Mrs. Lambton, Mrs. Lyttelton, Mrs. E. H. Loyd, Mrs. Hanbury Lennox, Mrs. Legh, Mrs. A. Liddell, Mrs. L. Lowther, Mrs. Lawley, Mrs. H. Gore-Lindsay, Misses Loch (2), Mrs. E. C. Leigh, Misses Littleton (2), Sybil Legh, Bertha Lambart, Mrs. F. D. Leigh, Cordelia Leigh, Mrs. C. Lawrence, Mary Lascelles, Misses Lawrence (2), Mrs. W. Lowther, Mrs. H. Lawrence, .Mrs. Mostyn, Alice Murray, Annette Monck, Mrs. C. Molyneux, Mrs. R. Moreton, Misses Henniker Major (2), Misses Constable Maxwell (2), Mrs. Maclagan, Mrs. Magniac, Aline Majendie, Mrs. Fuller-Maitland, Violet Monckton, Mrs. Percy Mitford, Flora Macdonald, Mrs. Mallet, Evelyn Moore, Violet Mills, Mrs. Mills, Mrs. Maguire, Mrs. Mackinnon, Maud de Moleyns, Mrs. Monck, Mrs. Massey-Mainwaring, Mrs. M'Calmont, Lady Macdonald, Mrs. Monson, Misses Mostyn (2), Lady Musgrave, Mrs. G. H. Murray, Napier, Mrs. Neeld, Emilia Napier, Mrs. Newdigate, Mrs. Scott Napier, Misses O'Brien (2), Mrs. Okeover, Myra Orde-Powlett, Mrs. Oliphant, Henrietta O'Neill, Mary O'Hagan, Mrs. Parsons, Misses Peel (2), Mrs. Heber Percy, Mrs. Parker, Mrs. E. S. Douglas-Pennant, Mrs. Pretyman, Misses Ponsonby (2), Mabel Parnell, Mrs. Ponsonby, Misses Palk (2), Mrs. Pirie, Mrs. Orde-Powlett, Mrs. Anderson Pelham, Mary Portman, Mrs. F. Parker, Mrs. W. Paton, Harriet Phipps, Mrs. A. Petre, Mrs. Portman, Mrs. Ritchie, Misses Rice (2), Misses Rendel (2), Evelina Rothschild, Lady White Ridley, Misses Hamilton Russell (2), Misses Russell (2), Mrs. Phillips Roberts, Mrs. C. Ramsay, Misses Roberts (of Kandahar) (2), Mrs W. Rowley, Eleanor Rolls, Mrs. J. D. Ryder, Lady Thelluson Rowley, Mrs. Ruthven, Misses Strutt (2), Lady Cowell-Stepney, Mrs. Maxwell Scott, Mrs. E. J. Stanley, Mrs. C. R. Spencer, Mrs. A. Somerset, Misses St. Clair (2), Mabel St. Aubyn, Mrs. Stirling, Mary Sidney, Alison Stourton, Misses Skeffington (2), Mrs. A. Saumarez, Mrs. G. Somerset, Mrs. Stanley, Mrs. V. A. Stanley, Lady Simeon, .Mrs. A. H. Smith, Mrs. E. J. Saunderson, Mrs. Strutt, Mrs. Stewart, Violet Somerset, Maude Stanley, Mrs. R. Stewart, Hilda Sugden, Horatia Stopford, Mrs. Hill-Trevor, Misses Hill-Trevor (2), Lady Thorold, Mary Thesiger, Mrs Tremayne, Mrs. Talbot, Mrs.F. Thesiger, Mrs. Marsham-Townshend, Misses Tollemache (2), Mrs. C. W. Trotter, Mrs. R. A. J. Talbot, Lady Tryon, Misses Trefusis (2), Mrs. W. le Poer Trench, Mrs. Trelawny, Katharine Thring, Mrs. E. Thesiger, Rosamond Tufton, Alice Hanbury-Tracy, Misses Thellusson (2), Misses Tyssen Amherst (2), Misses Vivian (2), Misses Verney (2), Misses Vereker (2), Mrs. R. G. Verney, Mrs. F. Villiers, Mrs. Whateley, Frances Wolseley, Misses Wyndham (2), Mrs. P. E. Warburton, Evelyn Wrottesley, Mrs. P. Wyndham, Lady Wilson, Mrs. West, Mrs. G. Wrottesley, Mrs. Dudley-Ward, Mrs. Wodehouse, Ella Williamson, Maud Wynn, Misses Wood (2), Lois Yarde-Buller, Mrs. J. Yorke, Mrs. E. C. Yorke #Sirs<ref name=":1" /> (4, Col. 5c–6a) — Augustus Adderley, Edwin Arnold, John Austin, George Arthur, John Heathcoat-Amory, A. Armstrong, Andrew Agnew, Frederick Abel, Henry Acland, A. Arnold, Alexander Arbuthnot, John Barran, G. Bower, J. W. Bonser, J. Crichton-Browne, Joseph Bailey, E. Ashmead-Bartlett, Henry Barkly, R. Beauchamp, Raymond Burrell, Charles Barrington, David Baird, Arthur Birch, Edward Birkbeck, W. Cunliffe Brooks, A. de Capel Brooke, Courtenay Boyle, F. Burton, F. Buxton, Steuart Bayley, John Bramston, John Baker, H. Bullard, J. T. Brunner, H. Bellingham, Henry Bergne, Thomas Boughey, F. J. Bramwell, E. Burne-Jones, James Blyth, Seymour Blane, Henry Chamberlain, Roderick Cameron, Hugh Cholmeley, John Conroy, Edward Clarke, C. Cameron, E. Carbutt, W. Coddington, Marshal Clarke, Reginald Cathcart, Savile Crossley, Edward Colebrooke, Reginald Cust, Charles Crosthwaite, John Colomb, Daniel Cooper, F. Astley-Corbett, Donald Currie, Henry Cunningham, Robert Cunliffe, Henry Cotterell, T. D. Gibson Carmichael, F. Curden, George Dallas, James Drummond, Mortimer Durand, G. Des Vieux, Henry Dering, J. N. Dick, Dyce Duckworth, T. Swinnerton Dyer, E. Hastings Doyle, John Dorington, William Dunn, Humphrey de Trafford, Charles Dalrymple, G. Dashwood, Gardner, Engleheart, Francis Evans, A. Edmonstone, Whittaker Ellis, W. H. Flower, Horace Farquhar, Joseph Fayrer, H. Fletcher, William Ffolkes, William Fraser, Bartle Frere, Gerald Seymour Fitz-Gerald, Robert Finlay, B. Walter Foster, Gerald FitzGerald, R. FitzGerald, Maurice FitzGerald, Forrest Fulton, William Flower, Andrew Fairbairn, John Gilbert, E. T. Gourley, Edward Grey, W. Gull, Walter Gilbey, Lepel Griffin, G. Macpherson-Grant, Reginald Graham, Philip Grey Egerton, Douglas Galton, R. Glyn, Arthur Godley, Charles Grant, R. Gresley, Alexander Acland-Hood, T. G. Fermor Hesketh, Arthur Haliburton, Brydges Henniker, F. Dixon-Hartland, R. Hanson, Alfred Hickman, W. Houldsworth, Henry Howorth, F. Seager Hunt, Charles Hall, E. W. Hamilton, Reginald Hardy, Clement Hill, Basil Hall, Joseph Hooker, Charles Hunter, Charles Hartopp, Victor Houlton, Augustus Hemming, Henry Irving, Frederic Johnstone, W. Jenner, J. Jenkins, James Joicey, Charles Jessell, Harry Johnston, Edward Jenkinson, James Hill Johnes, John Jackson, H. Seymour King, James Kitson, J. Lister-Kaye, V. Kennett-Barrington, George Kekewich, John Leslie, Thomas Dick Lander, T. Villiers Lister, James Linton, Charles Lees, Charles Legard, Thomas Lea, Wilfrid Lawson, Elliott Lees, A. C. Lyall, J. T. D. Llewelyn, Joseph Leese, Leonard Lyell, F. Laking, Godfrey Lushington, F. Lockwood, Henry Longley, George Lewis, F. Milner, Herbert Maxwell, Francis Montefiore, Graham Montgomery, Robert Moncreiffe, Musgrave, Colin Scott Moncrieff, Francis Mowatt, Evan MacGregor. J. G. Miller, F. D. Maclean, J. Blundell Maple, Allan Mackenzie, Lewis M'lver, F. Mappin, Theodore Martin, Samuel Montagu, William MacCormac, Hubert Miller, Lewis Morris, Clements Markham, A. C. Mackenzie, John Monckton, J. Stirling-Maxwell, J. Heron Maxwell, Kenneth Matheson, J. S. Montefiore, Acquin Martin, W. Maxwell, Oswald Moseley, Arthur Nicolson, Terence O'Brien, Reginald Ogilvy, Herbert Oakeley, Hush Owen, G. G. Petre, Walter Parratt, Frederick Pollock, Herbert Perrott, Douglas Powell, Weetman Pearson, Joseph Pease, Francis S. Powell, Reginald Palgrave, W. Priestley, E. G. Poynter, G. S. Baden-Powell, Charles Pontifex, J. Dickson-Poynder, James Paget, C. M. Palmer, C. Lennox Peel, James B. Peile, Westby Perceval, Charles Pigott, John Puleston, W. Plowden, Richard Quain, George Russell, C. Lister Ryan, W. H. Russell, J. Ramsay, Owen Roberts, R. T. Reid, Charles Robinson, J. Thellusson Rowley, James Reid, C. Euan-Smith, J. Barrington Simeon. J. B. Stone, M. Shaw-Stewart, Edward Sieveking, T. H. Sanderson, Augustus K. Stephenson, Thomas Sutherland, Mark Stewart, Andrew Scoble, Joseph Savory, Douglas Straight, Charles Shelley, S. Shippard, E. Sassoon, A. Condie Stephen, E. Sullivan, Arthur Sullivan, S. Scott, H. Simpson, E. Stafford, Ernest Satow, Tatton Sykes, John Tyler, Charles Tennant, John Tenniel, J. Thorold, John Thursby, Thomas Troubridge, Charles Turner, H. Meysey-Thompson, W. Vincent, Edgar Vincent, Arthur Vicars, W. Williams-Wynn, James Walker, R. Webster, George Wombwell, C. Rivers Wilson, W. H. Wills, Donald Mackenzie Wallace, George Warrender, F. Winnington, James Whitehead, Arthur Willshire, Henry Wood, Hugh Wyndham, W. White, Sidney Waterlow, Hedworth Williamson, Jacob Wilson, W. Windeyer, Albert Woods (Garter), Allen Young #Chairman of County Council (Dr. Collins) #Counts — Cassini, De Ganay, Gurowski, Hohenau, Theodor Bolesta Koziebrodski, Leon Mniszeek, Potocki, Raben #Countesses — De Ganay, Potocki, Raben #Barons — <sub> </sub>De Onethau, Alphonse de Rothschild, Ferdinand Rothschild, Schröder, von Deichmann, yon Heeckeren van Wassenaer, Campbell von Laurentz #Baronesses — De Brienen, D’Onethan, Alphonse de Rothschild, Schroder, von Deichmann, Emile Beaumont d'Erlanger, von Hügel, Gertrud von Hügel, Campbell von Laureutz, Wilhelm von Rothschild #Rev. the Moderator of the General Assembly of the Church of Scotland #Deans — Christ Church, St. Paul's, Westminster, Windsor #The Provost of Eton #Master of Trinity (Mr. Butler) #The Sub-Dean of the Chapels Royal #Canons — Blundell, Dalton, Duckworth, Fleming, Hervey, Teignmouth Shore, Wilberforce #Dr. Adler (Chief Rabbi) #Dr. M'Cormick #Chaplain of the Fleet #Chaplain General #Reverend Doctors — Edmund Warre, C. J. Welldon #Reverends — Prebendary Hawkshaw, Albert Baillie, W. H. Bliss, M. Ebrington Bisset, Lord W. Cecil, Lord Charles Fitzroy, J. H. Ellison, H. Haweis, W. R. Jolly, G. J. Martin, Newton Mant, Marquis of Normanby, A. Robins. W. Gunion Rutherford, Clement Smith, Montagu Villiers #Doctors — Lennox Browne, J. V. Bridge, Barlow, Robert Farquharson, J. F. Fox, Surgeon-Major Kilkelly, John Lowe, C. H. H. Parry, G. V. Poore, Dorrien Smith, S. Wilks #Messieurs<ref name=":1" /> (4, Col. 6b–7a) — Astor, B. F. Astley, W. Astor, Alfred Austin, Hamilton Aidé, Arthur Ash, W. Ambrose, E. H. Anson, Edward Alderson, John Aird, H. T. Anstruther, C. T. Dyke-Acland, Adeane, A. Asher, Ascroft, Allhusen, R. Anderson, George Alexander, Arbuthnot, Leonard Biddulph, Beresford, Stapleton Bretherton, F. Stapleton Bretherton, Bertier, R. G. Blennerhassett, Cosmo Bevan, R. Benson, Rupert Beckett, W. A. Baillie-Hamilton, Walter Baring, S. B. Bancroft (actor "Bancroft and his wife accepted with becoming grace the congratulations with which they were well-nigh overwhelmed"<ref name=":3" /> (5, Col. 6b)), Biddulph, H. R. Baird, J. Wolfe Barry, H. Bathurst, Victor Biddulph, Wentworth Beaumont, Wentworth B. Beaumont, F. Tress Barry, Baillie of Dochfour, Hamar Bass, G. Bridgman, C. G. O. Bridgeman, Edmund R. Boyle, Banbury, Sydney Buxton, C. H. Babington, A. O. Bruce, W. W. Beach, D. P. Barton, F. G. Barnes, J. Emmott Barlow, E. Bainbridge, James Bailey, J. G. A. Baird, Bolitho, H. C. O. Bonsor, E. W. Beckett, Boulnois. M. M. Bhownaggree, F. F. Begg, Charles Bell, M. Biddulph, Buchanan, A. Birrell, J. G. Butcher, W. R. Bousfield, Barton, Brookfield, T. G. Bowles, Brymer, A. H. Brown, W. Burns, Bucknill, E. Balfour, Baxendale, Bell, Barnes, Benson, Bischoffsheim, Beer, Charles Balfour, F. Bibby, Bigham, Baldwin, Bigwood, R. M. Beachcroft, Brigg, Banks, F. Bevan, H. L. C. Brassey, F. C Burnand, Bagge, Burges, F. Cavendish-Bentinck, Cavendish-Bentinck, Childe-Pemberton, Shepherd Cross, R. Cox, Cobbold, Richard Combe, Henry Pelham Clinton, J. R. G. Cotterell, C. Tyrall Cavendish, Kinloch Cooke, Compton, V. Seymour Corkran, F. Cawley, J. D. Clark, Croombie, Cooke, F. S. W. Cornwallis, Consett, George Courroux, Purdon Clarke, F. L. Cook, Colston, Cameron, R. K. Causton, Victor Cavendish, Henry Cavendish, Percy Crutchley, Austen Chamberlain, Cecil Chaplin, Ernest Clarke. J. D. Campbell, W. A. Cockerell, DOyly Carte, W. M. Cazalet, Burdett-Coutts, Clowes, C. A. Cripps, Cayzer, Clark, Cory, Clough, Evelyn Cecil, W. W. Carlile, Channing, Ward Cook, J. A. Campbell, Atkinson Clark, B. Cohen, Cavendish, Wentworth Cole, T. B. Cochrane, Crawshay, A. Cross, Daniel Cooper, Cameron Corbett, Cruddas, D. Coghill, Wilfrid Cripps, F. Cazenove, P. H. Calderon, Critchett, C. Kinloch Cooke, Lee Dillon, Louis Davidson, W. E. Denison, W. H. Dudley-Ward, W. de Winton, De Trafford, C. S. Dickson, W. Rees Davies, Coningsby Disraeli, A. Drummond, F. Dugdale, R. Disraeli, Gerard Dicconson, J. de la Cour, W. Bromley-Davenport, G. Drummond, J. Diggle, Ben Davies, de Soria, J. K. Digby, C. B. Dalison, Greville Douglas, Kenelm E. Digby, Darling, Dicken, Vaughan Davies, Doxford, Deverell, Thiselton Dyer, Edwin de Lisle, Du Plat Taylor, F. Elliot, Bevan Edwards, Cary-Elwes, T. H. Elliott, Erskine, W. H. Evans, T. E. Ellis, R. Edgcumb, C. C. Edwards, Eyre, F. Eaton, H. P. Ewart, Maurice Euphrussi, M. Eliot, Fitzgerald, Almeric Fitzroy, Alfred Farquhar, J. N. Farquharson, Farquharson of Invercauld, Cecil Fane, G. H. Fane, Herbert Fisher, H. St. George Foley, Hayes Fisher, Dyafer Fakhry, W. Farquhar, Arnold-Forster, Fardell, Munro-Ferguson, W. S. Foster, Johnson-Ferguson, L. Fry, Farmer, Fielden, Firbank, Fison, Flannery, E. Flower, H. W. Forster, Bevill Fortescue, Fane, F. G. Fitzgerald, E. Farquhar, Franklin, J. S. Forbes, Forbes, John Ford, John Gordon, Henry Graves, George Grossmith ("George Grossmith was not a little lionised by titled ladies"<ref name=":3">“The Queen’s Garden Party. Buckingham Palace Grounds. A Brilliant Scene. The Queen’s Cup of Tea.” ''Daily News'' (London) 29 June 1897, Tuesday: 5 [of 10], Col. 6a [of 7] – 6, Col. 2a. ''British Newspaper Archive'' https://www.britishnewspaperarchive.co.uk/viewer/bl/0000051/18970629/021/0005. Print pp. 5–6.</ref> (5, Col. 6b)), Howard of Greystoke, Hamilton Gatliff, G. P. Goldney, Goelet, Gye, Grifflth-Boscawen, A. Gosling, Geoffrey Drage, Otto Goldsmidt, Frank Gore, F. Graham, S. Hoffnung Goldnung Goldsmid, W. H. Kendal Grimston, Gilliat, Gadson, F. W. Gibbs, V. Gore, Goschen, J. E. Gordon, G. Leveson-Gower, E. A. Goulding, Graham, H. R. Graham, Ernest Gray, Montagu Guest, Garfit [?], H. D. Greene, W. R. Greene, J. A. Gretton, Henry Gladstone, W. H. Grenfell, S. W. Gore, Wilhelm Ganz, Scott Gatty, Charles Gold, Walter Gibson, Gurdon, W. Gillett, Sydney Gedge, Tyrell Giles, C. C. Graham, F. R. Gosset, A. C. Humphreys-Owen, G. M. Hutton, Heseltine, Claude Hay, Halford, E. Hope, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Hardcastle, Hanbury, L. V. Harcourt, R. K. Hodgson, Adrian Hope, Beresford-Hope, J. Hozier, E. S. Howard, Horner, Maurice Holzman, A. C. Howard, Cozens-Hardy, Thomas Halsey, Hardy, James Hope, R. Hallett Holt, T. Hare, Hatch, R. B. Haldane, C. Harrison, J. Henniker Heaton, Hermon-Hodge, E. Brodie Hoare, G. Hoare, H. Hobhouse, VV. H. Hornby, R. P. Houston, G. B. Hudson, John Hutton, A. E. Hutton, Lewis Hall, Augustus Hare, George Harwood, G. T. Hertslet, Hartmann, H. Higgins, Hughes, Francis Hamilton, John Hare, Hungerford, Joseph Howard, Hope, R. R. Holmes, H. Howard, Haggard, Cecil Higgins, J. C. Horsley, The Munshi Abdul Hafiz Karim, Wootton Isaacson, E. R. Jenkins, Arthur James, Jacobs, Jebb, A. F. Jeffreys, J. H. Johnstone, Brynmor-Jones, H. C. Jervoise, W. James, Atherley-Jones, Philip Burne Jones, Henry Joslin, George Kemp, Nigel Kingscote, C. Kempe, W. Kenny, A. Kennard, J. Kenyon, Kearley, King King, Lees Knowles, Knowles, Kimber, Kuhe, T. Kingscote, Landon, Reginald Lucas, Letchworth, Lyon, Henry Gore Lindsay, E. H. Loyd, Leonard Lindsey, Drury Lowe, Fairfax Lucy, E. Law, Cecil Lister-Kaye, H. B. Lindsay, H. T. Lopes, J. Grant Lawson, H. Lubbock, W. A. Lindsay, A. K. Loyd, Lecky, W. F. Laurence, Edwin Laurence, J. W. Lowther, Luttrell, Loder, S. Leighton, W. C. F. Luttrell, E. Lloyd, Heathcote Long, L’Estrange, T. C. March, C. J. Murray, Mount, Morrell, R. J. More, Moon, E. P. Monckton, Monk, F. Bingham Mildmay, Beresford Melville, M’Laren, M'Ewan, Martin, H. H. Marks, lan Z. Malcolm, H. L. B. MCalmont, J. W. Maclure, Campbell Munro, J. Maclean, J. C. Macdona, W. G. E. Macartney, Muir Mackenzie, Hugh Morrison, G. H. Murray, P. C. Milbank, Bingham Mildmay, Alpin Macgregor, M. Myther, V. Montagu, Frederick Macmillan, C. M’Neill, Arundel St. John Mildmay, C. Maud, Fuller Maitland, A. Milman, W. A M’Arthur, Marjoribanks, W. H. Myers, F. W. Maude, Muntz, Charles Morley, Murdoch, A. B. F. Mitford, B. Mallet, Mure, Madden, W. J. Mure, R. Maguire, Mackinnon, Montgomerie, Maxwell-Lyte, Mason, Ronald Moncrieffe, Milvain, T. G. Menzies, G. Manners, Nicol, F. A. Newdigate, G. Noel, T. W. Nussey, Charles Orde, R. A. Oswald, M. Oldroyd, J. C. O'Dowd, Oswald, Oppenheim, Arthur Oliphant, C. L. Orr-Ewing, J. L. Pattison, J. Balfour Paul, Paton, A. Peckover, Archibald Peel, Perks, J. Pender, J. Penn, Price, Powell, Paoli, Constantine Phipps[,] Charles Phipps, Leslie Probyn, B. Faudel-Phillips, Wilton Phipps, L. Faudel-Phillips, Joseph Pease, Pollock, Arthur Pease, Roland Protheroe, Walter Peace, J. M. Paulton, Platt-Higgins, Pennefather, Provand, Guy Pym , A. E. Pease, Godfrey Pearse, Algernon Peel, A. V. Pryor, Montagu Price, Phelips, John Ponsonby, Hussey Packe, Wyndham Portal, Henry Petre, Lort Phillips, H. W. Primrose, E. Parkes, Herbert Praed, Heber Percy, Quilter, J. Rankin, Renshaw, J. A. Rentoul, H. C. Richards, Read, T. Richardson, A. T. Phillips Roberts, Hugo von Ruffer, Alexander Ramsay, Alderman and Sheriff Ritchie, Richardson, Rebow, G. L. Ryder, G. A. Redford, G. W. E. Russell, H. J. H. Russell, Pandeli Ralli, John Rutherford, J. Rennell Rodd, Leopold Rothschild, T. W. RusseII, Forbes Robertson, Alfred Rothschild, Brooke Robinson, Edmund Robertson, Repton, James Round, Royds, Henry Raikes, Bowen Rowlands, J. D. Ryder, Sheriff Hargreaves Rogers, Skeffington Smyth, Augustus Spalding, H. H. Shaw, E. Strachey, J. Murray Scott, J. Stern, P. L. Sclater, R. Sassoon, W. Sidebottom, Abel Smith, Louis Sinclair, C. H. Seely, Lucas Shadwell, W. E. T. Sharpe, C. E. Shaw, E. B. Sparke, T. H. Sidebottom, Steward, Stibbert, H. Somerset, H. S. Samuel, J. P. Smith, Horace Seymour, A. H. Smith, H. M. Stanley, J. A. Swettenham, A. Spicer, Stevenson, J. H. Stock, J. Sturgis, H. C. Smith, C. J. Stewart, Leslie Stephen, T. Smith, Senhouse, Eames Storey, Christopher Sykes, H. Seton-Karr, Philip Somers-Cocks, T. Skewes-Cox, Shelley-Bontein, Salting, Leo Schuster, Smith, Arthur Sassoon, G. D. Smith, Shaw, Michael Shaw-Stewart, E. J. Stanley, Albert Sandeman, Scaramanga, Sant, F. Sutton, Dudley Smith, C. E. Tritton. W. E. M. Tomlinson, H. F. Tollemache, A. M. Torrance, Tarleton, Edward Tighe, Alma-Tadema, W. H. Wilson-Todd, P. Thornton, F. Taylor, Beerbohm Tree, Dan Tupper, Montagu Tharp, Abel Thomas, Algernon Turnor, Tudway, C. W. Trotter, H. J. Tennant, J. C. Thynne, H. D. Trelawny, C. E. Thynne, F. J. Thynne, Montagu Thorold, Tremayne, H. Graham Toler, John Taylor, A. J. R. Trendell, Tosti, Christopher Tower, T. Usher, A. Ure, T. Usborne, Chas van Raalte, Graham Vivian, R. C. de Grey Vyner, Hope Vere, F. E. Villiers, Von André, Venning, L. Van Loon, Van De Weyer, Val Prinsep, Walter, Thomas Wayman, Hwfa Williams, Cornwallis West, R. G. Webster, Sackville West, Wanklyn, A. S. Wiison, G. Fleetwood Wilson, A. F. Warr, F. W. Wilson, Piers Egerton Warburton, S. Wombwell, Weigall, Powell Williams, John Welby, Wingfleld, Whitbread, J. W. Wilson, Walton, D’Arcy Wyvill, Wodehouse, Wylie, A. Wilson, John Wilson, C. H. Wilson, Herbert Whiteley, Wynne, Lee Warner, W. West, G. Whiteley, Spencer Walpole, H. C. Woods, M.D., Deputy Inspector-General, Charles Wyndham, J. Humphrey Ward, F. Walker, Whateley, W. Woodall, Wyndham, Godfrey Webb, J. Welby, Charles Waldstein, H. Yorke,.[sic] and Yerburgh #Mesdames<ref name=":1" /> (4, Col. 7a–b) — Adair, A. H. Dyke Acland, Dyke Acland, Asquith, Alfred Austin, Adair, Evelyn Atherley, Ashton, Allhusen, Adeane, Alma-Tadema, Argles, Abdy, Agar, Antrobus, Alexander, Ascroft, Arkwright, Bowden-Smith, Browne, Barton, Bates, H. M. Biddulph, W. H. Bliss, Beresford, Ebrington Bissett, Bertier, R. P. Blennerlhasset, Brownrigg, Bridge, Cosmo Bevan, Rupert Beckett, Bradley, Birch-Reynardson, W. A. Baillie-Hamilton, Walter Baring, Bathurst, S.[?] B. Bancroft (actor "Bancroft and his wife accepted with becoming grace the congratulations with which they were well-nigh overwhelmed"<ref name=":3" /> (5, Col. 6b)), H. R. Baird, Wolfe Barry, Beer, Barlow, Bischoffsheim, F. Bibby, Bigham, Butler, Bankes, W. Borsel, Duncan Baillie, Bagge, Burges, Butler, Brocklehurst, C. H. Babington, Bailey, H. A. Brassey, Barlow, F. Bevan, Tresa [?] Barry, F. C. Burnand, Charles Bagot, Wentworth Beaumont, Charles Balfour, Baxendale, Benson, Blundell, Bryce, C. G. O. Bridgeman, S. Buxton, A. Barry, Banbury, F. G. Barnes, Beaumont, D. P. Barton, W. W. Beach, A. C. Bruce, J. F. Bagot, J. Bailey, J. G. A. Baird, Birrell, Bolitho, Bonsor, Griffith-Boscawen, Boulnois [?], Bowles. F. F. Begg, C. Bill, Buchanan, Brookfield, A. H. Brown, Bell, E. Balfour, Baldwin, R. Benson, C. E. Buckle, Barnes, W. Burns, C. K. Burn, H. Churchill, Crutchley, Curzon, F. Cavendish-Bentinck, W. G. Cavendish-Bentinck, Chamberlain. W. Chetwynd, Dick-Cunynghame, Archibald Calvert, Creignton, Daniel Cooper, Calley, Cox, Kinloch Cooke, Rivett Carnac, C. Kinloch Cooke, Henry Pelham Clinton, Colston, Coghill, Castance, B. F. Clark, Cavaye, Consett, G. D. Clark, A. B. Crosbie, Clerk, Wilfrid Cripps, Chapman, Crawshay, F. Campbell. W. W. Carlile, Channing, Cayzer, F. S. W. Cornwallis, Armar Corry, Cory, Critchett, Craik, W. Campbell, Atkinson Clark, R. Cox, Cruddas, Cavendish, Shepherd Cross, Clive, Crombie, F. L. Cook, C. Tyrall Cavendish, Clifford Corry, Hastings Campbell, Cameron Corbett, Carter, Corroux, Chaloner, Cecil Chapiin, J. D. Campbell, W. A. Cockerell, Compton, D'Oyly Carte, Stanley Clark, Cazalet, Seymour Corkran, Chaine, Carson, Boyd Carpenter, Causton, W. Campbell, Codrington, F. L. Campbell, D. B. O. Campbell, Cuninghame, Stapleton Coton, Coventry, Crabbe, Close, Courtney, E. H. Cooper, Carnegy, Randall Davidson, A. Hay Drummond, G. De Plat Taylor, Dickson, Lawrence Drummond, Louis Davidson, Dicken, Denis Daly, Dalton, R. C. de Grey Vyner, Durnford, W. de Winton, Edwin de Lisle, de Arcos, Drummond, Darling, A. L. Douglas, Doxford, Thiselton Dyer, Vanghan Davies, Denny, Coningsby Disraeli, Geoffrey Drage, Davis, Dundas, R. Disraeli, Dicconson, J. de la Cour, G. Drummond, J. Diggle, Akers-Douglas, Digby, Dunne, Dalbiac, de Salis, C. S. Dickson, Domvile, Ellicott, Edwards, Ellison, C. B. Ewart, Edis, East, Eliot, Egerton, F. Elliot, Floyd, Fenwick, E. Farquhar, Barrington Foote, G. M. Farquhar, Farquarson of Invercauld, Almeric Fitzroy, Lancelot Farmer, FitzGeorge, G. H. Finch, Fenn, Wynne Finch, R. Fitzwilliam, Fanshawe, Fullerton, Fane, Hayes Fisher, Fellowes, Houston French, Arnold-Forster, Fardell, Field, W. H. Foster, H. S. Foster, Johnson Ferguson, Farmer, Fielden, Fison, Firbank, Bevill Fortescue, Farnham, H. Fludyer, S. W. Gore, F. R. Gosset, Gregory, C. C. Graham, Guy-Pym, John Gordon, Gooenough, Henry Graves, Gordon, Garfit [?], S. Gedge, Tyrell Giles, Gilliat, Godson, S. Hoffmung Goldsmid, Kendal Grimston, Goldsworthy, J. E. Gordon, Gunter, W. H. Grenfell, H. Grenfell, G. G. Gordon, Gurney, Goodden, F. Gore, S. Gordon, A Goldsmid, Scott Gatty, Walter Gibson, Gordon, Grant, Goelet, Gye, Gardner, Gladstone, Gore, Green, Goschen, A. Gosling, Hargreaves-Rogers, Staveley Hill, Hanbury. James Hope, Claude Hay, Heneage, Heseltine, E. Hope, Arthur Heath, Philip Henriques, C. D. Hohler, Hornyold, Carl Haag, Marcus Hare, Harford, Hardcastle, Holmes, Beresford Hope, Adrian Hope, Hanbury, Horner, Hammet, Hall, A. C. Howard, Halsey, Hardy, Heath, Hermon Hodge, Brodie Hoare, S. Hoare, H. Hobhouse, W. H. Hornby, G B. Hudson, Platt-Higgins, Hildyard, Lewis Hall, G. M. Hutton, G. Hutton, W. G. G. Hutchinson, Haweis, Hartmann, Higgins, John Hare, Hungerford, Humphreys-Owen, R. W. Hamilton, Hills, Hippisley, Herbert, Hatton, Henderson, Haggard, Hervey, J. Howard, H. Howard, Ian Hamilton, Gathorne-Hardy, Howard, Marcus Hare, Inglefield, Wootton Isaacson, Joicey, Jenkinson, Inigo Jones, Jackson, A. James, Cotton-Jodrell, Jacoby, Jebb, A. F. Jeffreys, Jessel, Brynmor Jones, Pryce Jones, J. E. Jameson, H. C. Jervoise, W. James, Atherley Jones, G. Johnstone, J. H. Johnstone, A. Kennard, Kearley, Kimber, Hegan Kennard, Kitching, Kennion [?], Kennison, Knowles, W. Kenny, Kennedy, Keeley, Kuhe, Kingston, Kilkelly, Colin Keppel, Hanning Lee, A. K. Loyd, Lyon, Long, Lane, Lucas, Lockwood, S. Leighton, Lecky, E. Lawrence, Lawrie, Luck, Lloyd. A. P. Lake, J. W. Lowther, Lowe, Lidderdale, Liddell, Lascelles, Luttrell, H. Lubbock, Leslie, Lucas-Shadwell, Laurier, Naylor Leyland, Langenbach, E. Law, Fairfax Lucy, Lockhart, Lewis, Maxwell-Lyte, F. A. Lucas, G. Manners, Beresford Melville, Morrell, Victor Milward, Marshall, Maclure, J. Maclean, M'Laren, M'Ewan, R. B. Martin, Marks, Markham, J. M'Calmont, F. W. Maude, Napier Miles, M’Neill, Max Muller, Meeking, Manvers Moorson, Arundel St. John Mildmay, Frederick Macmillan, Mount, Muntz, Murdoch, Wyndham Murray, W. J. Mure, Graham Murray, Montefiore, W. C. F. Molyneux, Newton Mant, Millett, Malet, Ashurst Morris, May, Maurice, Milvain, Marjoribanks, J. C. Macdona, Moorhouse, Muir Mackenzie, G. Moncrieff, J. Murray, Montgomery, Milbank, Bingham Mildmay, Mellor, C. Maude, T. G. Menzies, J. M'Donald, W. A. M'Arthur, M'Neile, M'N'eill, Campbell Munro, Mostyn, A. Milman, Majoribanks, Noel, H. F. Nicholson, F. Neville, Nicol, Nevul [?], Nugent, Newhouse, Oppenheim, M. Oldroyd, Charles Orde, H. H. Oldham, R. A. Oswald, Oswald. A. Oliphant, Oakley, J. L Pattison, Price, Perowne, Perks, Constantine Phipps, Peacocke [?], R. Prothero, Powell, Leslie Probyn, Pitman, Upton Prior, Lort Phillips, Primrose, Powlett, Pakenham, Peyton, Parkes, Wyndham Portal, Pipon, Pender, Phillpotts, Pollock, Montagu Price, Phellps, John Ponsonby, Fox Pitt, A. Peel, Aldrich Pelham, J. Pease, Poe, G. Pearse, A. Paget, A. Pease. N. G. Philips, Pirie [?], Dampier Palmer, F. Post, Pakenham, Paget, H. Parr, Wilton[?]-Phipps, Quilter, Rebow, J. C. Russell, Rolfe, Rutherford, I[?]. Richardson. James Ronand, Robins, Rennell Rodd, W. W. Russon[?], Alexander Ramsay, Robinson, J. Rennell Rodd, Redford, Harcourt Rose, Royds, H. Raikes, Carl Rosa, Ronalds, Arrnold Royle [? Royce?], Rice, Leopold Rothschild, Raikes, J. Rankin, Renshaw, F. Russell, Ricardo, Riddel, Robertson, G. Royle, Teignmouth [?] Shore, Sandeman, Stopford, Graham Smith, Salting, Brinsley Sheridan, Salmon [?], Salmond, Edgar Shephard, Sant. A. Sandeman, H. Seymour, H. S. Samuel, St. Clair, AbeI Smith, J. P. Smith, H. M. Stanley, A. Spicer, Stevenson, Swaine, Sullivan, J. H. Stock. E. B. Sparke, J. Sturgis, Louis Sinclair, H. Seton-Karr, Slade, J. Stern, Skefflngton Smyth, P. L. Slater, A. C. Stewart, R. Sassoon, C. Smith, E. Strachey, Napier Sturt, Steward, Eames Storey, Starkie, Senhouse, Bridgman Simpson, Seddon, T. Smith, Leslie Stephen, Settle, Scaramanga [?], Arthur Sassoon, L. Seymour, Shaw. R. F. Synge, T. Skewes-Cox, Stevenson, H. C. Smith, Sterling, T. H. Sidebottom, C. H. Seely, Shelley-Bontem [?], Sandford, Hawley Smart, Sergison [?], Frederick Slade, Scobell, Graves Sawle, Scott, Settle, Smith-Barry, Stewart, J. A. Swettenham, Surtees, Synge, Dudley Smith, Thomson, M. Thorold, H. Graham Toler [?], J. W. Taylor, Christopher Tower, Tosti, Temple, Beerbohm Tree, Dan Tupper, R. T. Thynne, Montagu Tharp, Trotter, Anstruther Thomson, Tupper, Taylor, C. E. Tritton, C. F. Anstruther Thomson, Edward Tighe, F. Taylor, Tillard, Tillbrook, Brook Taylor, Tudway, C. E. Thynne, J. C. Thynne, H. Thomas, Thwaites, Tarleton, A. Ure, Usher, R. Vivian, Val Prinsep, Edmund Vaughan, E. Villiers, C. van Raalte, Von André, Verschoyle, F. E. Villiers, Vance, Hope Vere, Villiers, Venning, Sackviile West, Whatman, Williams Wynn, Watson, Wharton, John Wilson, Williams, Stuart Wortley, Wood, C. H. Wilson, S. J. Way, Walton, H. Whiteley, G. Whiteley, Ellis Williams, Wilson, Weywan, E. F. Wodehouse, John Welby, Wray, Wickham, Whatley, Spencer Walpole, Hwfa Williams. J. Woodford, Charles Wyndham, Wingfield, Charles Wood, Lee Warner, Warre, Humphrey Ward, Wallis, Wilberforce, Wynne, J. Welby, Eardley Wilmot, A. S. Wilson, C. [?] E. Ward, Walter, Warner, R. G. Webster, Wells, Cornwallis-West, F. Charteris Wemyss, Yerburgh #Misses<ref name=":1" /> (5, Col. 7c – 6, Col. 1a) — Ascroft, Arnott, Alexander, Armytage (2), Adye [?] (2), Alison, Heathcoat-Amory, Austin (2), Aird (2), Archer-Houblon, Rosomond Anstruther, Adam (2), Arbuthnott, Akers-Douglas, Florence Anderson, Arkwright, Birch-Reynardson (2), Bradley, Bowden-Smith (2), Browne (2), Bromley-Davenport, Barker, Burrell (2), Berkeley, Berkeley (2), Beresford, Berens, Bertier, Baird (2), Brownrigg, Bates, Alice Bagot, Barne, Bartlett (2), Barnardiston (2), Birch, Bourke, Brassey (2), Browne (2), Bruce (2), Hicks-Beach (2), Biddulph (2), Mariot [?] Bayley, Mabel Brackenbury, Browne (2), Stapleton Bretherton [?] (2), Beryl Bradford, Banbury, Evelyne Burne, Bolitho, Bonsor, Beach, Biddulph, Bill, Brunner, Blackwood (2), Bandanaratke [?], Barran (2), Brodie (2), Brookfield, Brown, Barnes (2), Burns, Bowen (2), Buxton (2), Bellingham, Bailey (2), Brooke, Bell (2), Baxendale, Burdett, Mary Bulteel, Burges (2), Bevan, Brassey (2), Duncan Baillie (2), Braddon, Rhoda Broughton, Blyth (2), Baring, Bathurst (2), Blundell, Balfour, Freda Biddulph, Hilda Beaumont, Budgett, Bramwell, Butler, Crutchley (2), Culme-Seymour, Carleton, Chapiin [sic?] (2), Cockerell, Lilah Campbell, Boyd Carpenter (2), Cowell-Stepney, Lucia Creighton, Chrichton-Maitland, Leila Crichton, Campbell, Calvert, Ronald Campbell, Cooper (2), Cochrane, Clarke, Clowes (2), Stanley Clarke, Commerell, Colville, Cayzer, Crosse, Chaning (2), Cunliffe, Chetwode (2), Chetwynd (2), Corry, Clark, J. A. Campbell, Cameron, Colomb, Custance, Clive (2), Grace de Capell-Brooke, Cook, Vera Consett, Cooper, Campbell (2), Cockerell, Cecil, Carlisle, Cholmeley (2), Cruddas (2), Cox, Cowell, Causton, Cust (2), Cuffe, Chitty, Chamberlain (2), Crabbe (2), Edith Chaplin, Corbett, Cameron (2), Chaplin, Cholmondeley, Carden, Cotterell (2), Spencer Churchill, Corkran, Commerell, Edith Drummond, Sybil Dudley-Ward, Gladys Dalgety [?], Drummond (2), Duncombe (2), De Winton, De Trafford, De Perpigna, Dalrymple, Dashwood, Duncombe (2), Dawnay (2), Du Cane  (2), De Brienen (2), La Baronne de Friesen, La Baronne Sirtema de Grovestins [?], Mary Drummond, De Winton, Davey, Digby (2), Dowell, Marion Dunne, Du Chair, De Winton, Domvile [?], Douglas (2), Dunn, Doxford, Deverell, Drummond (2), Digby, Disraeli, Adelizs [?] Drummond, May Dundas, Dillon (2), Bevan Edwards (2), Evans (2), Ellison, Eliot (2), Ellicott, Gertrude Elliot, Egerton (2), Ellis (2), Edis (2), Ellaby, Egerton, Grey Egerton, East (2), Elphinstone (2), Rachel Erskine, Evelyn Ellis, Amelia Farquharson, Henrietta Farquharson, Foster, Farmer, Fielden (2), Fison, Fersuson of Pitfour (2), Fitzwilliam (2), Flower, Keith Falconer (2), Fenwick (2), Forwood (2), Farquharson of Invercauld (2), FitzClarence (2), Olga FitzGeorge, Ethel Fitz-Roy, Fergusson, Dorothy Ffolkes, Finch (2), Fanshawe, Flower, Fullerton (2), Feilding (2), Fardell (2), Fisher (2), Fowler (2), Frere (2), Fitz Gerald, Gold, Graves, Gibbs (2), Gregory, Gough-Calthorpe (2), Helen Gladstone, Goschen (2), Glyn, Godley (2), Gardiner, Gillian [?] (2), Gunter (2), Gilbey, Maud Grenfell, Hamilton Gordon, Gurrney Goodden, Goldsmid, Gardiner, Grant, Victona Grant-Duff, Goelet, Gosling, Gore, Gathorne-Hardy, Gordon (2), Hood (2), Heneage, M. Carew Hunt, Hare (2), Hay  (2), Hickman, Adrian Hope (2), Hare (2), Agnes Beresford Hope, Carl Haag, Hardcastle (2), Heseltine, Hare, Hope, Heron Maxwell (2), Halford (2), Hamilton (2), Hamilton, Howard (2), Hardy (2), Hay (2), Herbert Margaret Acland Hood, Mary Hope, Hill, Hemming (2), Jean Hotham, Hall, Harrison, Gladys Higginson, (Brydges) Henniker, Halsey (2), V. Hanson, (Stock) Hill (2), (Brodie) Hoare (2), Hoare (2), Houldsworth (2), Haig, Hart, Hervey, (Lewis) Hall, Harwood (2), Hutchinson, Hughes (2), Hooker, Hart-Dyke (2), Hervey-Bathurst (2), Louisa Heathcote, Howard, Dora Hanbury, Howard (2), Hornby (2), Satyendra Bala Tagore, Grace Jackson, Jolliffe (2), Helena James, Jenner, Joicey, Cotton-Jodrell, Jenkins (2), Johnstone, Jameson (2), Jessel, Jervoise, S. L. Johnstone, Keith-Falconer (2), Ker (2), Ethel Kenny, Kennedy, Kennard, King King, Kennard (2), Kitson (2), Kerr (2), Kimber, Kennaway (2), Nona Kerr, Keppel, Kemball, C. Lees, Lyson, Gore Lindsay, Linton (2), Lindley (2), Lubbock, Aline Lambton, Lambart (2), Liddell, Alice Loch, Lindsay, Lucas-Shadwell, Hanning Lee (2), Emily Loch, Larking, Leese, Llewelyn, Leighton (2), Lawrence (2), Lopes (2), J. Lawson, Laurie (2), Lyte (2), Lloyd (2), Lyall, Luttrell, Lockwood, Lister, Lidderdale (2), Violet Leigh, Liddell (2), Drury Lowe, Lewis (2), Loftus, Lindsay, Lyell (2), Aimee Lowther, l’Estrange, Graham Murray, Mellor (2), Milward, Monk (2), Maxwell (2), Massey-Mainwaring, Mackworth (2), Markham (2), Macdonald, More-Molyneux, Cicely Monson, Maclure, Lena Milman, Morris (2), Macnaghten, Mowatt (2), Margaret Muir MacKenzie, Murray, Mundella, Mowbray, Ethel Morris, Beatrice Mildmay, May Milbank, Evelyn Moreton, Magniac (2), Mackenzie, M'Clintock, Madden, MacGregor(2) Mount (2), Muntz, Murdoch, Mitford, Montagu (2), Mure, Menzies, Macpherson-Grant, Malet, Moseley (2), Meeking, Macgregor, Mary Moore, Montgomery, St. John Mildmay, Madden (2), Milman (2), Constance Maude, Martyn, Campbell Munro, Nevill (2),Noel (2), Nevill, Nicol, Neville, Nelson (2). Olpherts [?] (2), Oakley, Ogilvy, Humphreys Owen, V. A. Okeover, O’Brien (2), Linda Oppenheim, Phoebe Otway, Alina O'Shee, Anderson Pelham, Pole, Pereira, Peyton, Pattison, Orde Powlett, Powlett, Pelly (2), Perowne, Charlotte Probyn, Julia Ponsonby, Peekover, Peel (2), Penn, Peace, Baden Powell, Powell (2), Pease, Priestley, Palgrave, Post, Parker, Pease, Palmer, Packe (2), Alice Paget, Paget, Paget of Cranmore (2), [?] Phillips, Phipps, Cecilia Peel, Chandos Pole, Pollock Phellps, Parry, Ponsonby, Wilton Phipps, Quain, Quilter (2), Russell of Killowen(2), Ritchie (2), Robins, Sibyl Robertson, Round (2), Royds (2), Russell, Rebow, Jane Ryan, Ramsay, Ricardo (2), Rigby, Russell (2), Lucy Raikes, Rankin, Frances Rod, Beatrix Rice, Russell (2), K. Reiss, Ricardo, Smith, Stafford, Stevenson, Stopford (2), M. Seymour, Kay Shuttleworth [?] (2), Seymour (2), Shaw, Shaw-Stewart, Evelyn Starling[?], Maxwell Scott, Abel Smith, Sartorius (2), Maud S[?]hey, Stewart, Magaret Stanley, Dorrien Smith, Smith (2), [?]-Smith, Saurin, Salmond (2), Sandeman (2), Sant, Dudley Smith[?], Swaine, Stephenson (2), Stewart (2), Dora Stone, Sparkes, [Stanley?], Nita Houston Stewart, Lily Severn, Evelyn Stanley, [Sheppart?], Saumarez Smith, Truda Saunderson, Swinburne, [Sullivan?], Mabel Seymour, Shute, R. Sterling, Stern (2), Sar[?] (2), Sassoon (2), P. L. Sclater, Sparke, Smith (Clement), [Sanderson?], Hilda Stewart, Seddon (2), Shelley, Sprigg (2), [?] Stephen, Ruby Spencer Churchill, Rachel Smith, [?], Tremayne (2), Ellen Terry, Ethel Thomas, Muriel [?], Taylor, Mary Talbot, Tomlinson, G. le M. Tupper, [?], Ella Taylor, Thorold, Taylor (2), E. Tuson, Trelawny [?], Adela[?] Trefusis, Rachel Thynne, Tritton (2), Thomson (2), [?], Thesiger, Thynne, I. C. (2), Thynne (2), Thornton (2), [Temple?], Turner, Talbot, Thynne, Usher, Van de Weyer (2), [Vivian?] (2), Dorothy Villiers, Freda Villiers, Verschoyle, Van [der Byl?], Villiers, Venning, Hilda von Deichmann, Wood[ford?], Fleetwood Wilson, Eardley-Wilmot, Maud Walpole, [?hend?] Wilson, Wilson, Wilberforce, Warren (2), [W?vil?] (2), Wills (2), Warrender (2), Walrond (2), Wynd[ham?] (2), Webster (2), Watson, Wombwell, Whitehead (2), [W?Ieyer?] (2), Evelyn Wellesley, Cornwallis West, Whatman {2), [?] (2), Rachel Weigall, F. Walker, Smart Walker, Wood (2), de la Wood[?], Ward, Wilbraham, Wilberforce (2), Walker, Williams, [Workham?] (2), Yeatman #Admirals of the Fleet [initial large caps, rest sm caps] — Earl of Clanwilliam, Lord John [Hay?], the Hon. Sir H. Keppel #Admirals — H. G. Andoe, C. E. Buckle, Sir F. Bedford, Britten, the Hon. W. Carpenter, H. F. Cleveland, Sir H. Chads, Close, [?], Carr, E. J. Church, Sir W. Dowell, R. G. Douglas, A. L. [?], C. E. Domvile, A. T. Dale, D’Eyncourt, Field, Sir A. [Farquhar?], Fitzgerald, Fellowes, Fanshawe, Sir H. Fairfax, Sir [?] Fisher, C. J. Fane, Fullerton, the Hon. Sir E. Fremantle, [?] FitzGeorge, Woods Pasha, Sir W. Hunt-Grubbe, Sir Anthony [?] Hoskin, Lord Hood of Avalon, Sir Leopold Heath, Sir [?] [F.?] Hotham, Sir Algernon Heneage, R. H. Hamond, the Right Hon. Sir [J.?] Hay, St. G. C. D’Arcy Irvine, Jones, Kennedy, Sir A. [?s], A. P. Lake, R. M. Lloyd, Sir L. Loraine, A. H. Markham, [Sir?] R. More-Molyneux, Sir F. L. M'Clintock, Sir R. Macdonald, [the?] Hon. V. Montagu, Nicholson, Noel, Marquis of Northampton, Sir E. Ommaney [?], Sir Augustus Phillimore, A. T. Powlett, [?], [?. ?.] Rowley, Sir F. Richards, Lord Charles Scott, [? St.? John?], W. H. C. St. Clair, Bowden Smith, Sulivan, E. H. Sey[mour?], H. Stephenson, Sir Nowell Salmon, Sir W. Houston [Stewart?], Sir M. [Cuhne?]-Seymour, E. W. Turnour, E. W. Van[?] Wharton, Sir G. Willes, the Hon. W. J. Ward #Captain, R.N. — W. A. D. Acland, C. J. Barlow, F. R. Board[?], H. Bainbridge, Hon. T. Brand, Bickford, Lord Charles [B?ford?], B. F. Clark, Colville, Carter, Hon. S. Cecil Colville, [?ford?], A. G. Douglas, Sir C. Domville, Hon. A. Hay Dru[?], [?] [W.?] [?] Gordon, Hammet, Hon. Curzon Howe, Hender[?], [?] Ingles, Jellicoe, Jephson, Johnstone, Jeffreys, H. C. [?], Hon. A. Littleton, Hon. Hedworth Lambton, Moore, May, [? Net?], Poe, Pipon [?], Aldrich Pelham, Alfred Paget, [Bi.idcl?], Rolleston, John Sinclair, Bridgeman Simpson, [?], Van Koughnet [?], Burges Watson, Eardley-Wilmot, [?ham, Winsloe, Hon. J. Yorke #[Lieutenants???] — Anson, G. R. Bethell, Blair, Bayley, Cave[?], [?] Cave,Hon. Cecil Cadogan, de Salis, Fraser, Floyd, Hon. [?] [F?], Alaric Grant, Morgan, Moore, Marescaux, [?] Stuart, Tupper, Wells, Williams, G. J. S. Warrender #[Lieutenants?] R.N. — Alton, Murray Aynsley, Boyle, Bather, [?], [R. F.?] Boyle, Chaytor, Sir Charles Cust, G. W. Davy, [?] Wyndham-Fiennes, Fair, Godfrey Faussett, Garforth, [L?]ord Clifford, Hopkinson, Henderson, Keyes, Keppel, [?] Lloyd, Majendie, Mitchell, Morant, Kerr-Pearse, [?] Richmond, Rae, Stewart, Hon. Victor Stanley, [?] [Calta?]-Seymoar, Trye, Thring, Hon. Cyril Ward, W[?], R. E. Wemyss, Woolcombe #[Captain?] Trinity House, Sir J. Sydney Webbe #[Field?] Marshall — Sir F. P. Haines, Sir Lintorn Simmons, Sir [?] Stewart, Lord Roberts of Kandahar, Viscount Wolseley #[Generals?] —Sir J. Ardagh, Sir A. Alison, Sir H. J. Alderson, [?n] Annesley, J. Alleyne, Sir J. M. Adye, Sir C. G. [Arbuth?]not, Sir H. Havelock-Allan, R. Bateson, Sir W. F. [B?er, Sir H. Brackenbury, H. M. Bengough, the Right Hon. [?] Buller, Sir Owen Tador-Burne, H. J. Buchanan, Sir C. H. [Brown?low], Sir S. Browne, Sir M. Biddulph, Viscount Bridport, [?. O.?] Barnard, E. F. Chapman, Lord Clarina, C. F. Clery, the Hon. S. Gough-Calthorpe, E. H. Clive, Godfrey Clerk, Lord [Ch?]sford, the Hon. Sir Andrew Clarke, Sir E. Du Cane, Crutchley [?], Lord de Ros, Sir John Donelly, J. H. Dunne, Sir Martin Dillon, Sir Collingwood Dickson, Sir H. de Bathe, Davis, Sir F. de Winton, Sir T. Dennehy, Sir H. Ewart, Sir J. B. Edwards, C. B. Ewart, Cecil East, Arthur French, Sir T. Fitz-Wygram, the Hon. Sir P. Feilding, Sir T. E. Gallwey, Sir T. Goldsmid, Sir R. Gipps, Sir R. Grant, Sir F. W. Grenfell, Coleridge Grove, Goldsworthy, J. J. H. Gordon, Sir E. A. Holdich, Sir E. W. Higginson, Sir R. J. Hay, Sir R. Harrison, Julian Hall, Earl Howe, the Hon. W. Home, J. Jameson, Sir Arnold Kemball, Kelly-Kenay, Lord Mark Kerr, F. T. Lloyd, Sir D. Lysons, Sir Drury Lowe, G. Luck, J. W. Laurie, F. Marshall, the Hon. R. Monck, Crichton Maitland, Sir J. M'Neill, Montgomery, the Hon. S. Mostyn, G. Moncrieff, E. Markham, Sir W. A. Mackinnon, Bryan Milman [?], H. M’Calmont [?], M'Donnell, W. C. F. Molyneux, Lord [Methuen?], J. F. Maurice, Sir F. Middleton, O. H. Nicolls, Sir E. [?] Newdegate, Sir H. N[orman?], Sir W. Olpherts, F. Peyton [?], G. [?] Upton Prior, T. H. Pakenham, G. W. T. Rich, Lord [?der] Russell, Robinson, Rowlands, J. C. Russell, F. [Russell?], A. C. Stewart, Sir Henry Smyth, Sterling, Sir C. [?] Shute, N. Stevenson, Swaine, Lord William Seymour, [?] [Sahmond?], Sir Frederick Stephenson, Sir John Stokes, Sir R. [?], Sir H. B. Tuson, the Hon. R. A. J. Talbot, G. le M. [Tupper?], Taylor, Hon. C. Thesiger, R. T. Thynne, Upperton, [?]H. Utterson, Sir J. Watson, Sir C. W. Wilson, Sir F. F. Walker, Sir Evelyn Wood, Sir C. Warren, Albert Williams, the Hon. G. Wrottesley, Sir G. H. Willis, Sir H. Wilmot #Colonels — Armytage, Arkwright, Pat Boyle, Burges, the Hon. [?] Byng, H. B. H. Blundell, M. S. Brownrigg, Sir E. Bradford, Sir A. [Blyge? Bigge?], the Hon. F. Bridgeman, Brassey, Lord William Beresford, St. John Barne, N. Barnardiston, Lord Blythswood, [?] Cunynghame, F. H. Custance, Clayton, Sir Henry Colville, [?] Carnac [?], Cavaye, Seymour Corkran, the Hon. Charles [?], W. Campbell, Chaloner, Archibald Calvert, the Hon. [?] Campbell, the Hon. Wenman C. Coke, the Hon. W. [?ton], the Hon. Sir W. Colville, Chaine, A. B. Crosbie, [T.?] [R?] Crosse, Lord Edward Pelham Clinton, the Hon. Henry [C?hton], E. H. Cooper, the Hon. H. Corry, John Clerk, Lord Dorchestcr, C. R. Dease, the Hon, Lewis Dawnay, [the?] Hon. H. Denison, Denny, Dalbiac, A. Davidson, the Hon. Cathbert Edwards, the Right Hon. Sir F. Edwards, [?son], R. Edis, the Hon. Charles Edgecumbe, Aubone Fife, [?], Wynne Finch, Ferguson of Pitfour, Forster, Lancelot [?r] H. Frudyer, Barrington Foote, Goldsmid, Gore, Grenfell, [?n], C. G. Gordon, R. Gunter, Alan Gardner, Hon. G. Gough, [?] [?iton], the Hon. A. Hood, the Earl of Home, Lord Claud [Hamilton?], Harford, Herbert, the Earl of Haddington, Haygarth, G. Hatton [?], Hillyard, Arthur Haig, Sir E. Stock Hill, R. Hennell, Archer Houblon [?], the Hon. Cospatrick Home, the Hon. C. Gathorne-Hardy, Johnstone, Cotton-Jodrell, Hegan, [H?nard], Sir N. Kingscote, H. A. Lascelles, the Hon. Heneage [L?], Hanning Lee, F. A. Lucas, the Hon. H. Lyttelton, Lockwood, L. V. Loyd, C. W. Long, Ronald Lane, Lucas, J. Leslie, the Hon. Caryl [?]Molyneux, John Murray, Sir A. W. Mackworth, J. M'Calmont [?], Milward, the Hon. F. C. Morgan, J. J. Mellor, Meeking, Manvers [?], Moorsom, H. Malet, the Earl of Mount Edgecumbe, the [Earl?] of March, Wyndham Murray, Sir V. Majendie, the Hon. G. [Napper?], H. H. Oldham, L. J. Oliphant, A. Paget, Dampier Palmer, [Earl?] Percy, George Paget, C. D. Patterson, Arthur Peel, [Birch?] [Richardson?], the Hon. F. W. Stopford, Sir W. G. Stirling, E J. [Sanderson?], T. M. Sandys, H. Smith, J. F. Sandeman, Renyon-[Surrey?], C. E Stewart, E. H. Sartorius, the Hon. Walter [Stewart?], L. Seymour, Settle, Stevenson, Starkie, C. H. Seafe, the Hon. Sir W. P. Talbot, J. Du Plat[?] Taylor, H. Thomas, A. W. [T?], the Hon. W. Ie Poer Trench, H. P. Vance, Sir C. E. Howard Vincent, M.P.; R. Vivian, A. P. Vivian, E. Villiers, the Duke of Westminster, the Earl of Wemyss, Lord Wantage, Ward, [Waring?], [Earle?] Welby, Lord Arthur Wellesley, Robert Williams, the Hon. H. L. Wood, Sir W. H. Walroud, F. Smart Walker, A. [Williams?] Wynn, Wardrop #Majors — Anne, Atherley, Ashton, F. H. Bowles, the Hon. [?] R. Bourke, Carnegy, H. Candy, Close, the Hon. F. Colborue, the Hon. Wenman Coke, Lawrence Drummond, Alfred [Edgecombe?], G. Egerton, E. H. Elliot, the Hon. A. Henniker, J. [H?a?h], the Hon. Assheton Harbord, the Hon. North Dalrymple [Hamilton?], Jameson, Pryce Jones, Larnach, the Hon. Osbert [Lumley?], C. Little, Marindin, the Hon. J. Scott Napier, Wyndham Quin, F. C Rasch, the Hon. A. Sidney, the Hon. J. T. St. Aubyn, Sir Edgar Sebright, Stirling, T. E. M. Swinnington-Parkington, [?.] M. Temple, Tillbrook, Anstruther Thomson, [E.?] [L.?] Woodhouse, and the Marquis of Winchester #Captains — O. Ames, J. Acland, Alan Boisragon, Bates, H. M. [Biddulph?], the Hon. Baring, Butler, the Hon. J. Byng, the Hon. [N.?] Yarde-Butler, E. W. Blunt, J. F. Bagot, the Hon. W. Bagot, Seymour Combe, W. Chetwynd, Dundas, Denis Daly, Cecil Drummond, M. Drummond, Ellison, Houston French, Gye, R. G. [Gilmour?], P. Green, W. G. Grice-Hutchinson, Ahmed Hussain, G. [L.?] Holford, Jessel, the Hon. W. Lambton, the Hon. G. H. [L?], Sir H. Naylor-Leyland, G. Lister, Matthews, A. D. Miller, [?],M. M'Neill, C. Norton, Phillpotts, N. G. Philips, Prety[man?], Duncan Pirie, Pitman, Fox Pitt, Petre, Harcourt Rose, [W.?] [J.?] Stopford, Sir Eyre Shaw, H. G. D. Shute, Spicer, the Hon. [?.] St. Aubyn, Sutton, Tillard, Webbe, Wray, and Gordon [Watson?] #Lieutenants — Baun, A. Cowell, the Hon. E. C. Lennox, F. Ponsonby, J. Ponsonby, Vandeleur, the Hon. C. Willoughby, and the Hon. C. S. H. D. Willoughby ===Entertainment=== "The Bands of the 1st Life Guards, Grenadier Guards, and Royal Artillery played a selection of music during the afternoon."<ref name=":1" /> (4, Col. 2c) ==Anthology== ====Quote Intro==== <quote></quote> () == Notes and Questions == # ==References== * <references /> duw3c2ui1aoslym3b180legstx1ski4 Motivation and emotion/Book/2024/Abusive relationships and emotional dependency 0 308915 2684176 2682794 2024-11-12T10:34:53Z Jtneill 10242 /* Overview */ Move image into scenario 2684176 wikitext text/x-wiki {{title|Abusive relationships and emotional dependency:<br>What psychological mechanisms drive emotional dependency and how does it perpetuate abusive relationships?}} {{MECR3|https://youtu.be/C6RDIcVIdR0}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} [[File:NounProject Abuse.png|thumb|Figure 1. Depicting two figures; one of them is being abused by the other.]] ; Case study Edwina has been in a romantic relationship with Zack for 2 months now, where in the beginning he appeared to be a good person, however over time she has come to realise he is the complete opposite; Zack has slowly isolated Edwina from her friends and family, heavily controls her social media, forbids her to go places without his permission, even if it's the grocery store, and criticises and insults her if she goes against his wishes. Edwina is extremely unhappy in this relationship, however due to being emotionally dependent on Zack, she feels trapped and unable to leave the relationship. {{RoundBoxBottom}} This chapter aims {{huh}} to the significant link between abusive relationships and emotional dependency; The Australian Bureau of Statistics 2022 defines partner emotional abuse as “when a person is subjected to certain behaviours or actions that are aimed at preventing or controlling their behaviour, causing them emotional harm or fear”.<ref>{{Cite web|url=https://www.abs.gov.au/articles/domestic-violence-experiences-partner-emotional-abuse#cite-window1.|title=Domestic Violence: Experiences of Partner Emotional Abuse {{!}} Australian Bureau of Statistics|date=2022-08-24|website=www.abs.gov.au|language=en|access-date=2024-11-07}}</ref> (see Figure 1). The document further highlights that these actions are "characterised in nature by their intent to manipulate, control, isolate or intimidate the person they are aimed at". Emotional dependency can be referred to as “a chronic pattern of unmet affective demands, which individuals desperately seek to meet through close interpersonal relationships”. <ref>{{Cite web|url=https://scholar.google.com/scholar_lookup?title=Dependencia%20emocional.%20Caracter%C3%ADsticas%20y%20tratamiento&author=J%20Castell%C3%B3&publication_year=2005&|title=Google Scholar|website=scholar.google.com|access-date=2024-11-07}}</ref> To further understand the connection between abusive relationships and emotional dependency, this chapter focuses on what specific psychological mechanisms drive emotional dependency, and how these mechanisms perpetuate abusive relationships. (see Figure 2) {{robelbox|theme=9|title=Focus questions:|icon=Nuvola_apps_kwrite.png|iconwidth=48px}} <div style="{{Robelbox/pad}}"> * What psychological mechanisms drive emotional dependency? * How do psychological mechanisms perpetuate abusive relationships? * How do individuals remove themselves from abusive relationships? </div> {{Robelbox/close}}[[File:Sunrise lovers.jpg|thumb|Figure 2. Two people in a romantic relationship. Emotional dependency and abuse can be present in these types of relationships.]] == What are some psychological mechanisms that drive emotional dependency? == Psychological mechanisms that significantly drive emotional dependency include attachment theory, low self-esteem, and codependency. Attachment theory is a key psychological mechanism that focuses on different attachment styles that may affect individuals in relationships. Additionally, individuals with low self-esteem tend to seek acceptance from others in order to validate themselves - codependency can complicate this; due to codependent individuals prioritising their partner's needs over their own, it results in individuals being heavily reliant on their relationship for their sense of identity. Overall, these mechanisms significantly promote emotional dependency, can further result in a toxic cycle for individuals. === [[w:Attachment_Theory|Attachment Theory]] === A fundamental psychological mechanism that is linked to emotional dependency is the attachment theory. An accredited psychoanalyst [[w:John_Bowlby|John Bowlby]] established this theory in order to investigate the intimate relationships and bonds between individuals, as well as relationships between parents and children and their link to relationships later in life<ref>Bowlby, J. (1969). ''Attachment and loss'' (No. 79). Random House. </ref>. Bowlby's second novel also explained how individuals are born with an attachment behavioural system which incites them to seek intimacy and closeness to attachment figures <ref>Bowlby J. Attachment and loss, Vol. 1. Attachment (2nd ed.) New York: Basic Books; 1982. https://mindsplain.com/wp-content/uploads/2020/08/ATTACHMENT_AND_LOSS_VOLUME_I_ATTACHMENT.pdf</ref>. Bowlby’s theory critically explores the emotional bonds and relationships between individuals through 4 main attachment styles: ==== Secure Attachment ==== This attachment style involves individuals being capable of setting healthy boundaries, able to feel safe and stable in their relationships with others, has a good sense of self-worth, able to adequately deal with disappointments and obstacles, and can express their thoughts and feelings adequately.{{RoundBoxTop|theme=2}} Case study Stephanie, a 28 year old art teacher, and Toby, a 29 year old business owner, have been together since graduating from university. Both individuals came from families who encouraged emotional communication, which has allowed for them to have a healthy and meaningful relationship. In their relationship, they calmly and effectively communicate their feelings openly, value and respect each other’s independence, and have confidence and trust in one another as they know time apart will not weaken their bond.{{RoundBoxBottom}} ==== Anxious Attachment ==== Anxious attachment is when “individuals worry about being underappreciated or abandoned by their romantic partners”, “are heavily fixated on their partner and their relationship”, and crave being “closer to their partners emotionally to feel more secure”. Anxious individuals also tend to have low self-esteem, but think highly of their intimate partners. <ref name=":0">{{Cite journal|last=Simpson|first=Jeffry A|last2=Rholes|first2=W Steven|date=2017-02|title=Adult attachment, stress, and romantic relationships|url=https://linkinghub.elsevier.com/retrieve/pii/S2352250X16300306|journal=Current Opinion in Psychology|language=en|volume=13|pages=19–24|doi=10.1016/j.copsyc.2016.04.006}}</ref> Simpson, J.A and Rholes, W.S. further researched through an “Attachment Diathesis-Stress Process Model” how people who have an anxious attachment think and behave when they encounter stress and/or arguments with their romantic partners. The key findings when researching this that the study found when anxious individuals are extremely distraught when removed or have to consider being removed from their partner, that these individuals display high levels of stress and dysfunctional behaviours when encountering relationship problems, and how certain events when transitioning to parenthood may incite or increase the main concerns of individuals with this attachment style.<ref name=":0" /> The study explores in depth of insecure attachment styles, limitations of the study that can be identified are that the study heavily focuses on specific stress situations which may not fully present the extent of stress responses that can be seen in these relationships. <ref name=":0" />{{RoundBoxTop|theme=2}} Case study Holly, a 21 year old university student, and Ryan, a 22 year old electrician have been in a relationship for 7 months. Holly has an anxious attachment style which plays a role in their relationship. An example of this in their relationship could include a situation where Ryan has explained to Holly that he is going to take her to a nice dinner out, however he has to be asleep by 10pm to wake up early for work. They have a nice night together, however as time grows closer to 10pm and Ryan reminds Holly he has to sleep soon, it makes Holly question if he even wants to hang out with her and even wants to be with her, even though he has a valid reason to go to bed early. This leads to Holly panicking and having an emotional outburst stating “you act like you don’t even want to hang out with me anymore!” and “all you do is prioritise work over me!”{{RoundBoxBottom}} ==== Avoidant-Dismissive Attachment ==== This attachment style mainly consists of individuals facing challenges with emotional intimacy<ref name=":0" /> (Simpson, J.A and Rholes, W.S., 2017), and being heavily independent and not fond of the idea of being too romantically invested in someone<ref>{{Cite journal|last=Pettigrew|first=Thomas F.|date=2016-01-04|title=In Pursuit of Three Theories: Authoritarianism, Relative Deprivation, and Intergroup Contact|url=https://www.annualreviews.org/doi/10.1146/annurev-psych-122414-033327|journal=Annual Review of Psychology|language=en|volume=67|issue=1|pages=1–21|doi=10.1146/annurev-psych-122414-033327|issn=0066-4308}}</ref>. This can be demonstrated through a relevant study by Mikulincer M and Shaver PR (2010), where the main focus is on investigating the attachment theory, including avoidant attachment where it found individuals who scored high with this attachment style tend to exhibit strategies to deactivate the relationship, such as not allowing their partner to be close to them, distancing themselves from their partner and not communicating what they want in a relationship.<ref>Mikulincer, M., & Shaver, P. R. (2010). ''Attachment in adulthood: Structure, dynamics, and change''. Guilford Publications.</ref> The topic of debate to how avoidant attachment styles change is explored in a longitudinal study; the study explored the different levels of attachment change over time and how avoidant attachment levels tend to “start low” in childhood” however “gradually increase over time”, in contrast to anxious attachment styles where they “start and remain low across time”.<ref>{{Cite journal|last=Theisen|first=Jaclyn C.|last2=Fraley|first2=R. Chris|last3=Hankin|first3=Benjamin L.|last4=Young|first4=Jami F.|last5=Chopik|first5=William J.|date=2018-06-01|title=How do attachment styles change from childhood through adolescence? Findings from an accelerated longitudinal Cohort study|url=https://www.sciencedirect.com/science/article/abs/pii/S0092656618300333?via=ihub|journal=Journal of Research in Personality|volume=74|pages=141–146|doi=10.1016/j.jrp.2018.04.001|issn=0092-6566}}</ref>{{RoundBoxTop|theme=2}} Case study Dan, a 20 year old rugby league player, and Rita, a 21 year old university student, have been seeing each other for 4 months now. Dan is well-known for having usual romantic flings and can never commit to anyone fully, due to the idea of relying on or being relied on is suffocating to him. So when Rita hints to him of when he is going to officially ask her out, he dismisses it and replies with “can we not talk about this please? Like why do you want to rush things, like can’t you just see how things go?” Additionally, Dan enjoys spending time with Rita however likes to keep to his routine, such as playing rugby and going out drinking with friends every weekend, separate from their relationship - one day, Rita asked Dan if she can come watch his rugby game then afterwards they go out to dinner together to celebrate. Dan replies with “no that’s a bit weird for you to come to my games, you’re not even my girlfriend. Besides, I go out every weekend with my friends after the games so it’s not going to work”. This is degrading to Rita who feels like Danl is emotionally distant and is unwilling to completely invest in being in a relationship with her.{{RoundBoxBottom}} ==== Disorganised-Disorientated Attachment ==== Disorganised attachment stems from childhood where the “child's attachment figure or parent is observably frightened or frightening when a child needs comforting or reassurance”.<ref>{{Cite book|url=https://www.sciencedirect.com/science/article/abs/pii/B9780123750006000872|title=Child Abuse|last=Lawler|first=M. J.|last2=Talbot|first2=E. B.|date=2012-01-01|publisher=Academic Press|isbn=978-0-08-096180-4|editor-last=Ramachandran|editor-first=V. S.|location=San Diego|pages=460–466}}</ref> These characteristics later appear in adult relationships where individuals have a “severe disturbance in threat responding, social cognition and identity development” which can further lead to the “ risk for personality disorders”.<ref name=":1">{{Cite journal|last=Beeney|first=Joseph E.|last2=Wright|first2=Aidan G. C.|last3=Stepp|first3=Stephanie D.|last4=Hallquist|first4=Michael N.|last5=Lazarus|first5=Sophie A.|last6=Beeney|first6=Julie R. S.|last7=Scott|first7=Lori N.|last8=Pilkonis|first8=Paul A.|date=2017-07|title=Disorganized attachment and personality functioning in adults: A latent class analysis.|url=https://doi.apa.org/doi/10.1037/per0000184|journal=Personality Disorders: Theory, Research, and Treatment|language=en|volume=8|issue=3|pages=206–216|doi=10.1037/per0000184|issn=1949-2723|pmc=PMC5026862|pmid=26986959}}</ref> A 2017 latent class analysis focused on researching the disorganised attachment style in adults in order to provide a clear understanding of “severity and stylistic differences in disorganised attachment than has been previously articulated”. The study found through the following attachment styles: secure, insecure, disorganised-oscillating, and disorganised-impoverished that the disorganised-oscillating class was “characterised by elevations on contradictory and preoccupied styles”, while the disorganised-impoverished class portrayed signs of “impoverished and dismissive styles”. This further enables readers to view the different attachment disorganisation patterns in adults, which differentiate based on severity and interpersonal styles. Overall, the study highly recommends early intervention for caregivers in order to prevent this attachment style developing.<ref name=":1" /> {{RoundBoxTop|theme=2}} Case study Angelina, a 23 year old public servant, and Ed, a 24 year old physiotherapist have been in a relationship for 9 months now. Angelina has developed this attachment style, which has caused a strain on her and Ed’s relationship: For example, Angelina often moves from wanting to be very close to Ed to pushing him away when he gets too close. This can be seen one night, at dinner where Angelina tells Ed how much she loves and appreciates him. The next conversation shifts to Ed saying how he has to go on a work AFL trip to help strap players for a month, to which triggers Angelina’s mood to change. She suddenly believes and voices to Ed that he wants to go on this work trip to purposefully avoid her, and that he doesn’t want to be around her anymore.{{RoundBoxBottom}}{{Robelbox|theme=6|title=Topic Review: Quiz Time!|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {What attachment style is most likely to be upset when removed from a partner?} - Avoidant + Anxious - Disorganised - Applies to any of the above {What is the Attachment Theory about?} - Focuses on different attachment styles - Focuses on romantic relationships and how they link to their childhood - Links to the concept of emotional dependency + Applies to any of the above </quiz> </div> {{Robelbox-close}}[[File:Is this me mental disorder of looking.jpg|thumb|Figure 3. A person looking into the mirror not liking their image and questioning their self-esteem.]] === Low self-esteem === A primary psychological device that influences emotional dependency is '''low [[w:Self-esteem|self-esteem.]]'''Self-esteem can be defined as “a person's positive or negative attitude toward oneself as well as a person's favourable or unfavourable view of himself or herself”. It can also be characterised as an individual considering themselves as “worthy or unworthy”.<ref>{{Cite journal|last=Mittal|first=Ella|last2=Rani|first2=Tamanna|date=2022-10-16|title=Association Between Secure Attachment Style and Subjective Well-being: Examining the sequential mediation effects|url=https://journal.achsm.org.au/index.php/achsm/article/view/1549|journal=Asia Pacific Journal of Health Management|language=en|volume=17|issue=2|doi=10.24083/apjhm.v17i2.1549|issn=2204-3136}}</ref> (See Figure 3). Some low self-esteem components that incite emotional dependency include: ===== '''Seeking external validation:''' ===== A 2019 observational study aimed to prove that low self-esteem was linked to the use and consequences of indirect support seeking during interactions in romantic relationships. The study proved that people with low self-esteem tend to “utilise indirect support” which may backfire “negative partner support” instead, and further “undermine the feelings of acceptance that low self-esteem individuals crave”, overall demonstrating how low self-esteem individuals can be emotionally dependent through heavily desiring external validation.<ref>{{Cite journal|last=Don|first=Brian P.|last2=Girme|first2=Yuthika U.|last3=Hammond|first3=Matthew D.|date=2019-07|title=Low Self-Esteem Predicts Indirect Support Seeking and Its Relationship Consequences in Intimate Relationships|url=https://pubmed.ncbi.nlm.nih.gov/30465478/|journal=Personality & Social Psychology Bulletin|volume=45|issue=7|pages=1028–1041|doi=10.1177/0146167218802837|issn=1552-7433|pmid=30465478}}</ref> [[File:Lonely boy.jpg|thumb|Figure 4. Person sitting alone, which is a key component of what people with low self-esteem fear.]] ===== '''Fear of [[w:Abandonment_(emotional)|abandonment]] and [[w:_Social_rejection|rejection]]:''' ===== According to a 2022 paper, low self-esteem and feelings of worthlessness are typically seen in individuals who have abandonment and rejection issues. The paper outlines how these individuals often internalise abandonment and rejection, believing it was their fault that they are inadequate of being loved and cared about. This negative perception of themselves can lead to a permanent sense of inadequacy and self-doubt, which can impact various areas of their lives, such as their perspective of their careers, platonic relationships, and romantic relationships.<ref>{{Cite journal|last=Cruz|first=Daniel|last2=Lichten|first2=Matthew|last3=Berg|first3=Kevin|last4=George|first4=Preethi|date=2022-07-22|title=Developmental trauma: Conceptual framework, associated risks and comorbidities, and evaluation and treatment|url=https://www.frontiersin.org/journals/psychiatry/articles/10.3389/fpsyt.2022.800687/full|journal=Frontiers in Psychiatry|language=English|volume=13|doi=10.3389/fpsyt.2022.800687|issn=1664-0640|pmc=PMC9352895|pmid=35935425}}</ref>. (See Figure 4). ===== '''Difficulty setting boundaries and prioritising personal needs:''' ===== A recent 2023 study found how there is little research on individuals setting boundaries in romantic situations, so researchers investigated the "correlations between mental boundaries, self-esteem, and social support". The study found that there were "significant negative correlations between mental boundaries, self-esteem, and social support" and that "mental boundaries and social support independently predicted self-esteem" in relationships, further demonstrating what factors contribute to individual's self esteem. The study additionally discussed that "individuals with thinner boundaries have lower self-esteem" and "individuals with more substantial levels of social support typically have higher self-esteem". The study concluded that its research is a good start to researching boundary setting in relationships, however identifies the limitations of the study; the survey could have surveyed a more diverse population of individuals, and lack of prior research on this topic. The study concludes that allows audience to understand the difference between "thick and thin boundaries", in order to establish higher levels of self-esteem. <ref>{{Cite journal|last=Mathe|first=John R.|last2=Kelly|first2=William E.|date=2023-09|title=Mental Boundaries Relationship with Self-Esteem and Social Support: New Findings for Mental Boundaries Research|url=https://journals.sagepub.com/doi/10.1177/02762366231158274|journal=Imagination, Cognition and Personality|language=en|volume=43|issue=1|pages=29–41|doi=10.1177/02762366231158274|issn=0276-2366}}</ref> === [[w:Codependency|Codependency]] === [[File:BPD 1.png|thumb|Figure 5. Depicts a person with chasing after another person, which clearly shows codependency.]]A major psychological mechanism that causes emotional dependency is codependency. Codependency is defined as a concept that "explains imbalanced relationships where one person enables another person's self-destructive behaviour, such as addiction, poor mental health, immaturity, irresponsibility, or under-achievement." <ref>{{Cite journal|date=2024-11-10|title=Codependency|url=https://en.wikipedia.org/wiki/Codependency|journal=Wikipedia|language=en}}</ref> Codependent relationships can be also be defined as "a dysfunctional helping relationship where one person supports or enables the other person’s addiction, poor mental health, immaturity, irresponsibility, or under-achievement".<ref name=":2">{{Cite web|url=https://bpdfamily.com/content/codependency-codependent-relationships|title=Codependency and Codependent Relationships|last=Johnson|first=R. Skip|date=2018-05-13|website=Borderline Personality Disorder|language=en|access-date=2024-11-10}}</ref> Both the enabler and enabled of the relationship tend to suffer from emotional dependency; the enabler feel the need for "people to validate them" in order to "find their own worth and identity", so through being in a codependent relationship, it "satisfies the need to feel competent and low self-esteem is boosted by comparing oneself to the dysfunctional partner". In contrast, the enabled, due to their lack of adequate functioning, feel fulfilled and accepted through being in a codependent relationship as they are "highly dependant on the enabler to satisfy [their] needs", which can be damaging for the enabled as it prevents them from "matur[ing] or advancing their life skills".<ref name=":2" /> == How do psychological mechanisms perpetuate abusive relationships? == [[File:Cycle of Abuse.png|thumb|512x512px|Figure 6. A diagram of the cycle of abuse. Intermittent reinforcement can further continue this cycle.]] A key mechanism that maintains abusive relationships is '''trauma bonding'''. Trauma bonding, which is where a person forms a deep emotional attachment that arises from the cycle of abuse. <ref name=":3">{{Cite journal|last=Dutton|first=Donald G.|last2=Painter|first2=Susan|date=1993-01|title=Emotional Attachments in Abusive Relationships: A Test of Traumatic Bonding Theory|url=http://connect.springerpub.com/lookup/doi/10.1891/0886-6708.8.2.105|journal=Violence and Victims|language=en|volume=8|issue=2|pages=105–120|doi=10.1891/0886-6708.8.2.105|issn=0886-6708}}</ref> The two key elements that significantly contribute to trauma bonding are "a power imbalance and intermittent reward and punishment". <ref name=":3" /> ==== Intermittent reinforcement ==== Intermittent reinforcement consists "schedules in which a particular behaviour produces a particular consequence, but not every time the behaviour occurs". <ref>{{Cite book|url=https://linkinghub.elsevier.com/retrieve/pii/B9780128094082000027|title=Chapter 2 - Autism Spectrum Disorder|last=Tarbox|first=Jonathan|last2=Tarbox|first2=Courtney|date=2017-01-01|publisher=Academic Press|isbn=978-0-12-809408-2|editor-last=Tarbox|editor-first=Jonathan|location=San Diego|pages=11–18|doi=10.1016/b978-0-12-809408-2.00002-7|editor-last2=Tarbox|editor-first2=Courtney}}</ref> This can be demonstrated in relationships through continuous cruel treatment with occasional moments of random affection. Research outlines how this unpredictably keeps victims craving and clinging onto occasional moments of affection, which is very similar to someone gambling in hope that they'll win. An example of this can include when the perpetrator gives out "rewards such as affection, a compliment, or gifts sporadically and unpredictably throughout the abuse cycle", which allows victim to remain trapped in this vicious cycle. <ref>{{Cite web|url=https://psychcentral.com/blog/recovering-narcissist/2019/03/narcissists-use-trauma-bonding-and-intermittent-reinforcement-to-get-you-addicted-to-them-why-abuse-survivors-stay|title=Narcissists Use Trauma Bonding and Intermittent Reinforcement To Get You Addicted To Them: Why Abuse Survivors Stay|date=2019-03-31|website=Psych Central|language=en|access-date=2024-11-10}}</ref> A relevant study in relation to this explored how the traumatic bonding theory has significant links to intermittent abuse, and how long it may take for the victim's symptoms attachment and trauma symptoms to no longer persist. The study was conducted on 75 women who had recently left an abusive relationship, which demonstrated how the time that it took for women to have reduced symptoms depended majorly on the extent of intermittent reinforcement and power differentials. The study overall found attachment symptoms decreased by 27% after six months, which further demonstrates the serious impact that intermittent reinforcement plays in relationships.<ref name=":3" /> === L[[w:Learned_helplessness|earned helplessness]] === Learned helplessness is characterised as “behaviour exhibited by a subject after enduring repeated aversive stimuli beyond their control”.<ref>{{Cite journal|last=Rakovec-Felser|first=Zlatka|date=2014-11-06|title=Domestic violence and abuse in intimate relationship from public health perspective|url=https://healthpsychologyresearch.openmedicalpublishing.org/article/22398|journal=Health Psychology Research|language=en|volume=2|issue=3|doi=10.4081/hpr.2014.1821|pmc=PMC4768593|pmid=26973948}}</ref> Learned helplessness can be demonstrated in relationships through victims being submissive to their partners and refusing to leave the relationship that is abusive.<ref>Torres Ruiz, N. (2021). ''Learned Helplessness and Domestic Violence Learned Helplessness and Domestic Violence Part of the Bilingual, Multilingual, and Multicultural Education Commons, Other Education Commons, and the Secondary Education Commons''. [https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1216&context=ncpacapstone. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1216&context=ncpacapstone.]</ref> A relevant 2014 study explored the extent of domestic violence and abuse in intimate relationships through observing survey data; the study found that learned helplessness plays a crucial role in the vicious cycle of abuse, stating “the perpetrator alternates between violent, abusive and apologetic behaviour with apparently heartfelt promises to change”. <ref>{{Cite journal|last=Rakovec-Felser|first=Zlatka|date=2014-11-06|title=Domestic violence and abuse in intimate relationship from public health perspective|url=https://healthpsychologyresearch.openmedicalpublishing.org/article/22398|journal=Health Psychology Research|language=en|volume=2|issue=3|doi=10.4081/hpr.2014.1821|pmc=PMC4768593|pmid=26973948}}</ref> Another key study demonstrated how learned helplessness can result in traumatic bonding with the perpetrator, which can develop into serious medical conditions such as "Stockholm Syndrome", or "Battered Woman Syndrome". The study also highlighted how the affects of learned helplessness in relationships can cause the victim to "completely lose their sense of self and system of meaning and to instead adopt their abuser’s view of the world".<ref>{{Cite web|url=https://did-research.org/origin/d-attachment/traumatic_bonding|title=Traumatic Bonding|website=DID-Research.org|access-date=2024-11-10}}</ref> === [[w:Gaslighting|Gaslighting]] and [[w:Manipulation|manipulation]] === A key mechanism that maintains abusive relationships is gaslighting and manipulation. ==== Gaslighting ==== Gaslighting is referred to as "a type of psychological abuse aimed at making victims seem or feel “crazy", which is often seen in romantic relationships. <ref>{{Cite journal|last=Sweet|first=Paige L.|date=2019-10|title=The Sociology of Gaslighting|url=https://journals.sagepub.com/doi/10.1177/0003122419874843|journal=American Sociological Review|language=en|volume=84|issue=5|pages=851–875|doi=10.1177/0003122419874843|issn=0003-1224}}</ref> It can also be defined as a type of abuse where "a sane and rational survivor is convinced of their own epistemic incompetence on false pretences by a perpetrator".<ref name=":4">{{Cite journal|last=Klein|first=Willis|last2=Li|first2=Sherry|last3=Wood|first3=Suzanne|date=2023-12|title=A qualitative analysis of gaslighting in romantic relationships|url=https://onlinelibrary.wiley.com/doi/10.1111/pere.12510|journal=Personal Relationships|language=en|volume=30|issue=4|pages=1316–1340|doi=10.1111/pere.12510|issn=1350-4126}}</ref> A recent qualitative analysis was conducted to study the characteristics of gaslighting in relationships. The study surveyed 65 individuals who stated that they had been in an intimate relationship that involved gaslighting. The study asked the individuals questions in relation to this such as describing examples of this abuse tactic occurring in their relationship, different characteristics of their relationships, and what were the mental health repercussions of this abuse occurring. Results showed "gaslighting victimisation was associated with a diminished sense of self, mistrust of others, and on occasion, post-traumatic growth" and those who recovered from gaslighting often emphasised the importance of separation from the perpetrator, prioritisation of healthier relationships, and engaging in meaningful and re-embodying activities". The study emphasises the need for further research on gaslighting in relationships and how victims can recover from this form of abuse, which can overall lead to minimise this type of abuse occurring and providing appropriate treatment to victims. <ref name=":4" /> ==== Manipulation ==== Manipulation is defined as “an action designed to influence or [[w:Control|control]] another, usually in an underhanded or unfair manner which facilitates one's personal aims" (see Figure 7). [[File:Manipulation-.png|thumb|Figure 7. A hand controlling which alludes to someone being controlled, which is a manipulation tactic.]] {| class="wikitable" |+Types of Manipulation !Having Control over Location |Manipulators may physically take victims to places they are unfamiliar with, or emotionally try to bring victims out of their comfort zone. The abuser does this in order to feel a sense of control. |- !Manipulating Facts |Manipulators will be dishonest with victims, make excuses, and blame them. Occasionally, these types of abusers will share some truth to their facts to strategically manipulate you. |- !Being [[w:Passive-Aggressive_behavior|Passive-Aggressive]] |Manipulators will voice subtle, indirect negative feelings towards victims to undermine them. |- !Guilt and Sympathy |Manipulators tend to make their victims feel guilty or have sympathy towards them in order to receive what they want. |- !Use of Silent Treatment |Abusers use this withdrawal tactic to punish their victims |- !Use of Comparison |Abusers may compare their victims to someone else to further evoke an upsetting or uncomfortable reaction from victims, or make them feel insecure about something. |- ![[w:Love_bombing|Love-bombing]] |Manipulators use this common abuse tactic to give enormous amounts of praise and affection to speed up their relationship between them and their victim. This causes the victim to be heavily attached to their abuser, which allows for the abuser to easily discard them later on. |} {{Robelbox|theme=6|title=Topic Review: Quiz Time!|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {Who is negatively affected in a codependent relationship?} - The enabler - The enabled + Both {What is the main reason why victims stay in learned helplessness relationships?} - They believe they deserve the abuse they're receiving + They believe the perpetrator can change their behaviour as they have apologised or given them gifts - They stay because they feel lonely and no one will love them </quiz> </div> {{Robelbox-close}} == How do individuals remove themselves from abusive relationships? == According to an [https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Australian psychology article], some ways to break free from emotional dependency to form healthy relationships include: # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Identifying your Attachment Style]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Improving your Self-Esteem]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Spending Time with Friends and Family]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Having Calm and Honest Communication with your Partner]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Setting and Upholding Healthy Boundaries]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Working with a Therapist through these Issues]''' == Conclusion == This chapter establishes the significant connection between emotional dependency and abusive relationships, which is key for creating healthier relationships with others. Through being aware of psychological mechanisms, such as attachment theory, low self-esteem, and codependency, it allows audiences to adequately understand how these devices drive emotional dependency. Additionally, the article explores certain crucial mechanisms that incite abuse, such as trauma bonding, learned helplessness, gaslighting, and manipulation. This valuable information also enables individuals to be educated on this specific topic and to start working on strategies to remove themselves from emotional dependency and unhealthy relationships. It is through these devices that individuals are capable in understanding the crucial link between emotional dependency and unhealthy relationships in order from them to foster healthier romantic relationships. == External Links == https://dictionary.cambridge.org/us/dictionary/english/manipulation https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ https://barbaraoakley.com/wp-content/uploads/2016/12/000Chapter-1-Pathological-Altruism-Oakley-Knafo-McGrath.pdf https://www.healthline.com/health/mental-health/trauma-bonding#takeaway https://www.helpguide.org/relationships/social-connection/attachment-and-adult-relationships https://doi.org/10.1177/0003122419874843 https://www.healthline.com/health/low-self-esteem#defining-low-self-esteem https://en.wikipedia.org/wiki/Learned_helplessness [http://www.community.nsw.gov.au/docs_menu/parents_carers_and_families/domestic_and_family_violence/dv_line.html/ Domestic Violence NSW] == See also == * [[w:Psychological_abuse|Psychological abuse]] (Wikipedia) * [[Motivation and emotion/Book/2019/Emotional abuse|Emotional abuse]] (Book Chapter 2019) * [[Motivation and emotion/Book/2014/Aggression in intimate relationships|Aggression in intimate relationships]] (Book Chapter 2014) == References == [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Abuse]] [[Category:Motivation and emotion/Book/Relationships]] [[Category:Moivation and emotion/Book/Trauma]] hbegnyxhmul3m2otrsy8kxefzcxq70u 2684177 2684176 2024-11-12T10:43:23Z Jtneill 10242 Move see also section up higher 2684177 wikitext text/x-wiki {{title|Abusive relationships and emotional dependency:<br>What psychological mechanisms drive emotional dependency and how does it perpetuate abusive relationships?}} {{MECR3|https://youtu.be/C6RDIcVIdR0}} __TOC__ == Overview == {{RoundBoxTop|theme=2}} [[File:NounProject Abuse.png|thumb|Figure 1. Depicting two figures; one of them is being abused by the other.]] ; Case study Edwina has been in a romantic relationship with Zack for 2 months now, where in the beginning he appeared to be a good person, however over time she has come to realise he is the complete opposite; Zack has slowly isolated Edwina from her friends and family, heavily controls her social media, forbids her to go places without his permission, even if it's the grocery store, and criticises and insults her if she goes against his wishes. Edwina is extremely unhappy in this relationship, however due to being emotionally dependent on Zack, she feels trapped and unable to leave the relationship. {{RoundBoxBottom}} This chapter aims {{huh}} to the significant link between abusive relationships and emotional dependency; The Australian Bureau of Statistics 2022 defines partner emotional abuse as “when a person is subjected to certain behaviours or actions that are aimed at preventing or controlling their behaviour, causing them emotional harm or fear”.<ref>{{Cite web|url=https://www.abs.gov.au/articles/domestic-violence-experiences-partner-emotional-abuse#cite-window1.|title=Domestic Violence: Experiences of Partner Emotional Abuse {{!}} Australian Bureau of Statistics|date=2022-08-24|website=www.abs.gov.au|language=en|access-date=2024-11-07}}</ref> (see Figure 1). The document further highlights that these actions are "characterised in nature by their intent to manipulate, control, isolate or intimidate the person they are aimed at". Emotional dependency can be referred to as “a chronic pattern of unmet affective demands, which individuals desperately seek to meet through close interpersonal relationships”. <ref>{{Cite web|url=https://scholar.google.com/scholar_lookup?title=Dependencia%20emocional.%20Caracter%C3%ADsticas%20y%20tratamiento&author=J%20Castell%C3%B3&publication_year=2005&|title=Google Scholar|website=scholar.google.com|access-date=2024-11-07}}</ref> To further understand the connection between abusive relationships and emotional dependency, this chapter focuses on what specific psychological mechanisms drive emotional dependency, and how these mechanisms perpetuate abusive relationships. (see Figure 2) {{robelbox|theme=9|title=Focus questions:|icon=Nuvola_apps_kwrite.png|iconwidth=48px}} <div style="{{Robelbox/pad}}"> * What psychological mechanisms drive emotional dependency? * How do psychological mechanisms perpetuate abusive relationships? * How do individuals remove themselves from abusive relationships? </div> {{Robelbox/close}}[[File:Sunrise lovers.jpg|thumb|Figure 2. Two people in a romantic relationship. Emotional dependency and abuse can be present in these types of relationships.]] == What are some psychological mechanisms that drive emotional dependency? == Psychological mechanisms that significantly drive emotional dependency include attachment theory, low self-esteem, and codependency. Attachment theory is a key psychological mechanism that focuses on different attachment styles that may affect individuals in relationships. Additionally, individuals with low self-esteem tend to seek acceptance from others in order to validate themselves - codependency can complicate this; due to codependent individuals prioritising their partner's needs over their own, it results in individuals being heavily reliant on their relationship for their sense of identity. Overall, these mechanisms significantly promote emotional dependency, can further result in a toxic cycle for individuals. === [[w:Attachment_Theory|Attachment Theory]] === A fundamental psychological mechanism that is linked to emotional dependency is the attachment theory. An accredited psychoanalyst [[w:John_Bowlby|John Bowlby]] established this theory in order to investigate the intimate relationships and bonds between individuals, as well as relationships between parents and children and their link to relationships later in life<ref>Bowlby, J. (1969). ''Attachment and loss'' (No. 79). Random House. </ref>. Bowlby's second novel also explained how individuals are born with an attachment behavioural system which incites them to seek intimacy and closeness to attachment figures <ref>Bowlby J. Attachment and loss, Vol. 1. Attachment (2nd ed.) New York: Basic Books; 1982. https://mindsplain.com/wp-content/uploads/2020/08/ATTACHMENT_AND_LOSS_VOLUME_I_ATTACHMENT.pdf</ref>. Bowlby’s theory critically explores the emotional bonds and relationships between individuals through 4 main attachment styles: ==== Secure Attachment ==== This attachment style involves individuals being capable of setting healthy boundaries, able to feel safe and stable in their relationships with others, has a good sense of self-worth, able to adequately deal with disappointments and obstacles, and can express their thoughts and feelings adequately.{{RoundBoxTop|theme=2}} Case study Stephanie, a 28 year old art teacher, and Toby, a 29 year old business owner, have been together since graduating from university. Both individuals came from families who encouraged emotional communication, which has allowed for them to have a healthy and meaningful relationship. In their relationship, they calmly and effectively communicate their feelings openly, value and respect each other’s independence, and have confidence and trust in one another as they know time apart will not weaken their bond.{{RoundBoxBottom}} ==== Anxious Attachment ==== Anxious attachment is when “individuals worry about being underappreciated or abandoned by their romantic partners”, “are heavily fixated on their partner and their relationship”, and crave being “closer to their partners emotionally to feel more secure”. Anxious individuals also tend to have low self-esteem, but think highly of their intimate partners. <ref name=":0">{{Cite journal|last=Simpson|first=Jeffry A|last2=Rholes|first2=W Steven|date=2017-02|title=Adult attachment, stress, and romantic relationships|url=https://linkinghub.elsevier.com/retrieve/pii/S2352250X16300306|journal=Current Opinion in Psychology|language=en|volume=13|pages=19–24|doi=10.1016/j.copsyc.2016.04.006}}</ref> Simpson, J.A and Rholes, W.S. further researched through an “Attachment Diathesis-Stress Process Model” how people who have an anxious attachment think and behave when they encounter stress and/or arguments with their romantic partners. The key findings when researching this that the study found when anxious individuals are extremely distraught when removed or have to consider being removed from their partner, that these individuals display high levels of stress and dysfunctional behaviours when encountering relationship problems, and how certain events when transitioning to parenthood may incite or increase the main concerns of individuals with this attachment style.<ref name=":0" /> The study explores in depth of insecure attachment styles, limitations of the study that can be identified are that the study heavily focuses on specific stress situations which may not fully present the extent of stress responses that can be seen in these relationships. <ref name=":0" />{{RoundBoxTop|theme=2}} Case study Holly, a 21 year old university student, and Ryan, a 22 year old electrician have been in a relationship for 7 months. Holly has an anxious attachment style which plays a role in their relationship. An example of this in their relationship could include a situation where Ryan has explained to Holly that he is going to take her to a nice dinner out, however he has to be asleep by 10pm to wake up early for work. They have a nice night together, however as time grows closer to 10pm and Ryan reminds Holly he has to sleep soon, it makes Holly question if he even wants to hang out with her and even wants to be with her, even though he has a valid reason to go to bed early. This leads to Holly panicking and having an emotional outburst stating “you act like you don’t even want to hang out with me anymore!” and “all you do is prioritise work over me!”{{RoundBoxBottom}} ==== Avoidant-Dismissive Attachment ==== This attachment style mainly consists of individuals facing challenges with emotional intimacy<ref name=":0" /> (Simpson, J.A and Rholes, W.S., 2017), and being heavily independent and not fond of the idea of being too romantically invested in someone<ref>{{Cite journal|last=Pettigrew|first=Thomas F.|date=2016-01-04|title=In Pursuit of Three Theories: Authoritarianism, Relative Deprivation, and Intergroup Contact|url=https://www.annualreviews.org/doi/10.1146/annurev-psych-122414-033327|journal=Annual Review of Psychology|language=en|volume=67|issue=1|pages=1–21|doi=10.1146/annurev-psych-122414-033327|issn=0066-4308}}</ref>. This can be demonstrated through a relevant study by Mikulincer M and Shaver PR (2010), where the main focus is on investigating the attachment theory, including avoidant attachment where it found individuals who scored high with this attachment style tend to exhibit strategies to deactivate the relationship, such as not allowing their partner to be close to them, distancing themselves from their partner and not communicating what they want in a relationship.<ref>Mikulincer, M., & Shaver, P. R. (2010). ''Attachment in adulthood: Structure, dynamics, and change''. Guilford Publications.</ref> The topic of debate to how avoidant attachment styles change is explored in a longitudinal study; the study explored the different levels of attachment change over time and how avoidant attachment levels tend to “start low” in childhood” however “gradually increase over time”, in contrast to anxious attachment styles where they “start and remain low across time”.<ref>{{Cite journal|last=Theisen|first=Jaclyn C.|last2=Fraley|first2=R. Chris|last3=Hankin|first3=Benjamin L.|last4=Young|first4=Jami F.|last5=Chopik|first5=William J.|date=2018-06-01|title=How do attachment styles change from childhood through adolescence? Findings from an accelerated longitudinal Cohort study|url=https://www.sciencedirect.com/science/article/abs/pii/S0092656618300333?via=ihub|journal=Journal of Research in Personality|volume=74|pages=141–146|doi=10.1016/j.jrp.2018.04.001|issn=0092-6566}}</ref>{{RoundBoxTop|theme=2}} Case study Dan, a 20 year old rugby league player, and Rita, a 21 year old university student, have been seeing each other for 4 months now. Dan is well-known for having usual romantic flings and can never commit to anyone fully, due to the idea of relying on or being relied on is suffocating to him. So when Rita hints to him of when he is going to officially ask her out, he dismisses it and replies with “can we not talk about this please? Like why do you want to rush things, like can’t you just see how things go?” Additionally, Dan enjoys spending time with Rita however likes to keep to his routine, such as playing rugby and going out drinking with friends every weekend, separate from their relationship - one day, Rita asked Dan if she can come watch his rugby game then afterwards they go out to dinner together to celebrate. Dan replies with “no that’s a bit weird for you to come to my games, you’re not even my girlfriend. Besides, I go out every weekend with my friends after the games so it’s not going to work”. This is degrading to Rita who feels like Danl is emotionally distant and is unwilling to completely invest in being in a relationship with her.{{RoundBoxBottom}} ==== Disorganised-Disorientated Attachment ==== Disorganised attachment stems from childhood where the “child's attachment figure or parent is observably frightened or frightening when a child needs comforting or reassurance”.<ref>{{Cite book|url=https://www.sciencedirect.com/science/article/abs/pii/B9780123750006000872|title=Child Abuse|last=Lawler|first=M. J.|last2=Talbot|first2=E. B.|date=2012-01-01|publisher=Academic Press|isbn=978-0-08-096180-4|editor-last=Ramachandran|editor-first=V. S.|location=San Diego|pages=460–466}}</ref> These characteristics later appear in adult relationships where individuals have a “severe disturbance in threat responding, social cognition and identity development” which can further lead to the “ risk for personality disorders”.<ref name=":1">{{Cite journal|last=Beeney|first=Joseph E.|last2=Wright|first2=Aidan G. C.|last3=Stepp|first3=Stephanie D.|last4=Hallquist|first4=Michael N.|last5=Lazarus|first5=Sophie A.|last6=Beeney|first6=Julie R. S.|last7=Scott|first7=Lori N.|last8=Pilkonis|first8=Paul A.|date=2017-07|title=Disorganized attachment and personality functioning in adults: A latent class analysis.|url=https://doi.apa.org/doi/10.1037/per0000184|journal=Personality Disorders: Theory, Research, and Treatment|language=en|volume=8|issue=3|pages=206–216|doi=10.1037/per0000184|issn=1949-2723|pmc=PMC5026862|pmid=26986959}}</ref> A 2017 latent class analysis focused on researching the disorganised attachment style in adults in order to provide a clear understanding of “severity and stylistic differences in disorganised attachment than has been previously articulated”. The study found through the following attachment styles: secure, insecure, disorganised-oscillating, and disorganised-impoverished that the disorganised-oscillating class was “characterised by elevations on contradictory and preoccupied styles”, while the disorganised-impoverished class portrayed signs of “impoverished and dismissive styles”. This further enables readers to view the different attachment disorganisation patterns in adults, which differentiate based on severity and interpersonal styles. Overall, the study highly recommends early intervention for caregivers in order to prevent this attachment style developing.<ref name=":1" /> {{RoundBoxTop|theme=2}} Case study Angelina, a 23 year old public servant, and Ed, a 24 year old physiotherapist have been in a relationship for 9 months now. Angelina has developed this attachment style, which has caused a strain on her and Ed’s relationship: For example, Angelina often moves from wanting to be very close to Ed to pushing him away when he gets too close. This can be seen one night, at dinner where Angelina tells Ed how much she loves and appreciates him. The next conversation shifts to Ed saying how he has to go on a work AFL trip to help strap players for a month, to which triggers Angelina’s mood to change. She suddenly believes and voices to Ed that he wants to go on this work trip to purposefully avoid her, and that he doesn’t want to be around her anymore.{{RoundBoxBottom}}{{Robelbox|theme=6|title=Topic Review: Quiz Time!|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {What attachment style is most likely to be upset when removed from a partner?} - Avoidant + Anxious - Disorganised - Applies to any of the above {What is the Attachment Theory about?} - Focuses on different attachment styles - Focuses on romantic relationships and how they link to their childhood - Links to the concept of emotional dependency + Applies to any of the above </quiz> </div> {{Robelbox-close}}[[File:Is this me mental disorder of looking.jpg|thumb|Figure 3. A person looking into the mirror not liking their image and questioning their self-esteem.]] === Low self-esteem === A primary psychological device that influences emotional dependency is '''low [[w:Self-esteem|self-esteem.]]'''Self-esteem can be defined as “a person's positive or negative attitude toward oneself as well as a person's favourable or unfavourable view of himself or herself”. It can also be characterised as an individual considering themselves as “worthy or unworthy”.<ref>{{Cite journal|last=Mittal|first=Ella|last2=Rani|first2=Tamanna|date=2022-10-16|title=Association Between Secure Attachment Style and Subjective Well-being: Examining the sequential mediation effects|url=https://journal.achsm.org.au/index.php/achsm/article/view/1549|journal=Asia Pacific Journal of Health Management|language=en|volume=17|issue=2|doi=10.24083/apjhm.v17i2.1549|issn=2204-3136}}</ref> (See Figure 3). Some low self-esteem components that incite emotional dependency include: ===== '''Seeking external validation:''' ===== A 2019 observational study aimed to prove that low self-esteem was linked to the use and consequences of indirect support seeking during interactions in romantic relationships. The study proved that people with low self-esteem tend to “utilise indirect support” which may backfire “negative partner support” instead, and further “undermine the feelings of acceptance that low self-esteem individuals crave”, overall demonstrating how low self-esteem individuals can be emotionally dependent through heavily desiring external validation.<ref>{{Cite journal|last=Don|first=Brian P.|last2=Girme|first2=Yuthika U.|last3=Hammond|first3=Matthew D.|date=2019-07|title=Low Self-Esteem Predicts Indirect Support Seeking and Its Relationship Consequences in Intimate Relationships|url=https://pubmed.ncbi.nlm.nih.gov/30465478/|journal=Personality & Social Psychology Bulletin|volume=45|issue=7|pages=1028–1041|doi=10.1177/0146167218802837|issn=1552-7433|pmid=30465478}}</ref> [[File:Lonely boy.jpg|thumb|Figure 4. Person sitting alone, which is a key component of what people with low self-esteem fear.]] ===== '''Fear of [[w:Abandonment_(emotional)|abandonment]] and [[w:_Social_rejection|rejection]]:''' ===== According to a 2022 paper, low self-esteem and feelings of worthlessness are typically seen in individuals who have abandonment and rejection issues. The paper outlines how these individuals often internalise abandonment and rejection, believing it was their fault that they are inadequate of being loved and cared about. This negative perception of themselves can lead to a permanent sense of inadequacy and self-doubt, which can impact various areas of their lives, such as their perspective of their careers, platonic relationships, and romantic relationships.<ref>{{Cite journal|last=Cruz|first=Daniel|last2=Lichten|first2=Matthew|last3=Berg|first3=Kevin|last4=George|first4=Preethi|date=2022-07-22|title=Developmental trauma: Conceptual framework, associated risks and comorbidities, and evaluation and treatment|url=https://www.frontiersin.org/journals/psychiatry/articles/10.3389/fpsyt.2022.800687/full|journal=Frontiers in Psychiatry|language=English|volume=13|doi=10.3389/fpsyt.2022.800687|issn=1664-0640|pmc=PMC9352895|pmid=35935425}}</ref>. (See Figure 4). ===== '''Difficulty setting boundaries and prioritising personal needs:''' ===== A recent 2023 study found how there is little research on individuals setting boundaries in romantic situations, so researchers investigated the "correlations between mental boundaries, self-esteem, and social support". The study found that there were "significant negative correlations between mental boundaries, self-esteem, and social support" and that "mental boundaries and social support independently predicted self-esteem" in relationships, further demonstrating what factors contribute to individual's self esteem. The study additionally discussed that "individuals with thinner boundaries have lower self-esteem" and "individuals with more substantial levels of social support typically have higher self-esteem". The study concluded that its research is a good start to researching boundary setting in relationships, however identifies the limitations of the study; the survey could have surveyed a more diverse population of individuals, and lack of prior research on this topic. The study concludes that allows audience to understand the difference between "thick and thin boundaries", in order to establish higher levels of self-esteem. <ref>{{Cite journal|last=Mathe|first=John R.|last2=Kelly|first2=William E.|date=2023-09|title=Mental Boundaries Relationship with Self-Esteem and Social Support: New Findings for Mental Boundaries Research|url=https://journals.sagepub.com/doi/10.1177/02762366231158274|journal=Imagination, Cognition and Personality|language=en|volume=43|issue=1|pages=29–41|doi=10.1177/02762366231158274|issn=0276-2366}}</ref> === [[w:Codependency|Codependency]] === [[File:BPD 1.png|thumb|Figure 5. Depicts a person with chasing after another person, which clearly shows codependency.]]A major psychological mechanism that causes emotional dependency is codependency. Codependency is defined as a concept that "explains imbalanced relationships where one person enables another person's self-destructive behaviour, such as addiction, poor mental health, immaturity, irresponsibility, or under-achievement." <ref>{{Cite journal|date=2024-11-10|title=Codependency|url=https://en.wikipedia.org/wiki/Codependency|journal=Wikipedia|language=en}}</ref> Codependent relationships can be also be defined as "a dysfunctional helping relationship where one person supports or enables the other person’s addiction, poor mental health, immaturity, irresponsibility, or under-achievement".<ref name=":2">{{Cite web|url=https://bpdfamily.com/content/codependency-codependent-relationships|title=Codependency and Codependent Relationships|last=Johnson|first=R. Skip|date=2018-05-13|website=Borderline Personality Disorder|language=en|access-date=2024-11-10}}</ref> Both the enabler and enabled of the relationship tend to suffer from emotional dependency; the enabler feel the need for "people to validate them" in order to "find their own worth and identity", so through being in a codependent relationship, it "satisfies the need to feel competent and low self-esteem is boosted by comparing oneself to the dysfunctional partner". In contrast, the enabled, due to their lack of adequate functioning, feel fulfilled and accepted through being in a codependent relationship as they are "highly dependant on the enabler to satisfy [their] needs", which can be damaging for the enabled as it prevents them from "matur[ing] or advancing their life skills".<ref name=":2" /> == How do psychological mechanisms perpetuate abusive relationships? == [[File:Cycle of Abuse.png|thumb|512x512px|Figure 6. A diagram of the cycle of abuse. Intermittent reinforcement can further continue this cycle.]] A key mechanism that maintains abusive relationships is '''trauma bonding'''. Trauma bonding, which is where a person forms a deep emotional attachment that arises from the cycle of abuse. <ref name=":3">{{Cite journal|last=Dutton|first=Donald G.|last2=Painter|first2=Susan|date=1993-01|title=Emotional Attachments in Abusive Relationships: A Test of Traumatic Bonding Theory|url=http://connect.springerpub.com/lookup/doi/10.1891/0886-6708.8.2.105|journal=Violence and Victims|language=en|volume=8|issue=2|pages=105–120|doi=10.1891/0886-6708.8.2.105|issn=0886-6708}}</ref> The two key elements that significantly contribute to trauma bonding are "a power imbalance and intermittent reward and punishment". <ref name=":3" /> ==== Intermittent reinforcement ==== Intermittent reinforcement consists "schedules in which a particular behaviour produces a particular consequence, but not every time the behaviour occurs". <ref>{{Cite book|url=https://linkinghub.elsevier.com/retrieve/pii/B9780128094082000027|title=Chapter 2 - Autism Spectrum Disorder|last=Tarbox|first=Jonathan|last2=Tarbox|first2=Courtney|date=2017-01-01|publisher=Academic Press|isbn=978-0-12-809408-2|editor-last=Tarbox|editor-first=Jonathan|location=San Diego|pages=11–18|doi=10.1016/b978-0-12-809408-2.00002-7|editor-last2=Tarbox|editor-first2=Courtney}}</ref> This can be demonstrated in relationships through continuous cruel treatment with occasional moments of random affection. Research outlines how this unpredictably keeps victims craving and clinging onto occasional moments of affection, which is very similar to someone gambling in hope that they'll win. An example of this can include when the perpetrator gives out "rewards such as affection, a compliment, or gifts sporadically and unpredictably throughout the abuse cycle", which allows victim to remain trapped in this vicious cycle. <ref>{{Cite web|url=https://psychcentral.com/blog/recovering-narcissist/2019/03/narcissists-use-trauma-bonding-and-intermittent-reinforcement-to-get-you-addicted-to-them-why-abuse-survivors-stay|title=Narcissists Use Trauma Bonding and Intermittent Reinforcement To Get You Addicted To Them: Why Abuse Survivors Stay|date=2019-03-31|website=Psych Central|language=en|access-date=2024-11-10}}</ref> A relevant study in relation to this explored how the traumatic bonding theory has significant links to intermittent abuse, and how long it may take for the victim's symptoms attachment and trauma symptoms to no longer persist. The study was conducted on 75 women who had recently left an abusive relationship, which demonstrated how the time that it took for women to have reduced symptoms depended majorly on the extent of intermittent reinforcement and power differentials. The study overall found attachment symptoms decreased by 27% after six months, which further demonstrates the serious impact that intermittent reinforcement plays in relationships.<ref name=":3" /> === L[[w:Learned_helplessness|earned helplessness]] === Learned helplessness is characterised as “behaviour exhibited by a subject after enduring repeated aversive stimuli beyond their control”.<ref>{{Cite journal|last=Rakovec-Felser|first=Zlatka|date=2014-11-06|title=Domestic violence and abuse in intimate relationship from public health perspective|url=https://healthpsychologyresearch.openmedicalpublishing.org/article/22398|journal=Health Psychology Research|language=en|volume=2|issue=3|doi=10.4081/hpr.2014.1821|pmc=PMC4768593|pmid=26973948}}</ref> Learned helplessness can be demonstrated in relationships through victims being submissive to their partners and refusing to leave the relationship that is abusive.<ref>Torres Ruiz, N. (2021). ''Learned Helplessness and Domestic Violence Learned Helplessness and Domestic Violence Part of the Bilingual, Multilingual, and Multicultural Education Commons, Other Education Commons, and the Secondary Education Commons''. [https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1216&context=ncpacapstone. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1216&context=ncpacapstone.]</ref> A relevant 2014 study explored the extent of domestic violence and abuse in intimate relationships through observing survey data; the study found that learned helplessness plays a crucial role in the vicious cycle of abuse, stating “the perpetrator alternates between violent, abusive and apologetic behaviour with apparently heartfelt promises to change”. <ref>{{Cite journal|last=Rakovec-Felser|first=Zlatka|date=2014-11-06|title=Domestic violence and abuse in intimate relationship from public health perspective|url=https://healthpsychologyresearch.openmedicalpublishing.org/article/22398|journal=Health Psychology Research|language=en|volume=2|issue=3|doi=10.4081/hpr.2014.1821|pmc=PMC4768593|pmid=26973948}}</ref> Another key study demonstrated how learned helplessness can result in traumatic bonding with the perpetrator, which can develop into serious medical conditions such as "Stockholm Syndrome", or "Battered Woman Syndrome". The study also highlighted how the affects of learned helplessness in relationships can cause the victim to "completely lose their sense of self and system of meaning and to instead adopt their abuser’s view of the world".<ref>{{Cite web|url=https://did-research.org/origin/d-attachment/traumatic_bonding|title=Traumatic Bonding|website=DID-Research.org|access-date=2024-11-10}}</ref> === [[w:Gaslighting|Gaslighting]] and [[w:Manipulation|manipulation]] === A key mechanism that maintains abusive relationships is gaslighting and manipulation. ==== Gaslighting ==== Gaslighting is referred to as "a type of psychological abuse aimed at making victims seem or feel “crazy", which is often seen in romantic relationships. <ref>{{Cite journal|last=Sweet|first=Paige L.|date=2019-10|title=The Sociology of Gaslighting|url=https://journals.sagepub.com/doi/10.1177/0003122419874843|journal=American Sociological Review|language=en|volume=84|issue=5|pages=851–875|doi=10.1177/0003122419874843|issn=0003-1224}}</ref> It can also be defined as a type of abuse where "a sane and rational survivor is convinced of their own epistemic incompetence on false pretences by a perpetrator".<ref name=":4">{{Cite journal|last=Klein|first=Willis|last2=Li|first2=Sherry|last3=Wood|first3=Suzanne|date=2023-12|title=A qualitative analysis of gaslighting in romantic relationships|url=https://onlinelibrary.wiley.com/doi/10.1111/pere.12510|journal=Personal Relationships|language=en|volume=30|issue=4|pages=1316–1340|doi=10.1111/pere.12510|issn=1350-4126}}</ref> A recent qualitative analysis was conducted to study the characteristics of gaslighting in relationships. The study surveyed 65 individuals who stated that they had been in an intimate relationship that involved gaslighting. The study asked the individuals questions in relation to this such as describing examples of this abuse tactic occurring in their relationship, different characteristics of their relationships, and what were the mental health repercussions of this abuse occurring. Results showed "gaslighting victimisation was associated with a diminished sense of self, mistrust of others, and on occasion, post-traumatic growth" and those who recovered from gaslighting often emphasised the importance of separation from the perpetrator, prioritisation of healthier relationships, and engaging in meaningful and re-embodying activities". The study emphasises the need for further research on gaslighting in relationships and how victims can recover from this form of abuse, which can overall lead to minimise this type of abuse occurring and providing appropriate treatment to victims. <ref name=":4" /> ==== Manipulation ==== Manipulation is defined as “an action designed to influence or [[w:Control|control]] another, usually in an underhanded or unfair manner which facilitates one's personal aims" (see Figure 7). [[File:Manipulation-.png|thumb|Figure 7. A hand controlling which alludes to someone being controlled, which is a manipulation tactic.]] {| class="wikitable" |+Types of Manipulation !Having Control over Location |Manipulators may physically take victims to places they are unfamiliar with, or emotionally try to bring victims out of their comfort zone. The abuser does this in order to feel a sense of control. |- !Manipulating Facts |Manipulators will be dishonest with victims, make excuses, and blame them. Occasionally, these types of abusers will share some truth to their facts to strategically manipulate you. |- !Being [[w:Passive-Aggressive_behavior|Passive-Aggressive]] |Manipulators will voice subtle, indirect negative feelings towards victims to undermine them. |- !Guilt and Sympathy |Manipulators tend to make their victims feel guilty or have sympathy towards them in order to receive what they want. |- !Use of Silent Treatment |Abusers use this withdrawal tactic to punish their victims |- !Use of Comparison |Abusers may compare their victims to someone else to further evoke an upsetting or uncomfortable reaction from victims, or make them feel insecure about something. |- ![[w:Love_bombing|Love-bombing]] |Manipulators use this common abuse tactic to give enormous amounts of praise and affection to speed up their relationship between them and their victim. This causes the victim to be heavily attached to their abuser, which allows for the abuser to easily discard them later on. |} {{Robelbox|theme=6|title=Topic Review: Quiz Time!|iconwidth=48px|icon=Nuvola_apps_korganizer.svg}}<div style="{{Robelbox/pad}}"> <quiz display=simple> {Who is negatively affected in a codependent relationship?} - The enabler - The enabled + Both {What is the main reason why victims stay in learned helplessness relationships?} - They believe they deserve the abuse they're receiving + They believe the perpetrator can change their behaviour as they have apologised or given them gifts - They stay because they feel lonely and no one will love them </quiz> </div> {{Robelbox-close}} == How do individuals remove themselves from abusive relationships? == According to an [https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Australian psychology article], some ways to break free from emotional dependency to form healthy relationships include: # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Identifying your Attachment Style]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Improving your Self-Esteem]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Spending Time with Friends and Family]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Having Calm and Honest Communication with your Partner]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Setting and Upholding Healthy Boundaries]''' # '''[https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ Working with a Therapist through these Issues]''' == Conclusion == This chapter establishes the significant connection between emotional dependency and abusive relationships, which is key for creating healthier relationships with others. Through being aware of psychological mechanisms, such as attachment theory, low self-esteem, and codependency, it allows audiences to adequately understand how these devices drive emotional dependency. Additionally, the article explores certain crucial mechanisms that incite abuse, such as trauma bonding, learned helplessness, gaslighting, and manipulation. This valuable information also enables individuals to be educated on this specific topic and to start working on strategies to remove themselves from emotional dependency and unhealthy relationships. It is through these devices that individuals are capable in understanding the crucial link between emotional dependency and unhealthy relationships in order from them to foster healthier romantic relationships. == See also == * [[w:Psychological_abuse|Psychological abuse]] (Wikipedia) * [[Motivation and emotion/Book/2019/Emotional abuse|Emotional abuse]] (Book Chapter 2019) * [[Motivation and emotion/Book/2014/Aggression in intimate relationships|Aggression in intimate relationships]] (Book Chapter 2014) == References == == External Links == https://dictionary.cambridge.org/us/dictionary/english/manipulation https://northsidepsychology.com.au/how-to-break-free-from-co-dependency-in-relationships/ https://barbaraoakley.com/wp-content/uploads/2016/12/000Chapter-1-Pathological-Altruism-Oakley-Knafo-McGrath.pdf https://www.healthline.com/health/mental-health/trauma-bonding#takeaway https://www.helpguide.org/relationships/social-connection/attachment-and-adult-relationships https://doi.org/10.1177/0003122419874843 https://www.healthline.com/health/low-self-esteem#defining-low-self-esteem https://en.wikipedia.org/wiki/Learned_helplessness [http://www.community.nsw.gov.au/docs_menu/parents_carers_and_families/domestic_and_family_violence/dv_line.html/ Domestic Violence NSW] [[Category:{{#titleparts:{{PAGENAME}}|3}}]] [[Category:Motivation and emotion/Book/Abuse]] [[Category:Motivation and emotion/Book/Relationships]] [[Category:Moivation and emotion/Book/Trauma]] 1b8bdm9ehkmqbgm9f59fp9rmn39p8do Linear mapping/Linear subspaces/Kernel/Introduction/Section 0 309405 2683452 2671432 2024-11-11T14:05:36Z Bocardodarapti 289675 2683452 wikitext text/x-wiki {{ Mathematical section{{{opt|}}} |Content= A typical property of a linear mapping is that it maps lines to lines {{ Extra/Bracket |text=or to a point| |Ipm=|Epm=. }} More general is following statement. {{ inputfactproofexercise |Linear mapping/Image and preimage/Linear subspaces/Fact|Lemma|| |extra1= ={{Setcond|\varphi(v)|v \in S}} |extra2= ={{Setcond|v \in V|\varphi(v) \in T}} }} {{ inputdefinition |Linear mapping/Kernel/Definition|| }} Due to the statement above, the kernel is a linear subspace of {{mat|term=V|pm=.}} {{ inputremark |Linear system/Kernel/Relation/Remark|| }} The following {{Keyword|criterion for injectivity|pm=}} is important. {{ inputfactproof |Linear mapping/Kernel/Injectivity/Fact|Lemma|| }} |Textform=Section |Category= |}} mmj4xtkqyhxosd5agi355n034mn1gy2 Talk:Motivation and emotion/Book/2024/Abusive relationships and emotional dependency 1 310111 2684178 2679223 2024-11-12T10:46:00Z Jtneill 10242 Book chapter resubmission feedback 2684178 wikitext text/x-wiki == Feedback == Hi @[[User:Lucywilson 546|Lucywilson 546]] I really like your chapter so far, it goes super in depth! Just wanted to give some feedback surrounding the presentation of Bowlby's Attachment theory and the 4 main attachment styles. I really enjoyed your approach of giving and overview of and providing a case study of each attachment style, it gives alot of good info and describes everything clearly. however since its presented in a table it can make it quite difficult to read and follow, I myself had to scroll up and down a few times to remind myself of the titles and in general had a bit of trouble reading such a large amount of text in the smaller font size. I personally believe that the information would be better suited for paragraphs, with each of the case studies in feature boxes to break everything up. another good option could also be separating each attachment style into its own table, again with the case studies separate in there own feature boxes. Good work with the chapter overall, I hope this helps a bit. [[User:U3230258|U3230258]] ([[User talk:U3230258|discuss]] • [[Special:Contributions/U3230258|contribs]]) 19:55, 5 October 2024 (UTC) <!-- Official book chapter feedback --> {{MEBF/2024 |1= <!-- Overall comments... --> # Overall, this is an insufficient chapter # The main area for potential improvement is the use of the best peer-reviewed psychological theory and research about this topic <!-- Overall – Citations --> # Insufficient use of primary, peer-reviewed sources as citations (e.g., see the {{fact}} tags) # Move embedded non-peer-reviewed links into the [[{{PAGENAME}}#External links|External links]] section <!-- Overall – Copyedits --> # For additional feedback, see the following comments and [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAbusive_relationships_and_emotional_dependency&diff=2676676&oldid=2665872 these copyedits] |2= <!-- Overview comments... --> # Underdeveloped # Remove subheadings (fixed) <!-- Overview – Case study --> # Engage reader via a case study or scenario in a feature box with a relevant image <!-- Overview – Explains problem --> # Briefly explains the psychological problem or phenomenon; provide more detail <!-- Overview – Focus questions --> # Provide focus questions in a feature box to help guide the reader |3= <!-- Theory comments... --> <!-- Theory – Breadth --> # A promising range of ideas are presented but it is far from clear how this material is derived from a first person reading of the best peer-reviewed psychological theory and research about this topic <!-- Theory – Builds on --> # Builds exceptionally well on related chapters and Wikipedia articles <!-- Theory – Depth --> # Reasonably good depth is provided about relevant theory(ies) <!-- Theory – Tables/Figures/Lists --> # Promising use of tables, figures, and/or lists to help clearly convey key theoretical information <!-- Theory – Citations --> # Insufficient use of academic, peer-reviewed citations (e.g., see the {{fact}} tags) <!-- Theory – Examples --> # Basic use of examples to illustrate theoretical concepts # Consider using more examples to illustrate theoretical concepts |4= <!-- Research comments... --> <!-- Research – Key findings --> # Insufficient review of relevant research # Insufficient use of academic, peer-reviewed citations (e.g., see the {{f}} tags) # Provide more detail about key studies including systematic reviews and/or meta-analyses in this area <!-- Research – Critical thinking --> # Insufficient critical thinking about relevant research is evident # Critical thinking about research could be evidenced by: ## describing the methodology (e.g., sample, measures) in important studies ## considering the strength of relationships ## acknowledging limitations ## pointing out critiques/counterarguments ## suggesting ''specific'' directions for future research |5= <!-- Integration comments... --> # Insufficient integration between theory and research |6= <!-- Conclusion comments... --> # Basic summary and conclusion |7= <!-- Written expression – Style comments... --> <!-- Written expression – Written expression --> # Written expression ## Overall, the quality of written expression is basic <!-- Written expression – Paragraphs --> ## Avoid one sentence paragraphs. Communicate one idea per paragraph using three to five sentences. <!-- Written expression – Layout --> # Layout ## The structure is overly complicated; aim for 3 to 6 top-level headings between the Introduction and Conclusion ## Include an introductory paragraph before branching into the sub-sections (see {{expand}} tags) ## Use the default heading style (e.g., remove additional italics and/or bold) ## Move links from headings into their first mention in text <!-- Written expression – Grammar --> # Grammar ## The grammar for some/many sentences could be improved (e.g., see the {{g}} tags) ### Consider using a [https://www.google.com/search?q=grammar+checking+tools grammar checking tool] ### Another option is to use a services provided by UC, such as Studiosity ### Another option is to share draft work with peers and ask for their assistance ## Check and correct use of possessive apostrophes (e.g., cats vs cat's vs cats')[https://grammar.yourdictionary.com/punctuation/apostrophe-rules.html] <!-- Written expression – APA style --> # APA style ## Direct quotes need citations and page numbers. They are overused – communicate about concepts in your own words. <!-- Written expression – Figures --> ## Figures ### Very well captioned ### Use this format for captions: ''Figure X''. Descriptive caption goes here in sentence casing. [[Motivation and emotion/Assessment/Chapter/Figures|See example]]. ### Each Figure is referred to at least once within the main text using APA style <!-- Written expression – Tables --> ## Tables ### Use APA style for captions ([[Motivation and emotion/Assessment/Chapter/Tables|see example]]) ### Refer to each Table at least once within the main text (e.g., see Table 1) ### The table is way too long (> 1300 words) and lacks sufficient relationship to the target topic. Abbreviate. ### Was the table created with AI? If so, this hasn't been acknowledged which would be a violation of academic integrity. Please see [[Motivation and emotion/Assessment/Using generative AI|genAI content]]. <!-- Written expression – Citations --> ## Citations use poor APA style (7th ed.). <!-- Written expression – References --> ## References use poor APA style: ### Check and correct use of capitalisation[https://apastyle.apa.org/style-grammar-guidelines/capitalization] ### Check and correct use of italicisation ### Remove "Retrieved ..." ### Include hyperlinked dois (fixed) ### Move non-peer reviewed links into the [[{{PAGENAME}}#External links|External links]] section ### Move Wikipedia links into the see See also section |8= <!-- Learning features comments... --> # Basic use of learning features <!-- Learning features - Embedded links to Wikipedia --> # Excellent use of embedded in-text [[m:Help:Interwiki linking|interwiki links]] to Wikipedia articles <!-- Learning features - Embedded links to Wikiversity --> # No use of embedded in-text links to related [[Motivation and emotion/Book|book chapters]]. Embedding in-text links to related book chapters helps to integrate this chapter into the broader book project. # Move links to non-peer-reviewed sources to the [[{{PAGENAME}}#External links|External links]] section <!-- Learning features – Images etc. --> # Very good use of image(s) # Promising use of table(s) # No use of feature box(es) # Some non-integrated use of case studies or examples (move out of the table) <!-- Learning features – Quizzes --> # No use of quiz(zes) and/or reflection question(s) <!-- Learning features – See also --> # No use of interwiki links in the "See also" section <!-- Learning features – External links --> # No use of external links in the "External links" section |9= <!-- Social contribution comments... --> # ~2 logged, useful, mostly minor contributions with indirect links to evidence, so unable to easily verify and assess. See tutorials for guidance about how to make and record direct links to evidence. }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 05:27, 27 October 2024 (UTC) ===Resubmission feedback== [https://en.wikiversity.org/w/index.php?title=Motivation_and_emotion%2FBook%2F2024%2FAbusive_relationships_and_emotional_dependency&diff=2682794&oldid=2676676 These changes were reviewed]: # Overview ## considerably improved ## overly focused on Australia ## overuses direct quotes # Theory ## improved # Research ## improved # Style ## improved slightly # Learning features ## improved Sincerely, James -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 10:45, 12 November 2024 (UTC) {{MEMF/2024 |1= <!-- Overall comments ... --> <!-- Overall - Overall --> # Overall, this is an insufficient presentation <!-- Overall - Time --> # The presentation is over the maximum time limit — content beyond 3 mins is ignored for marking and feedback purposes |2= <!-- Overview comments ... --> <!-- Overview - Opening --> # An opening slide with the title and sub-title is displayed. Also narrate the title and sub-title — this helps to clearly convey the purpose of the presentation. <!-- Overview - Introduction --> # Create an engaging introduction to hook audience interest (e.g., by introducing a case study or scenario) <!-- Overview - Context --> # A basic context for the presentation is established <!-- Overview - Focus --> # Consider asking focus questions that lead to take-away messages. This will help to focus and discipline the presentation. |3= <!-- Content comments ... --> # Comments about the book chapter may also apply to this section <!-- Content - Addresses topic --> # The presentation addresses the topic <!-- Content - Amount --> # There is too much content to fit within the allocated time frame <!-- Content - Theory --> # The presentation makes very basic use of relevant psychological theory <!-- Content - Research --> # The presentation makes no use of relevant psychological research <!-- Content - Citations --> # The presentation makes no use of citations to support claims <!-- Content - Examples --> # The presentation makes no use of examples # The presentation provides useful practical advice <!-- Content - Easy to understand --> # The presentation provides easy to understand information |4= <!-- Conclusion comments ... --> <!-- Conclusion - Slide --> # The conclusion provides basic take-home message(s) <!-- Conclusion - Time --> # The Conclusion only partly fitted within the time limit |5= <!-- Audio comments ... --> <!-- Audio - Narration --> # The presentation makes basic use of narrated audio <!-- Audio - Pacing --> # Audio communication is well paced <!-- Audio - Voice --> # Basic [[w:Intonation (linguistics)|intonation]] <!-- Audio - Practice --> # The narration is reasonably well practiced and/or performed <!-- Audio - Recording quality --> # Audio recording quality was basic # Review microphone set-up to achieve higher recording quality. Probably an on-board microphone was used (e.g., keyboard and/or mouse clicks were audible). Consider using an external microphone. <!-- Audio - Topic --> # The narrated [[#Content|content]] is well/reasonably well matched to the target topic but lacked synthesis of the best psychological research about this topic |6= <!-- Video comments ... --> <!-- Video - Overall --> # Overall, visual display quality is basic # It is unclear why: #* A video of a screen is used (rather than a screencast) #* The camera is unsteady #* The slides are branded with Larana University #* There is a generic face icon in the bottom left of the slides <!-- Video - Video, Image, Text --> # The presentation makes reasonably good use of text based slides <!-- Video - Font --> # The font size is sufficiently large to make it easy to read <!-- Video - Images --> # The visual communication could be improved by including some relevant images and/or diagrams <!-- Video - Production --> # The presentation is basically produced using simple tools <!-- Video - Topic --> # The visual [[#Content|content]] is reasonably well matched to the target topic but lacked synthesis of the best psychological research about this topic |7= <!-- Meta-data comments ... --> <!-- Meta-data - Title/sub-title --> # The chapter title is used, but the sub-title (or a shortened version of it) is not used, as the name of the presentation. The sub-title (or an abbreviation of the sub-title that fits within the 100 character limit) would help to clearly convey the purpose of the presentation. <!-- Meta-data - Description --> # A good written description of the presentation is provided. Consider expanding. <!-- Meta-data - Links --> # Links to and from the book chapter are provided # A link to the book chapter is not provided # A link from the book chapter is provided |8= <!-- Licensing comments ... --> <!-- Licensing - Images --> # Source of slide template is communicated in a general way <!-- Licensing - Presentation --> # A copyright license for the presentation is provided # A copyright license for the presentation is provided in the presentation description but not in the [https://support.google.com/youtube/answer/57404 meta-data] # A copyright license for the presentation is not provided }} -- [[User:Jtneill|Jtneill]] - <small>[[User talk:Jtneill|Talk]] - [[Special:Contributions/Jtneill|c]]</small> 06:57, 4 November 2024 (UTC) mg4q33lk8t3zelr5x0ll2vdp89j75ng Institute for Mental and Behavioral Health Research (IMBHR) at Nationwide Children's Hospital 0 310605 2683663 2671932 2024-11-11T16:00:56Z Parodda 2936296 /* Current Research Showcase */ adding reference management sops section 2683663 wikitext text/x-wiki == Institute for Mental and Behavioral Health Research (IMBHR) == === Overview === The Institute for Mental and Behavioral Health Research is located in the state-of-the-art Big Lots Behavioral Health Pavilion. The mission of faculty within the institute is to conduct innovative translational, clinical and epidemiological research focused on etiology, prevention and treatment of mental, emotional and behavioral disorders. In addition to collaborative efforts across the Nationwide Children’s Hospital campus, institute members work in collaboration with the Ohio State University Department of Psychiatry and Behavioral Health and the OSU Institute for Behavioral Medicine Research. With 25,000 square feet of current research space and additional research space in development, the institute has flexibility for growth and offers ample room for staff and trainees. Embedded within the institute is the Center for Suicide Prevention and Research. Recently awarded a P50 grant from the National Institute of Mental Health, the CSPR hosts four principal investigators and a large staff to sustain the work of multiple NIMH-funded projects. '''[https://www.nationwidechildrens.org/research/awri-landing The Abigail Wexner Research Institute]''' is ranked among the top 10 for NIH funding among free-standing children's hospitals. === Center for Suicide Prevention and Research === '''''To save children's lives and reduce suicide in Ohio and beyond though prevention efforts and cutting-edge research.''''' The Center for Suicide Prevention and Research (CSPR) is a cornerstone of IMBHR. CSPR was created to address the growing problem of suicide among youth in central Ohio. Find out more about CSPR here: '''[[Institute for Mental and Behavioral Health Research (IMBHR) at Nationwide Children's Hospital/Center for Suicide Prevention and Research (CSPR)|Center for Suicide Prevention and Research (CSPR)]]''' === Current Research Showcase === [[File:RISE 2024 Cohort.jpg|thumb|This picture shows the 2024 Research at IMBHR Summer Experience (RISE) cohort.''Top (left to right): Emily Glatt, Maya Garg, Eric Youngstrom, Noreen Xu, Shannon Price.'' ''Bottom (left to right): Aarav Kukreja, Jeremy Baggs, Zachery Mondlak, Halle Deericks, Hannah Brockstein.'']] Congratulations to the RISE 2024 cohort! This past summer Nationwide Children's Hospital selected 9 undergraduate, post-baccalaureate, and graduate students from around the country to participate in the first annual installment of the Research at IMBHR Summer Experience (RISE) program. These students worked to further a diverse array of research efforts to NCH, building meaningful connections and developing their own careers along the way. Stay tuned for more information about RISE 2025! Check out this page for more information about RISE, including an in-depth recap of RISE 2024: '''[[Institute for Mental and Behavioral Health Research (IMBHR) at Nationwide Children's Hospital/Research at IMBHR Summer Experience (RISE)#Research at IMBHR Summer Experience (RISE)|Research at IMBHR Summer Experience (RISE)]]''' IMBHR Clinical Research Coordinators Marissa McClellan and Charles Sabgir are currently working on building a repository of notable publications authored by IMBHR members and collaborators on Zotero. For more information on this project, see the page below: '''[[Institute for Mental and Behavioral Health Research (IMBHR) at Nationwide Children's Hospital/Reference Management SOPs|Reference Management SOPs]]''' === Leadership === [[File:IMBHR Banyan Tree.png|thumb|This figure visually depicts the members of the Institute of Mental and Behavioral Health at Nationwide Children's Hospital using a Banyan tree to highlight the importance of collaboration at IMBHR.]] The Institute for Mental and Behavioral Health Research is led by Eric Youngstrom, PhD, a nationally renowned psychologist specializing in the relationship of mood and psychopathology, and the clinical assessment of children and families. Dr. Youngstrom’s research focuses on improving clinical assessment instruments for differential diagnoses and on predicting a child’s treatment progress, especially for bipolar disorder. In addition to being the institute’s inaugural director, he will be the first recipient of the DiMarco Family Endowed Chair in Mental and Behavioral Health Research at Nationwide Children’s Hospital. Dr. Youngstrom was twice elected President of the Society of Clinical Child and Adolescent Psychology, and was President of the Society of Quantitative and Qualitative Methods. He consulted on the 5th revision of the Diagnostic and Statistical Manual (DSM-5) and the International Classification of Diseases (ICD-11) and chaired the Work Group on Child Diagnosis for the International Society for Bipolar Disorders. He is the first recipient of the Early Career Award from the Society of Child and Adolescent Clinical Psychology; an elected full member of the American College of Neuropsychopharmacology; and a fellow of the American Psychological Association (Divisions 5, 12, and 53), as well as the Association for Psychological Science and the Association for Behavioral and Cognitive Therapies. === Contact === '''Jacqueline Pazaropoulos''' - Administrative Support Lead The Institute for Mental and Behavioral Health Research Big Lots Behavioral Health Pavilion 444 Butterfly Gardens Dr. Columbus, OH 42315 pvw50lj3ialu2feolkpi0hisupxgn6r Illustrated Companion to the Latin Dictionary 0 311099 2683975 2683301 2024-11-11T20:11:10Z CalRis25 911425 slight change to main page of RICH-2K 2683975 wikitext text/x-wiki {{Color|Red|'''WARNING: THIS PAGE AND ALL ITS SUBPAGES IS CURRENTLY UNDER CONSTRUCTION. PLEASE DO NOT EDIT AS LONG AS THIS WARNING HAS NOT BEEN REMOVED.'''}} {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{languages}} {{non-formal education}} {{0% done}} '''Welcome to the ''Illustrated Companion to the Latin Dictionary''''', a glossary of words representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans. This learning resource incorporates the complete content of the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''<ref>{{cite book | last = Rich | first = Anthony | author-link = w:Anthony Rich | date = 1849 | title = The illustrated companion to the Latin dictionary, and Greek lexicon | url = https://archive.org/details/illustratedcompa00rich | page = vi | oclc = 894670115 | ol = 205965W}}</ref> (referred to henceforth as ''RICH-1849''. For the sake of brevity this project may be referred to simply as ''Illustrated Companion'' or ''RICH-2K''). {{Quote box |quote='''The mission of this learning resource:''' # Define the true meaning of all the terms, technical or otherwise, expressive of any particular object, artificial production, manual operation, etc., which can be submitted to ocular inspection. # Impart a distinct notion of that meaning, by exhibiting a virtual representation of the thing itself, faithfully copied from some classic original, thus presenting the same forms as the ancients were accustomed to look upon, and suggestive of the same ideas as they themselves conceived. # Furnish a general knowledge of the social customs, and every-day life, of the Romans and Greeks, in the shape of a vocabulary, containing all the written terms which have reference to such matters # All of this illustrated by a series of pictures, after their [= Romans and Greeks] own designs, of the dress they wore, the houses they lived in, the utensils they used, or the pursuits they followed, by which we may be said to acquire a sort of personal acquaintance with the people themselves, and to see them, as it were, in a glass, under the genuine characters, and familiar aspects, which they presented to one another. |source=Anthony Rich, ''The illustrated companion to the Latin dictionary, and Greek lexicon''}} '''More information:''' * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project description|Project description]]: A more detailed description of the project ''Illustrated Companion to the Latin Dictionary''. What ''is'' this project? What is it ''not''? * [[Illustrated Companion to the Latin Dictionary/RICH-2K/How to contribute|How to contribute]]: Although having Anthony Rich's articles (and images) as its foundation, this project is designed to be improved and expanded. Learn how you can help to improve this project. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Classed Index 1849|Classed Index 1849]]: Articles from RICH-1849 arranged by subject and in such a way as to convey to the reader a comprehensive knowledge of everything pertaining to any given subject.<!--Note: A complete overview of all articles of RICH-2K will be provided using Wikiversity-categories--> * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Greek Index 1849|Greek Index]]: A list of Greek words, with their Latin synonymes, under which the Greek terms are explained. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Preface to RICH-1849|Preface 1849]]: The original preface to the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Technical aspects|Technical aspects]]: This page explains how the ''Illustrated Companion to the Latin Dictionary'' has been implemented, thereby making it easier to a) understand the structure, and b) change some aspects should that be deemed necessary. It also lists and explains some of the design decisions. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Categories of the Classed Index|Categories of the Classed Index]]: This page provides an overview of the ''Classed Index'', a two-level subject-hierarchy. An article may belong to several subjects. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Recommended editions|Recommended editions]]: This page provides an overview of the editions of text, which should be preferentially used when citing these texts. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project guidelines|Project guidelines]] * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Articles from RICH-1849|Articles from RICH-1849]]: Complete list of all pages, which were originally based on RICH-1849. This list does ''not'' include REDIRECT-pages implementing secondary lemmas. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/REDIRECT-pages for RICH-1849|REDIRECT-pages for RICH-1849]]: Complete list of all REDIRECT-pages implementing secondary lemmas. == References == {{reflist}} [[Category:Illustrated Companion to the Latin Dictionary|*]] [[Category:RICH-2K/Project pages]] dzgs422e6pbv4j1f6d1xmazs4lwsaxr 2683976 2683975 2024-11-11T20:20:10Z CalRis25 911425 Reorganize main page of project RICH-2K 2683976 wikitext text/x-wiki {{Color|Red|'''WARNING: THIS PAGE AND ALL ITS SUBPAGES IS CURRENTLY UNDER CONSTRUCTION. PLEASE DO NOT EDIT AS LONG AS THIS WARNING HAS NOT BEEN REMOVED.'''}} {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{languages}} {{non-formal education}} {{0% done}} '''Welcome to the ''Illustrated Companion to the Latin Dictionary''''', a glossary of words representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans. This learning resource incorporates the complete content of the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''<ref>{{cite book | last = Rich | first = Anthony | author-link = w:Anthony Rich | date = 1849 | title = The illustrated companion to the Latin dictionary, and Greek lexicon | url = https://archive.org/details/illustratedcompa00rich | page = vi | oclc = 894670115 | ol = 205965W}}</ref> (referred to henceforth as ''RICH-1849''. For the sake of brevity this project may be referred to simply as ''Illustrated Companion'' or ''RICH-2K''). {{Quote box |quote='''The mission of this learning resource:''' # Define the true meaning of all the terms, technical or otherwise, expressive of any particular object, artificial production, manual operation, etc., which can be submitted to ocular inspection. # Impart a distinct notion of that meaning, by exhibiting a virtual representation of the thing itself, faithfully copied from some classic original, thus presenting the same forms as the ancients were accustomed to look upon, and suggestive of the same ideas as they themselves conceived. # Furnish a general knowledge of the social customs, and every-day life, of the Romans and Greeks, in the shape of a vocabulary, containing all the written terms which have reference to such matters # All of this illustrated by a series of pictures, after their [= Romans and Greeks] own designs, of the dress they wore, the houses they lived in, the utensils they used, or the pursuits they followed, by which we may be said to acquire a sort of personal acquaintance with the people themselves, and to see them, as it were, in a glass, under the genuine characters, and familiar aspects, which they presented to one another. |source=Anthony Rich, ''The illustrated companion to the Latin dictionary, and Greek lexicon''}} '''More information:''' * The Project ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project description|Project description]]: A more detailed description of the project ''Illustrated Companion to the Latin Dictionary''. What ''is'' this project? What is it ''not''? ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Preface to RICH-1849|Preface 1849]]: The original preface to the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/How to contribute|How to contribute]]: Although having Anthony Rich's articles (and images) as its foundation, this project is designed to be improved and expanded. Learn how you can help to improve this project. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project guidelines|Project guidelines]] ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Recommended editions|Recommended editions]]: This page provides an overview of the editions of text, which should be preferentially used when citing these texts. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Technical aspects|Technical aspects]]: This page explains how the ''Illustrated Companion to the Latin Dictionary'' has been implemented, thereby making it easier to a) understand the structure, and b) change some aspects should that be deemed necessary. It also lists and explains some of the design decisions. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Categories of the Classed Index|Categories of the Classed Index]]: This page provides an overview of the ''Classed Index'', a two-level subject-hierarchy. An article may belong to several subjects. * The Content ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Classed Index 1849|Classed Index 1849]]: Articles from RICH-1849 arranged by subject and in such a way as to convey to the reader a comprehensive knowledge of everything pertaining to any given subject.<!--Note: A complete overview of all articles of RICH-2K will be provided using Wikiversity-categories--> ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Greek Index 1849|Greek Index]]: A list of Greek words, with their Latin synonymes, under which the Greek terms are explained. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Articles from RICH-1849|Articles from RICH-1849]]: Complete list of all pages, which were originally based on RICH-1849. This list does ''not'' include REDIRECT-pages implementing secondary lemmas. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/REDIRECT-pages for RICH-1849|REDIRECT-pages for RICH-1849]]: Complete list of all REDIRECT-pages implementing secondary lemmas. == References == {{reflist}} [[Category:Illustrated Companion to the Latin Dictionary|*]] [[Category:RICH-2K/Project pages]] apqzlc5s7kpyk3o863uwua03v8aryan 2683977 2683976 2024-11-11T20:22:19Z CalRis25 911425 2683977 wikitext text/x-wiki {{Color|Red|'''WARNING: THIS PAGE AND ALL ITS SUBPAGES IS CURRENTLY UNDER CONSTRUCTION. PLEASE DO NOT EDIT AS LONG AS THIS WARNING HAS NOT BEEN REMOVED.'''}} {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{languages}} {{non-formal education}} {{90% done}} '''Welcome to the ''Illustrated Companion to the Latin Dictionary''''', a glossary of words representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans. This learning resource incorporates the complete content of the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''<ref>{{cite book | last = Rich | first = Anthony | author-link = w:Anthony Rich | date = 1849 | title = The illustrated companion to the Latin dictionary, and Greek lexicon | url = https://archive.org/details/illustratedcompa00rich | page = vi | oclc = 894670115 | ol = 205965W}}</ref> (referred to henceforth as ''RICH-1849''. For the sake of brevity this project may be referred to simply as ''Illustrated Companion'' or ''RICH-2K''). {{Quote box |quote='''The mission of this learning resource:''' # Define the true meaning of all the terms, technical or otherwise, expressive of any particular object, artificial production, manual operation, etc., which can be submitted to ocular inspection. # Impart a distinct notion of that meaning, by exhibiting a virtual representation of the thing itself, faithfully copied from some classic original, thus presenting the same forms as the ancients were accustomed to look upon, and suggestive of the same ideas as they themselves conceived. # Furnish a general knowledge of the social customs, and every-day life, of the Romans and Greeks, in the shape of a vocabulary, containing all the written terms which have reference to such matters # All of this illustrated by a series of pictures, after their [= Romans and Greeks] own designs, of the dress they wore, the houses they lived in, the utensils they used, or the pursuits they followed, by which we may be said to acquire a sort of personal acquaintance with the people themselves, and to see them, as it were, in a glass, under the genuine characters, and familiar aspects, which they presented to one another. |source=Anthony Rich, ''The illustrated companion to the Latin dictionary, and Greek lexicon''}} '''More information:''' * The Project ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project description|Project description]]: A more detailed description of the project ''Illustrated Companion to the Latin Dictionary''. What ''is'' this project? What is it ''not''? ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Preface to RICH-1849|Preface 1849]]: The original preface to the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/How to contribute|How to contribute]]: Although having Anthony Rich's articles (and images) as its foundation, this project is designed to be improved and expanded. Learn how you can help to improve this project. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project guidelines|Project guidelines]] ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Recommended editions|Recommended editions]]: This page provides an overview of the editions of text, which should be preferentially used when citing these texts. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Technical aspects|Technical aspects]]: This page explains how the ''Illustrated Companion to the Latin Dictionary'' has been implemented, thereby making it easier to a) understand the structure, and b) change some aspects should that be deemed necessary. It also lists and explains some of the design decisions. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Categories of the Classed Index|Categories of the Classed Index]]: This page provides an overview of the ''Classed Index'', a two-level subject-hierarchy. An article may belong to several subjects. * The Content ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Classed Index 1849|Classed Index 1849]]: Articles from RICH-1849 arranged by subject and in such a way as to convey to the reader a comprehensive knowledge of everything pertaining to any given subject.<!--Note: A complete overview of all articles of RICH-2K will be provided using Wikiversity-categories--> ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Greek Index 1849|Greek Index]]: A list of Greek words, with their Latin synonymes, under which the Greek terms are explained. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/Articles from RICH-1849|Articles from RICH-1849]]: Complete list of all pages, which were originally based on RICH-1849. This list does ''not'' include REDIRECT-pages implementing secondary lemmas. ** [[Illustrated Companion to the Latin Dictionary/RICH-2K/REDIRECT-pages for RICH-1849|REDIRECT-pages for RICH-1849]]: Complete list of all REDIRECT-pages implementing secondary lemmas. == References == {{reflist}} [[Category:Illustrated Companion to the Latin Dictionary|*]] [[Category:RICH-2K/Project pages]] qqum64p164wozmuna3x9ea492p6ivee 2683978 2683977 2024-11-11T20:44:46Z CalRis25 911425 Cosmetic changes to the main page of project RICH-2K 2683978 wikitext text/x-wiki {{Color|Red|'''WARNING: THIS PAGE AND ALL ITS SUBPAGES IS CURRENTLY UNDER CONSTRUCTION. PLEASE DO NOT EDIT AS LONG AS THIS WARNING HAS NOT BEEN REMOVED.'''}} {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{languages}} {{non-formal education}} {{90% done}} '''Welcome to the ''Illustrated Companion to the Latin Dictionary''''', a glossary of words representing visible objects connected with the arts, manufactures, and every-day life of the Greeks and Romans. This learning resource incorporates the complete content of the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''<ref>{{cite book | last = Rich | first = Anthony | author-link = w:Anthony Rich | date = 1849 | title = The illustrated companion to the Latin dictionary, and Greek lexicon | url = https://archive.org/details/illustratedcompa00rich | page = vi | oclc = 894670115 | ol = 205965W}}</ref> (referred to henceforth as ''RICH-1849''. For the sake of brevity this project may be referred to simply as ''Illustrated Companion'' or ''RICH-2K''). {{Quote box |quote='''The purpose of this learning resource:''' # Define the true meaning of all the terms, technical or otherwise, expressive of any particular object, artificial production, manual operation, etc., which can be submitted to ocular inspection. # Impart a distinct notion of that meaning, by exhibiting a virtual representation of the thing itself, faithfully copied from some classic original, thus presenting the same forms as the ancients were accustomed to look upon, and suggestive of the same ideas as they themselves conceived. # Furnish a general knowledge of the social customs, and every-day life, of the Romans and Greeks, in the shape of a vocabulary, containing all the written terms which have reference to such matters # All of this illustrated by a series of pictures, after their [= Romans and Greeks] own designs, of the dress they wore, the houses they lived in, the utensils they used, or the pursuits they followed, by which we may be said to acquire a sort of personal acquaintance with the people themselves, and to see them, as it were, in a glass, under the genuine characters, and familiar aspects, which they presented to one another. |source=Anthony Rich, ''The illustrated companion to the Latin dictionary, and Greek lexicon''}} '''The Project''' * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project description|Project description]]: A more detailed description of the project ''Illustrated Companion to the Latin Dictionary''. What ''is'' this project? What is it ''not''? * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Preface to RICH-1849|Preface 1849]]: The original preface to the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/How to contribute|How to contribute]]: Although having Anthony Rich's articles (and images) as its foundation, this project is designed to be improved and expanded. Learn how you can help to improve this project. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Project guidelines|Project guidelines]] * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Recommended editions|Recommended editions]]: This page provides an overview of the editions of text, which should be preferentially used when citing these texts. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Technical aspects|Technical aspects]]: This page explains how the ''Illustrated Companion to the Latin Dictionary'' has been implemented, thereby making it easier to a) understand the structure, and b) change some aspects should that be deemed necessary. It also lists and explains some of the design decisions. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Categories of the Classed Index|Categories of the Classed Index]]: This page provides an overview of the ''Classed Index'', a two-level subject-hierarchy. An article may belong to several subjects. '''The Content''' * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Classed Index 1849|Classed Index 1849]]: Articles from RICH-1849 arranged by subject and in such a way as to convey to the reader a comprehensive knowledge of everything pertaining to any given subject.<!--Note: A complete overview of all articles of RICH-2K will be provided using Wikiversity-categories--> * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Greek Index 1849|Greek Index]]: A list of Greek words, with their Latin synonymes, under which the Greek terms are explained. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/Articles from RICH-1849|Articles from RICH-1849]]: Complete list of all pages, which were originally based on RICH-1849. This list does ''not'' include REDIRECT-pages implementing secondary lemmas. * [[Illustrated Companion to the Latin Dictionary/RICH-2K/REDIRECT-pages for RICH-1849|REDIRECT-pages for RICH-1849]]: Complete list of all REDIRECT-pages implementing secondary lemmas. == References == {{reflist}} [[Category:Illustrated Companion to the Latin Dictionary|*]] [[Category:RICH-2K/Project pages]] boiccr9i9df0sqs7x8eb4ndv12wc63j Illustrated Companion to the Latin Dictionary/RICH-2K/Greek Index 1849 0 311102 2683967 2674019 2024-11-11T18:18:51Z CalRis25 911425 Convert transcriber's note to footnote. 2683967 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} '''GREEK INDEX''', containing a list of Greek words, with their Latin synonymes, under which the Greek terms are explained. == ''Α.'' == ''ἀβακίσκος'', [[Illustrated Companion to the Latin Dictionary/Abaculus|abaculus]]. ''ἄβαξ'', [[Illustrated Companion to the Latin Dictionary/Abacus|abacus]]. ''ἀγαθοδαίμων'', [[Illustrated Companion to the Latin Dictionary/Genius|genius]]. ''ἄγκιστρον'', [[Illustrated Companion to the Latin Dictionary/Hamus|hamus]]. ''ἀγκοίνα'', [[Illustrated Companion to the Latin Dictionary/Anquina|anquina]]. ''ἄγκος, ἀγκή'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]]. ''ἀγκύλη'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 3. ''ἀγκυλητόν'', [[Illustrated Companion to the Latin Dictionary/Ansatus|ansatum telum]]. ''ἀγκύλιον'', [[Illustrated Companion to the Latin Dictionary/Ancile|ancile]]. ''ἀγκυλωτός'', [[Illustrated Companion to the Latin Dictionary/Ansatus|ansatus]]. ''ἀγκύρα'', [[Illustrated Companion to the Latin Dictionary/Ancora|ancora]]. ''ἀγκών'', [[Illustrated Companion to the Latin Dictionary/Ancon|ancon]]. ''ἀγορά'', [[Illustrated Companion to the Latin Dictionary/Forum|forum]], 2. 3. ''ἀγωνοθέτης'', [[Illustrated Companion to the Latin Dictionary/Agonotheta|agonotheta]]. ''ἄδυτον'', [[Illustrated Companion to the Latin Dictionary/Adytum|adytum]]. ''ἄζωστος'', [[Illustrated Companion to the Latin Dictionary/Discinctus|discinctus]]. ''ἀθληταί'', [[Illustrated Companion to the Latin Dictionary/Athletae|athletæ]]. ''ἀέτωμα'', [[Illustrated Companion to the Latin Dictionary/Aquila|aquila]], 2. ''αἰγίς'', [[Illustrated Companion to the Latin Dictionary/Aegis|ægis]]. ''αἰπόλος'', [[Illustrated Companion to the Latin Dictionary/Caprarius|caprarius]]. ''αἰχμή'', [[Illustrated Companion to the Latin Dictionary/Cuspis|cuspis]]. ''αἰώρα'', [[Illustrated Companion to the Latin Dictionary/Oscillatio|oscillatio]]. ''ἄκαπνα'', [[Illustrated Companion to the Latin Dictionary/Acapna|acapna]]. ''ἀκάτιον'', [[Illustrated Companion to the Latin Dictionary/Acatium|acatium]]. ''ἀκερσεκόμης'', [[Illustrated Companion to the Latin Dictionary/Intonsus|intonsus]], 1. ''ἀκέστρα'', [[Illustrated Companion to the Latin Dictionary/Acus|acus]]. ''ἀκινάκης'', [[Illustrated Companion to the Latin Dictionary/Acinaces|acinaces]]. ''ἄκμων'', [[Illustrated Companion to the Latin Dictionary/Incus|incus]]. ''ἀκόλουθος'', [[Illustrated Companion to the Latin Dictionary/Comes|comes]]. ''ἀκόνη'', [[Illustrated Companion to the Latin Dictionary/Cos|cos]]. ''ἄκουρος'', [[Illustrated Companion to the Latin Dictionary/Intonsus|intonsus]], 2. ''ἀκράτισμα'', [[Illustrated Companion to the Latin Dictionary/Jentaculum|jentaculum]]. ''ἄκρατον'', [[Illustrated Companion to the Latin Dictionary/Merum|merum]]. ''ἀκρατοφόρον'', [[Illustrated Companion to the Latin Dictionary/Acratophorum|acratophorum]]. ''ἀκρόπολις'', [[Illustrated Companion to the Latin Dictionary/Arx|arx]]. ''ἀκρωτήρια'', [[Illustrated Companion to the Latin Dictionary/Acroteria|acroteria]]. ''ἀκτίς'', [[Illustrated Companion to the Latin Dictionary/Radius|radius]], 2. 3. ''ἀλάβαστρος'', [[Illustrated Companion to the Latin Dictionary/Alabaster|alabaster]]. ''ἀλείπτης'', [[Illustrated Companion to the Latin Dictionary/Aliptes|aliptes]]. ''ἁλιεύς'', [[Illustrated Companion to the Latin Dictionary/Piscator|piscator]]. ''ἀλλαντοπώλης'', [[Illustrated Companion to the Latin Dictionary/Botularius|botularius]]. ''ἀλλᾶς'', [[Illustrated Companion to the Latin Dictionary/Botulus|botulus]]. ''ἁλμαῖα τὰ'', [[Illustrated Companion to the Latin Dictionary/Salgama|salgama]]. ''ἁλμευτής'', [[Illustrated Companion to the Latin Dictionary/Salgamarius|salgamarius]]. ''ἀλόησις'', [[Illustrated Companion to the Latin Dictionary/Tritura|tritura]]. ''ἁλοπήγιον'', [[Illustrated Companion to the Latin Dictionary/Salinae|salinæ]]. ''ἁλοπηγός'', [[Illustrated Companion to the Latin Dictionary/Salinator|salinator]]. ''ἁλτῆρες'', [[Illustrated Companion to the Latin Dictionary/Halteres|halteres]]. ''ἁλυσίδιον'', [[Illustrated Companion to the Latin Dictionary/Catella|catella]]. ''ἅλυσις'', [[Illustrated Companion to the Latin Dictionary/Catena|catena]]. ''ἀλών'', [[Illustrated Companion to the Latin Dictionary/Area|area]], 4. ''Ἁμαζών'', [[Illustrated Companion to the Latin Dictionary/Amazon|Amazon]]. ''ἄμαλλα'', [[Illustrated Companion to the Latin Dictionary/Manipulus|manipulus]]. ''ἅμαξα'', [[Illustrated Companion to the Latin Dictionary/Plaustrum|plaustrum]]. ''ἁμαξεύς'', [[Illustrated Companion to the Latin Dictionary/Plaustrarius|plaustrarius]], 2. ''ἁμαξίς'', [[Illustrated Companion to the Latin Dictionary/Plostellum|plostellum]]. ''ἁμαξοπηγός'', [[Illustrated Companion to the Latin Dictionary/Plaustrarius|plaustrarius]], 1. ''ἁμαξόποδες'', [[Illustrated Companion to the Latin Dictionary/Arbusculae|arbusculæ]]. ''ἄμβιξ'', [[Illustrated Companion to the Latin Dictionary/Obba|obba]]. ''ἄμβων'', [[Illustrated Companion to the Latin Dictionary/Umbo|umbo]]. ''ἀμείβοντες'', [[Illustrated Companion to the Latin Dictionary/Canterius|canterii]]. ''ἄμη'', [[Illustrated Companion to the Latin Dictionary/Hama|hama]]. ''ἀμητήρ'', [[Illustrated Companion to the Latin Dictionary/Messor|messor]]. ''ἀμίς'', [[Illustrated Companion to the Latin Dictionary/Matula|matula]]. ''ἀμολγεύς'', [[Illustrated Companion to the Latin Dictionary/Mulctra|mulctra]]. ''ἄμπυξ'', [[Illustrated Companion to the Latin Dictionary/Frontale|frontale]]. ''ἀμφίβληστρον'', [[Illustrated Companion to the Latin Dictionary/Funda|funda]], 2. ''ἀμφιθέατρον'', [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatrum]]. ''ἀμφίμαλλον'', [[Illustrated Companion to the Latin Dictionary/Amphimallum|amphimallum]]. ''ἄμφιππος'', [[Illustrated Companion to the Latin Dictionary/Desultor|desultor]]. ''ἀμφιπρόστυλος'', [[Illustrated Companion to the Latin Dictionary/Amphiprostylos|amphiprostylos]]. ''ἀμφίταπος'', [[Illustrated Companion to the Latin Dictionary/Amphitapus|amphitapus]]. ''ἄμφοδος'', [[Illustrated Companion to the Latin Dictionary/Ambivium|ambivium]]. ''ἀμφορεύς'', [[Illustrated Companion to the Latin Dictionary/Amphora|amphora]]. ''ἀνάβαθρον'', [[Illustrated Companion to the Latin Dictionary/Anabathrum|anabathrum]]. ''ἀναβόλαιον'', [[Illustrated Companion to the Latin Dictionary/Anabolium|anabolium]]. ''ἀναβολεύς'', [[Illustrated Companion to the Latin Dictionary/Strator|strator]]. ''ἀναβολη'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]], 2. ''ἀνάγλυπτα'', [[Illustrated Companion to the Latin Dictionary/Anaglypta|anaglypta]]. ''ἀναγνώστης'', [[Illustrated Companion to the Latin Dictionary/Anagnostes|anagnostes]]. ''ἀνάδημα'', [[Illustrated Companion to the Latin Dictionary/Anadema|anadema]]. ''ἀνακλιντήριον'', [[Illustrated Companion to the Latin Dictionary/Anaclinterium|anaclinterium]]. ''ἀνάλημμα'', [[Illustrated Companion to the Latin Dictionary/Substructio|substructio]]. ''ἀναξυρίδες'', [[Illustrated Companion to the Latin Dictionary/Bracae|bracæ]], 1. ''ἀνάφορον'', [[Illustrated Companion to the Latin Dictionary/Jugum|jugum]], 2. ''ἀνδρών'', [[Illustrated Companion to the Latin Dictionary/Andron|andron]]. ''ἀνδρωνίτις'', [[Illustrated Companion to the Latin Dictionary/Andronitis|andronitis]]. ''ἀντίον'', [[Illustrated Companion to the Latin Dictionary/Insubulum|insubulum]]. ''ἀντιστράτηγος'', [[Illustrated Companion to the Latin Dictionary/Legatus|legatus]], 1. ''ἀντλία'', [[Illustrated Companion to the Latin Dictionary/Antlia|antlia]]. ''ἄντλος'', [[Illustrated Companion to the Latin Dictionary/Sentina|sentina]]. ''ἀξίνη'', [[Illustrated Companion to the Latin Dictionary/Dolabra|dolabra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Bipennis|bipennis]]. ''ἄξων'', [[Illustrated Companion to the Latin Dictionary/Axis|axis]]. ''ἀποβάθρα'', [[Illustrated Companion to the Latin Dictionary/Pons|pons]], 5. ''ἀποδέσμος'', [[Illustrated Companion to the Latin Dictionary/Fascia|fascia]], 3. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Mamillare|mamillare]]. ''ἀποδυτήριον'', [[Illustrated Companion to the Latin Dictionary/Apodyterium|apodyterium]]. ''ἀποθέωσις'', [[Illustrated Companion to the Latin Dictionary/Consecratio|consecratio]]. ''ἀποθήκη'', [[Illustrated Companion to the Latin Dictionary/Apotheca|apotheca]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Horreum|horreum]], 3. ''ἀποσφράγισμα'', [[Illustrated Companion to the Latin Dictionary/Aposphragisma|aposphragisma]]. ''ἀποφόρητα'', [[Illustrated Companion to the Latin Dictionary/Apophoreta|apophoreta]]. ''ἀραιοστύλος'', [[Illustrated Companion to the Latin Dictionary/Araeostylos|aræostylos]]. ''ἀρβύλη'', [[Illustrated Companion to the Latin Dictionary/Pero|pero]]. ''ἀρδιοθήρα'', [[Illustrated Companion to the Latin Dictionary/Forceps|forceps]], 4. ''ἄριστον'', [[Illustrated Companion to the Latin Dictionary/Prandium|prandium]]. ''ἄρκυς'', [[Illustrated Companion to the Latin Dictionary/Cassis 2|cassis]]. ''ἅρμα'', [[Illustrated Companion to the Latin Dictionary/Currus|currus]]. ''ἅρμα θεῶν'', [[Illustrated Companion to the Latin Dictionary/Tensa|tensa]]. ''ἁρμάμαξα'', [[Illustrated Companion to the Latin Dictionary/Harmamaxa|harmamaxa]]. ''ἁρμογή'', [[Illustrated Companion to the Latin Dictionary/Harmoge|harmoge]]. ''ἀρνευτήρ'', [[Illustrated Companion to the Latin Dictionary/Urinator|urinator]]. ''ἀροτήρ'', [[Illustrated Companion to the Latin Dictionary/Arator|arator]]. ''ἄροτρον'', [[Illustrated Companion to the Latin Dictionary/Aratrum|aratrum]]. ''ἁρπάγη'', [[Illustrated Companion to the Latin Dictionary/Harpago|harpago]]. ''ἁρπαστόν'', [[Illustrated Companion to the Latin Dictionary/Harpastum|harpastum]]. ''ἅρπη'', [[Illustrated Companion to the Latin Dictionary/Harpe|harpe]]. ''ἅρπη καρχαρόδος'', [[Illustrated Companion to the Latin Dictionary/Falx|falx denticulata]]. ''ἀρτέμων'', [[Illustrated Companion to the Latin Dictionary/Artemon|artemon]]. ''ἀρτοθήκη'', [[Illustrated Companion to the Latin Dictionary/Panarium|panarium]]. ''ἀρτολάγανον'', [[Illustrated Companion to the Latin Dictionary/Artolaganus|artolaganus]]. ''ἀρτόπτη'', [[Illustrated Companion to the Latin Dictionary/Artopta|artopta]]. ''ἄρτος'', [[Illustrated Companion to the Latin Dictionary/Panis|panis]]. ''ἀρχίμιμος'', [[Illustrated Companion to the Latin Dictionary/Archimimus|archimimus]]. ''ἄσιλλα'', [[Illustrated Companion to the Latin Dictionary/Jugum|jugum]], 2. ''ἀσκαύλης'', [[Illustrated Companion to the Latin Dictionary/Ascaules|ascaules]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Utricularius|utricularius]]. ''ἀσκοπήρα'', [[Illustrated Companion to the Latin Dictionary/Ascopera|ascopera]]. ''ἀσκός'', [[Illustrated Companion to the Latin Dictionary/Uter|uter]]. ''ἄσκωμα'', [[Illustrated Companion to the Latin Dictionary/Folliculare|folliculare]]. ''ἀσπαλιεύς'', [[Illustrated Companion to the Latin Dictionary/Hamiota|hamiota]]. ''ἀσπιδηφόρος'', [[Illustrated Companion to the Latin Dictionary/Clipeatus|clipeatus]]. ''ἀσπίς'', [[Illustrated Companion to the Latin Dictionary/Clipeus|clipeus]]. ''ἀστραβηλάτης'', [[Illustrated Companion to the Latin Dictionary/Mulio|mulio]], 2. ''ἀστραγαλίζοντες'', [[Illustrated Companion to the Latin Dictionary/Astragalizontes|astragalizontes]]. ''ἀστράγαλος'', [[Illustrated Companion to the Latin Dictionary/Astragalus|astragalus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Talus|talus]]. ''Ἄτλαντες'', [[Illustrated Companion to the Latin Dictionary/Telamones|Telamones]]. ''ἄτρακτος'', [[Illustrated Companion to the Latin Dictionary/Fusus|fusus]]. ''αὐθέψης'', [[Illustrated Companion to the Latin Dictionary/Authepsa|authepsa]]. ''αὐλαία'', [[Illustrated Companion to the Latin Dictionary/Aulaea|aulæa]]. ''αὐλή'', [[Illustrated Companion to the Latin Dictionary/Aula|aula]]. ''αὐλητής'', [[Illustrated Companion to the Latin Dictionary/Tibicen|tibicen]]. ''αὐλητρίς'', [[Illustrated Companion to the Latin Dictionary/Tibicina|tibicina]]. ''αὐλός'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia]]. ''αὐλός ἀνδρήϊος'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia dextra]]. ''αὐλός γυναικήϊος'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia sinistra]]. ''αὐλῳδός'', [[Illustrated Companion to the Latin Dictionary/Auloedus|aulœdus]]. ''αὐτόπυρος'', [[Illustrated Companion to the Latin Dictionary/Autopyros|autopyrus]]. ''ἁφή'', [[Illustrated Companion to the Latin Dictionary/Haphe|haphe]]. ''ἀφιέρωσις'', [[Illustrated Companion to the Latin Dictionary/Consecratio|consecratio]]. ''ἄφλαστον'', [[Illustrated Companion to the Latin Dictionary/Aplustre|aplustre]]. ''ἄφρακτον'', [[Illustrated Companion to the Latin Dictionary/Aphractus|aphractum]]. ''Ἀφροδίτη'', [[Illustrated Companion to the Latin Dictionary/Venus|Venus]]. == ''Β.'' == ''βακτήριον'', [[Illustrated Companion to the Latin Dictionary/Bacillum|bacillum]]. ''βάκτρον'', [[Illustrated Companion to the Latin Dictionary/Baculus|baculus]]. ''Βάκχη'', [[Illustrated Companion to the Latin Dictionary/Baccha|Baccha]]. ''βαλάντιον'', [[Illustrated Companion to the Latin Dictionary/Crumena|crumena]]. ''βάναυσοι'', [[Illustrated Companion to the Latin Dictionary/Sellularii|sellularii]]. ''βάρβιτος'', [[Illustrated Companion to the Latin Dictionary/Barbitos|barbitos]]. ''βᾶρις'', [[Illustrated Companion to the Latin Dictionary/Baris|baris]]. ''βαύκαλις'', [[Illustrated Companion to the Latin Dictionary/Gillo|gillo]]. ''βαφεῖον'', [[Illustrated Companion to the Latin Dictionary/Baphium|baphium]]. ''βελόνη'', [[Illustrated Companion to the Latin Dictionary/Acus|acus]]. ''βέμβιξ'', [[Illustrated Companion to the Latin Dictionary/Turbo|turbo]], 1. ''βηλός'', [[Illustrated Companion to the Latin Dictionary/Limen|limen]]. ''βῆμα'', [[Illustrated Companion to the Latin Dictionary/Pulpitum|pulpitum]], 1. ''βιβλιοθήκη'', [[Illustrated Companion to the Latin Dictionary/Bibliotheca|bibliotheca]]. ''βιβλίον'', [[Illustrated Companion to the Latin Dictionary/Libellus|libellus]], 1. ''βιβλιοπώλης'', [[Illustrated Companion to the Latin Dictionary/Bibliopola|bibliopola]]. ''βίβλος'', [[Illustrated Companion to the Latin Dictionary/Liber|liber]]. ''βιός'', [[Illustrated Companion to the Latin Dictionary/Arcus|arcus]], 1, 2, 3. ''βόαυλος'', [[Illustrated Companion to the Latin Dictionary/Bubile|bubile]]. ''βολίς'', [[Illustrated Companion to the Latin Dictionary/Catapirates|catapirates]]. ''βοτανισμός'', [[Illustrated Companion to the Latin Dictionary/Runcatio|runcatio]]. ''βουκόλος'', [[Illustrated Companion to the Latin Dictionary/Bubulcus|bubulcus]]. ''βούτυρον'', [[Illustrated Companion to the Latin Dictionary/Butyrum|butyrum]]. ''βραβεῖον'', [[Illustrated Companion to the Latin Dictionary/Brabeum|brabeum]]. ''βραβευτής'', [[Illustrated Companion to the Latin Dictionary/Brabeuta|brabeuta]]. ''βρόχος'', [[Illustrated Companion to the Latin Dictionary/Laqueus|laqueus]]. ''βυκάνη'', [[Illustrated Companion to the Latin Dictionary/Bucina|bucina]]. ''βυκανητής'', [[Illustrated Companion to the Latin Dictionary/Bucinator|bucinator]]. ''βωλοκοπία'', [[Illustrated Companion to the Latin Dictionary/Occatio|occatio]]. ''βωλοκόπος'', [[Illustrated Companion to the Latin Dictionary/Occator|occator]]. ''βωμος'', [[Illustrated Companion to the Latin Dictionary/Ara|ara]]. == ''Γ.'' == ''γαῖσον'', [[Illustrated Companion to the Latin Dictionary/Gaesum|gæsum]]. ''γάμος'', [[Illustrated Companion to the Latin Dictionary/Nuptiae|nuptiæ]]. ''γάρον'', [[Illustrated Companion to the Latin Dictionary/Garum|garum]]. ''γαυλός'', [[Illustrated Companion to the Latin Dictionary/Gaulus|gaulus]], 1. ''γαῦλος'', [[Illustrated Companion to the Latin Dictionary/Gaulus|gaulus]], 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cupa|cupa]], 1. ''γαύσαπης'', [[Illustrated Companion to the Latin Dictionary/Gausapa|gausapa]]. ''γεῖσσον'', [[Illustrated Companion to the Latin Dictionary/Projectura|projectura]]. ''γέρῥον'', [[Illustrated Companion to the Latin Dictionary/Gerrae|gerræ]]. ''γέφυρα'', [[Illustrated Companion to the Latin Dictionary/Pons|pons]]. ''γεφυροποιός'', [[Illustrated Companion to the Latin Dictionary/Pontifex|pontifex]]. ''γίγγλυμος'', [[Illustrated Companion to the Latin Dictionary/Ginglymus|ginglymus]]. ''γίγγρας'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia gingrina]]. ''γλύφανον'', [[Illustrated Companion to the Latin Dictionary/Caelum|cælum]]. ''γλῶσσα, γλωττίς'', [[Illustrated Companion to the Latin Dictionary/Ligula|ligula]], 1. ''γόμφος'', [[Illustrated Companion to the Latin Dictionary/Gomphus|gomphus]]. ''γνώμων'', [[Illustrated Companion to the Latin Dictionary/Gnomon|gnomon]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Groma|groma]]. ''γνωρίσματα'', [[Illustrated Companion to the Latin Dictionary/Monumentum|monumenta]], 3. ''γραμματεύς'', [[Illustrated Companion to the Latin Dictionary/Scriba|scriba]]. ''γραμματικός'', [[Illustrated Companion to the Latin Dictionary/Literatus|literatus]], 3. ''γραμματοφόρος'', [[Illustrated Companion to the Latin Dictionary/Tabellarius|tabellarius]]. ''γραμμή'', [[Illustrated Companion to the Latin Dictionary/Linea|linea]], 4. ''γραφή'', [[Illustrated Companion to the Latin Dictionary/Pictura|pictura]]. ''γραφεύς'', [[Illustrated Companion to the Latin Dictionary/Pictor|pictor]]. ''γραφίον'', [[Illustrated Companion to the Latin Dictionary/Graphium|graphium]]. ''γραφίς'', [[Illustrated Companion to the Latin Dictionary/Stilus|stilus]]. ''γρῖπος, γρῖφος'', [[Illustrated Companion to the Latin Dictionary/Griphus|griphus]]. ''γροσφομάχοι'', [[Illustrated Companion to the Latin Dictionary/Velites|velites]]. ''γρόσφος'', [[Illustrated Companion to the Latin Dictionary/Hasta|hasta velitaris]]. ''γρύψ'', [[Illustrated Companion to the Latin Dictionary/Gryps|gryps]]. ''γυαλοθώραξ'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 1. ''γύαλον'', [[Illustrated Companion to the Latin Dictionary/Pectorale|pectorale]]. ''γύης'', [[Illustrated Companion to the Latin Dictionary/Bura|bura]]. ''γυμνασίαρχος'', [[Illustrated Companion to the Latin Dictionary/Gymnasiarchus|gymnasiarchus]]. ''γυμνάσιον'', [[Illustrated Companion to the Latin Dictionary/Gymnasium|gymnasium]]. ''γυμνός'', [[Illustrated Companion to the Latin Dictionary/Nudus|nudus]]. ''γυναικεῖον'', [[Illustrated Companion to the Latin Dictionary/Gynaeceum|gynæceum]]. ''γυναικωνῖτις'', [[Illustrated Companion to the Latin Dictionary/Gynaeceum|gynæconitis]]. ''γωρυτός'', [[Illustrated Companion to the Latin Dictionary/Corytus|corytus]]. == ''Δ.'' == ''δᾳδοῦχος'', [[Illustrated Companion to the Latin Dictionary/Daduchus|daduchus]]. ''δαιμόνιον'', [[Illustrated Companion to the Latin Dictionary/Daemonium|dæmonium]]. ''δαίμων'', [[Illustrated Companion to the Latin Dictionary/Daemon|dæmon]]. ''δαἷς'', [[Illustrated Companion to the Latin Dictionary/Taeda|tæda]]. ''δακτυλήθρα'', [[Illustrated Companion to the Latin Dictionary/Digitale|digitale]]. ''δακτυλιοθήκη'', [[Illustrated Companion to the Latin Dictionary/Dactyliotheca|dactyliotheca]]. ''δακτύλιος'', [[Illustrated Companion to the Latin Dictionary/Anulus|anulus]]. ''δανά'', [[Illustrated Companion to the Latin Dictionary/Coctilis|coctilia]]. ''δάπεδον'', [[Illustrated Companion to the Latin Dictionary/Pavimentum|pavimentum]]. ''δαρεικός'', [[Illustrated Companion to the Latin Dictionary/Darius|daricus]]. ''δεῖπνον'', [[Illustrated Companion to the Latin Dictionary/Coena|cœna]]. ''δεκήρης'', [[Illustrated Companion to the Latin Dictionary/Decemremis|decemremis]]. ''δεσμός'', [[Illustrated Companion to the Latin Dictionary/Vinculum|vinculum]]. ''δήμαρχος'', [[Illustrated Companion to the Latin Dictionary/Tribunus|tribunus plebis]]. ''διάβαθρον'', [[Illustrated Companion to the Latin Dictionary/Diabathrum|diabathrum]]. ''διαβήτης'', [[Illustrated Companion to the Latin Dictionary/Circinus|circinus]]. ''διάδημα'', [[Illustrated Companion to the Latin Dictionary/Diadema|diadema]]. ''διάζωμα'', [[Illustrated Companion to the Latin Dictionary/Cinctus 1|cinctus]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]], 5. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Subligaculum|subligaculum]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Praecinctio|præcinctio]]. ''διάθυρον'', [[Illustrated Companion to the Latin Dictionary/Prothyrum|prothyrum]]. ''δίαιτα'', [[Illustrated Companion to the Latin Dictionary/Diaeta|diæta]], 1. ''διάπασμα'', [[Illustrated Companion to the Latin Dictionary/Diapasma|diapasma]]. ''διάστυλος'', [[Illustrated Companion to the Latin Dictionary/Diastylos|diastylos]]. ''διάτονοι'', [[Illustrated Companion to the Latin Dictionary/Diatoni|diatoni]]. ''διάτρετα'', [[Illustrated Companion to the Latin Dictionary/Diatreta|diatreta]]. ''διδασκαλεῖον'', [[Illustrated Companion to the Latin Dictionary/Ludus|ludus]]. ''δίδραχμον'', [[Illustrated Companion to the Latin Dictionary/Didrachma|didrachmum]]. ''δίθυροσ'', [[Illustrated Companion to the Latin Dictionary/Biforis|biforis]]. ''δικαστήριον'', [[Illustrated Companion to the Latin Dictionary/Tribunal|tribunal]]. ''δίκελλα'', [[Illustrated Companion to the Latin Dictionary/Bidens|bidens]]. ''δίκρανον'', [[Illustrated Companion to the Latin Dictionary/Furca|furca]], 1. ''δίκροτος'', [[Illustrated Companion to the Latin Dictionary/Biremis|biremis]], 2. ''δίκτύδιον'', [[Illustrated Companion to the Latin Dictionary/Reticulum|reticulum]], 1. ''δίκτυον'', [[Illustrated Companion to the Latin Dictionary/Rete|rete]]. ''δίκωπος'', [[Illustrated Companion to the Latin Dictionary/Biremis|biremis]], 1. ''διμάχαι'', [[Illustrated Companion to the Latin Dictionary/Dimachae|dimachæ]]. ''διμάχαιροι'', [[Illustrated Companion to the Latin Dictionary/Dimachaeri|dimachæri]]. ''διμέτωπος'', [[Illustrated Companion to the Latin Dictionary/Bifrons|bifrons]]. ''δίμιτος'', [[Illustrated Companion to the Latin Dictionary/Bilix|bilix]]. ''δίμυξος'', [[Illustrated Companion to the Latin Dictionary/Bilychnis|bilychnis]]. ''δίνος'', [[Illustrated Companion to the Latin Dictionary/Sinum|sinum]]. ''δίοπτρα'', [[Illustrated Companion to the Latin Dictionary/Dioptra|dioptra]]. ''δίπλαξ'', [[Illustrated Companion to the Latin Dictionary/Diplois|diplois]]. ''διπλοἷς'', [[Illustrated Companion to the Latin Dictionary/Diplois|diplois]]. ''δίπλωμα'', [[Illustrated Companion to the Latin Dictionary/Diploma|diploma]]. ''δίπρωρος'', [[Illustrated Companion to the Latin Dictionary/Biprorus|biprorus]]. ''δίπτερος'', [[Illustrated Companion to the Latin Dictionary/Dipteros|dipteros]]. ''δίπτυχα'', [[Illustrated Companion to the Latin Dictionary/Diptycha|diptycha]]. ''δισκοβόλος'', [[Illustrated Companion to the Latin Dictionary/Discobolus|discobolus]]. ''δισκος'', [[Illustrated Companion to the Latin Dictionary/Discus|discus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Superficies|superficies]], 2. ''διφθέρα'', [[Illustrated Companion to the Latin Dictionary/Membrana|membrana]], 2. ''διφρίσκος'', [[Illustrated Companion to the Latin Dictionary/Sedecula|sedecula]]. ''δίφρος'', [[Illustrated Companion to the Latin Dictionary/Sella|sella]]. ''δίφρος ἀγκυλόπους'', [[Illustrated Companion to the Latin Dictionary/Sella|sella curulis]]. ''δίφρος κατάστεγος'', [[Illustrated Companion to the Latin Dictionary/Sella|sella gestatoria]]. ''δίχαλκον'', [[Illustrated Companion to the Latin Dictionary/Dichalcon|dichalcon]]. ''δίωτη'', [[Illustrated Companion to the Latin Dictionary/Diota|diota]]. ''δόλων'', [[Illustrated Companion to the Latin Dictionary/Dolon|dolon]]. ''δορυδρέπανον'', [[Illustrated Companion to the Latin Dictionary/Falx|falx muralis]]. ''δορυφόρος'', [[Illustrated Companion to the Latin Dictionary/Doryphorus|doryphorus]]. ''δράγμα'', [[Illustrated Companion to the Latin Dictionary/Manipulus|manipulus]]. ''δραχμή'', [[Illustrated Companion to the Latin Dictionary/Drachma|drachma]]. ''δρεπάνον'', [[Illustrated Companion to the Latin Dictionary/Falx|falx]]. ''δρόμων'', [[Illustrated Companion to the Latin Dictionary/Dromo|dromon]]. ''δρύφακτον'', [[Illustrated Companion to the Latin Dictionary/Cancelli|cancelli]]. == ''Ε.'' == ''ἐγγυθήκη'', [[Illustrated Companion to the Latin Dictionary/Incitega|incitega]]. ''ἔγκαρπα'', [[Illustrated Companion to the Latin Dictionary/Encarpa|encarpa]]. ''ἐγκαυστική'', [[Illustrated Companion to the Latin Dictionary/Encaustica|encaustica]]. ''ἐγκόμβωμα'', [[Illustrated Companion to the Latin Dictionary/Encomboma|encomboma]]. ''ἐγχειρίδιον'', [[Illustrated Companion to the Latin Dictionary/Pugio|pugio]]. ''ἔγχος'', [[Illustrated Companion to the Latin Dictionary/Hasta|hasta]]. ''ἔδαφος'', [[Illustrated Companion to the Latin Dictionary/Pavimentum|pavimentum]]. ''ἕδρα'', [[Illustrated Companion to the Latin Dictionary/Sedes|sedes]]. ''ἑκατοντάρχης'', [[Illustrated Companion to the Latin Dictionary/Centurio|centurio]]. ''ἐκμαγεῖον'', [[Illustrated Companion to the Latin Dictionary/Mantele|mantele]]. ''ἔκτυπος'', [[Illustrated Companion to the Latin Dictionary/Ectypus|ectypus]]. ''ἐλαιοθέσιον'', [[Illustrated Companion to the Latin Dictionary/Elaeothesium|elæothesium]]. ''ἐλατήρ'', [[Illustrated Companion to the Latin Dictionary/Clavis|clavis trochi]]. ''ἑλέπολις'', [[Illustrated Companion to the Latin Dictionary/Helepolis|helepolis]]. ''ἕλιξ'', [[Illustrated Companion to the Latin Dictionary/Cincinnus|cincinnus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Helix|helix]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Voluta|voluta]], 2. ''ἐλλιμενιστής'', [[Illustrated Companion to the Latin Dictionary/Portitor|portitor]]. ''ἐλλόβιον'', [[Illustrated Companion to the Latin Dictionary/Inauris|inauris]]. ''ἐλλύχνιον'', [[Illustrated Companion to the Latin Dictionary/Ellychnium|ellychnium]]. ''ἔλυμα'', [[Illustrated Companion to the Latin Dictionary/Dentale|dentale]]. ''ἔλυμος'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia curva]]. ''ἔμβλημα'', [[Illustrated Companion to the Latin Dictionary/Emblema|emblema]]. ''ἔμβολος'', [[Illustrated Companion to the Latin Dictionary/Rostrum|rostrum]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Embolus|embolus]]. ''ἐμπίλια'', [[Illustrated Companion to the Latin Dictionary/Impilia|impilia]]. ''ἔμπλεκτον'', [[Illustrated Companion to the Latin Dictionary/Emplecton|emplecton]]. ''ἐμπόριον'', [[Illustrated Companion to the Latin Dictionary/Emporium|emporium]]. ''ἔμπορος'', [[Illustrated Companion to the Latin Dictionary/Emporos|emporus]]. ''ἐνδρομίς'', [[Illustrated Companion to the Latin Dictionary/Endromis|endromis]], 3. ''ἕνδυμα'', [[Illustrated Companion to the Latin Dictionary/Indutus|indutus]]. ''ἐνετή'', [[Illustrated Companion to the Latin Dictionary/Fibula|fibula]]. ''ἐνήλατον'', [[Illustrated Companion to the Latin Dictionary/Sponda|sponda]]. ''ἐνόδιον'', [[Illustrated Companion to the Latin Dictionary/Plaga|plaga]]. ''ἔνοπτρον'', [[Illustrated Companion to the Latin Dictionary/Speculum|speculum]]. ''ἐνώτιον'', [[Illustrated Companion to the Latin Dictionary/Inauris|inauris]]. ''ἐξέδρα'', [[Illustrated Companion to the Latin Dictionary/Exedra|exedra]]. ''ἐξήρης'', [[Illustrated Companion to the Latin Dictionary/Hexeris|hexeris]]. ''ἐξωμίς'', [[Illustrated Companion to the Latin Dictionary/Exomis|exomis]]. ''ἐξώστρα'', [[Illustrated Companion to the Latin Dictionary/Exostra|exostra]]. ''ἐπιβάθρα'', [[Illustrated Companion to the Latin Dictionary/Pons|pons]], 5. ''ἐπιβάται'', [[Illustrated Companion to the Latin Dictionary/Classiarii|classiarii]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Epibatae|epibatæ]]. ''ἐπίβλημα'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Stragulum|stragulum]], 2. ''ἐπίδειπνις'', [[Illustrated Companion to the Latin Dictionary/Epidipnis|epidipnis]]. ''ἐπίδρομος'', [[Illustrated Companion to the Latin Dictionary/Epidromus|epidromus]]. ''ἐπίκρανον'', [[Illustrated Companion to the Latin Dictionary/Capitulum|capitulum]]. ''ἐπίκριον'', [[Illustrated Companion to the Latin Dictionary/Antenna|antenna]]. ''ἐπίκροκον'', [[Illustrated Companion to the Latin Dictionary/Epicrocum|epicrocum]]. ''ἐπισπαστήρ'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 2. ''ἐπιστόμιον'', [[Illustrated Companion to the Latin Dictionary/Epistomium|epistomium]]. ''ἐπιστύλιον'', [[Illustrated Companion to the Latin Dictionary/Epistylium|epistylium]]. ''ἐπισφύριον'', [[Illustrated Companion to the Latin Dictionary/Luna|luna]]. ''ἐπίσωτρον'', [[Illustrated Companion to the Latin Dictionary/Canthus|canthus]]. ''ἐπίτονος'' (sc. ''ἱμάς''), [[Illustrated Companion to the Latin Dictionary/Chalatorius|chalatorius funis]]. ''ἐπίτυρον'', [[Illustrated Companion to the Latin Dictionary/Epityrum|epityrum]]. ''ἐπίχυσις'', [[Illustrated Companion to the Latin Dictionary/Epichysis|epichysis]]. ''ἐποχεύς'', [[Illustrated Companion to the Latin Dictionary/Sufflamen|sufflamen]]. ''ἑπτήρης'', [[Illustrated Companion to the Latin Dictionary/Hepteris|hepteris]]. ''ἐπωμίς'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 4. ''ἐργαστήριον'', [[Illustrated Companion to the Latin Dictionary/Officina|officina]]. ''ἐργατης'', [[Illustrated Companion to the Latin Dictionary/Ergata|ergata]]. ''ἐργολάβος'', [[Illustrated Companion to the Latin Dictionary/Redemptor|redemptor]]. ''ἐρείσματα'', [[Illustrated Companion to the Latin Dictionary/Anterides|anterides]]. ''ἐρέτης'', [[Illustrated Companion to the Latin Dictionary/Remex|remex]]. ''ἐρετμός'', [[Illustrated Companion to the Latin Dictionary/Remus|remus]]. ''Ἑρμαῖ'', [[Illustrated Companion to the Latin Dictionary/Hermae|Hermæ]]. ''ἑστία'', [[Illustrated Companion to the Latin Dictionary/Focus|focus]]. ''ἑστίασις'', [[Illustrated Companion to the Latin Dictionary/Convivium|convivium]]. ''ἐρχάρα'', [[Illustrated Companion to the Latin Dictionary/Focus|focus]]. ''ἐρχάριον'', [[Illustrated Companion to the Latin Dictionary/Foculus|foculus]], 2. ''εὐνή'', [[Illustrated Companion to the Latin Dictionary/Lectus|lectus genialis]]. ''εὔστυλος'', [[Illustrated Companion to the Latin Dictionary/Eustylos|eustylos]]. ''εὐχωλιμαῖοι'', [[Illustrated Companion to the Latin Dictionary/Soldurii|soldurii]]. ''ἐφαπτίς'', [[Illustrated Companion to the Latin Dictionary/Sagum|sagum]]. ''ἐφηβεῖον'', [[Illustrated Companion to the Latin Dictionary/Ephebeum|ephebeum]]. ''ἐφημερίς'', [[Illustrated Companion to the Latin Dictionary/Ephemeris|ephemeris]]. ''ἐφίππιον'', [[Illustrated Companion to the Latin Dictionary/Ephippium|ephippium]]. ''ἐφύφη'', [[Illustrated Companion to the Latin Dictionary/Subtemen|subtemen]]. ''εχέτλη'', [[Illustrated Companion to the Latin Dictionary/Stiva|stiva]]. ''ἐχῖνος'', [[Illustrated Companion to the Latin Dictionary/Echinus|echinus]]. == ''Ζ.'' == ''ζεύγη'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibiæ pares]]. ''ζύγιος ἵππος'', [[Illustrated Companion to the Latin Dictionary/Jugalis|jugalis equus]]. ''ζυγόδεσμος'', [[Illustrated Companion to the Latin Dictionary/Cohum|cohum]]. ''ζυγόν'', [[Illustrated Companion to the Latin Dictionary/Jugum|jugum]]. ''ζυθός'', [[Illustrated Companion to the Latin Dictionary/Zythum|zythum]]. ''ζωγρεῖον'', [[Illustrated Companion to the Latin Dictionary/Vivarium|vivarium]]. ''ζώνη'', [[Illustrated Companion to the Latin Dictionary/Zona|zona]]. ''ζωοφόρος'', [[Illustrated Companion to the Latin Dictionary/Zophorus|zophorus]]. ''ζωστήρ'', [[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]], 3. & 4. == ''Η.'' == ''ἠθμός'', [[Illustrated Companion to the Latin Dictionary/Colum|colum]]. ''ἠλακάτη'', [[Illustrated Companion to the Latin Dictionary/Colus|colus]]. ''ἡλιαστήριον'', [[Illustrated Companion to the Latin Dictionary/Solarium|solarium]], 2. ''ἡλιοκάμινος'', [[Illustrated Companion to the Latin Dictionary/Heliocaminus|heliocaminus]]. ''ἦλος'', [[Illustrated Companion to the Latin Dictionary/Clavus|clavus]]. ''ἡμερόκοιτος'', [[Illustrated Companion to the Latin Dictionary/Dormitator|dormitator]]. ''ἡμερολόγιον'', [[Illustrated Companion to the Latin Dictionary/Calendarium|calendarium]]. ''ἡμιθωράκιον'', [[Illustrated Companion to the Latin Dictionary/Pectorale|pectorale]]. ''ἡμικύκλιον'', [[Illustrated Companion to the Latin Dictionary/Hemicyclium|hemicyclium]]. ''ἡμιολία'', [[Illustrated Companion to the Latin Dictionary/Hemiolia|hemiolia]]. ''ήμιονηγός'', [[Illustrated Companion to the Latin Dictionary/Mulio|mulio]], 2. ''ἡνίαι'', [[Illustrated Companion to the Latin Dictionary/Habena|habena]], 1. ''ἡνιοχος'', [[Illustrated Companion to the Latin Dictionary/Auriga|auriga]]. ''ήπατοσκόπος'', [[Illustrated Companion to the Latin Dictionary/Extispex|extispex]]. ''ἡρῷον'', [[Illustrated Companion to the Latin Dictionary/Heroum|heroum]]. == ''Θ.'' == ''θαλαμηγός'', [[Illustrated Companion to the Latin Dictionary/Thalamegus|thalamegus]]. ''θάλαμος'', [[Illustrated Companion to the Latin Dictionary/Thalamus|thalamus]]. ''θαλασσίτης'', [[Illustrated Companion to the Latin Dictionary/Thalassites|thalassites]]. ''θαυματοποιός'', [[Illustrated Companion to the Latin Dictionary/Praestigiator|præstigiator]]. ''θέατρον'', [[Illustrated Companion to the Latin Dictionary/Theatrum|theatrum]], 2. ''θεριστής'', [[Illustrated Companion to the Latin Dictionary/Messor|messor]]. ''θέριστρον'', [[Illustrated Companion to the Latin Dictionary/Theristrum|theristrum]]. ''θέρμαι'', [[Illustrated Companion to the Latin Dictionary/Thermae|thermæ]]. ''θερμοπώλιον'', [[Illustrated Companion to the Latin Dictionary/Thermopolium|thermopolium]]. ''θήρα'', [[Illustrated Companion to the Latin Dictionary/Venatio|venatio]]. ''θηρατής'', [[Illustrated Companion to the Latin Dictionary/Venator|venator]], 1. ''θηριομάχης'', [[Illustrated Companion to the Latin Dictionary/Bestiarius|bestiarius]]. ''θόλος'', [[Illustrated Companion to the Latin Dictionary/Tholus|tholus]]. ''θρίαμβος'', [[Illustrated Companion to the Latin Dictionary/Triumphus|triumphus]]. ''θρίξ'', [[Illustrated Companion to the Latin Dictionary/Crinis|crinis]]. ''θρῖναξ'', [[Illustrated Companion to the Latin Dictionary/Ventilabrum|ventilabrum]]. ''θρόνος'', [[Illustrated Companion to the Latin Dictionary/Solium|solium]]. ''θρυαλλίς'', [[Illustrated Companion to the Latin Dictionary/Ellychnium|ellychnium]]. ''θύλακος'', [[Illustrated Companion to the Latin Dictionary/Bracae|bracæ]], 2. ''θυμιατήριον'', [[Illustrated Companion to the Latin Dictionary/Turibulum|turibulum]]. ''θυμέλη'', [[Illustrated Companion to the Latin Dictionary/Thymele|thymele]]. ''θυμελικοί'', [[Illustrated Companion to the Latin Dictionary/Thymelici|thymelici]]. ''θύρα'', [[Illustrated Companion to the Latin Dictionary/Ostium|ostium]]. ''θύρα αὔλειος'', [[Illustrated Companion to the Latin Dictionary/Janua|janua]]. ''θύραι διάπριστοι'', [[Illustrated Companion to the Latin Dictionary/Valvae|valvæ]]. ''θυρεός'', [[Illustrated Companion to the Latin Dictionary/Scutum|scutum]]. ''θυρίς'', [[Illustrated Companion to the Latin Dictionary/Fenestra|fenestra]]. ''θυρίς δικλίς'', [[Illustrated Companion to the Latin Dictionary/Fenestra|fenestra biforis]]. ''θύρσος'', [[Illustrated Companion to the Latin Dictionary/Thyrsus|thyrsus]]. ''θυρωρός'', [[Illustrated Companion to the Latin Dictionary/Janitor|janitor]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Ostiarius|ostiarius]]. ''θύσανοι'', [[Illustrated Companion to the Latin Dictionary/Fimbria|fimbriæ]]. ''θυσανωτός'', [[Illustrated Companion to the Latin Dictionary/Fimbriatus|fimbriatus]]. ''θυτήριον'', [[Illustrated Companion to the Latin Dictionary/Ara|ara]]. ''θύτης'', [[Illustrated Companion to the Latin Dictionary/Popa|popa]]. ''θῶμιξ'', [[Illustrated Companion to the Latin Dictionary/Tomix|tomix]]. ''θωράκιον'', [[Illustrated Companion to the Latin Dictionary/Loricula|loricula]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pluteus|pluteus]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Carchesium|carchesium]], 2. ''θώραξ'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]]. ''{{mdash}}{{mdash}} στάδιος'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 2. ''{{mdash}}{{mdash}} λεπιδωτός'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 3. ''{{mdash}}{{mdash}} φολιδωτός'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 4. ''{{mdash}}{{mdash}} ἁλυσιδωτός'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 8. ''{{mdash}}{{mdash}} λίνεος'', [[Illustrated Companion to the Latin Dictionary/Lorica|lorica]], 9. == ''Ι.'' == ''ἰατραλείπτης'', [[Illustrated Companion to the Latin Dictionary/Iatralipta|iatralipta]]. ''ἰατρός'', [[Illustrated Companion to the Latin Dictionary/Medicus|medicus]]. ''ἴγδη'', [[Illustrated Companion to the Latin Dictionary/Pila 1|pila]], 1. ''ἱερεῖον'', [[Illustrated Companion to the Latin Dictionary/Hostia|hostia]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Victima|victima]]. ''ἱερονίκης'', [[Illustrated Companion to the Latin Dictionary/Hieronica|hieronica]]. ''ἱεροσκόπος'', [[Illustrated Companion to the Latin Dictionary/Haruspex|haruspex]]. ''ἱεροφάντης'', [[Illustrated Companion to the Latin Dictionary/Hierophanta|hierophantes]]. ''ἱεροφυλάκιον'', [[Illustrated Companion to the Latin Dictionary/Sacrarium|sacrarium]]. ''ἱεροφύλαξ'', [[Illustrated Companion to the Latin Dictionary/Aedituus|ædituus]]. ''ίκετήρια'', [[Illustrated Companion to the Latin Dictionary/Velamentum|velamenta]]. ''ἱμάς'', [[Illustrated Companion to the Latin Dictionary/Lorum|lorum]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Caestus|cæstus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Corrigia|corrigia]]. ''ίμάτιον'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]. ''ἰξευτης'', [[Illustrated Companion to the Latin Dictionary/Auceps|auceps]]. ''ἰός'', [[Illustrated Companion to the Latin Dictionary/Sagitta|sagitta]]. ''ἰπνός'', [[Illustrated Companion to the Latin Dictionary/Laterna|laterna]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Furnus|furnus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Culina|culina]]. ''ίππαγωγοί'', [[Illustrated Companion to the Latin Dictionary/Hippagines|hippagogi]]. ''ἱππεύς'', [[Illustrated Companion to the Latin Dictionary/Eques|eques]], 1. ''ἱππίατρος'', [[Illustrated Companion to the Latin Dictionary/Equarius|equarius medicus]]. ''ἱππόδρομος'', [[Illustrated Companion to the Latin Dictionary/Hippodromus|hippodromus]], 2. ''ἱπποκάμπος'', [[Illustrated Companion to the Latin Dictionary/Hippocampus|hippocampus]]. ''ἱπποκένταυρος'', [[Illustrated Companion to the Latin Dictionary/Hippocentauros|hippocentaurus]]. ''ίπποκόμος'', [[Illustrated Companion to the Latin Dictionary/Agaso|agaso]]. ''ἱπποπήρα'', [[Illustrated Companion to the Latin Dictionary/Hippopera|hippopera]]. ''ἱππόστασις'', [[Illustrated Companion to the Latin Dictionary/Equile|equile]]. ''ίπποτοξότης'', [[Illustrated Companion to the Latin Dictionary/Hippotoxota|hippotoxota]]. ''ἰσόδομος'', [[Illustrated Companion to the Latin Dictionary/Isodomos|isodomus]]. ''ἱστίον'', [[Illustrated Companion to the Latin Dictionary/Velum|velum]]. ''ἱστοβοεύς'', [[Illustrated Companion to the Latin Dictionary/Temo|temo]], 2. ''ἱστός'', [[Illustrated Companion to the Latin Dictionary/Malus|malus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Tela|tela]]. ''ἱστών'', [[Illustrated Companion to the Latin Dictionary/Textrina|textrina]]. ''ἰχθυοτροφεῖον'', [[Illustrated Companion to the Latin Dictionary/Piscina|piscina]], 2. ''ἰχνογραφία'', [[Illustrated Companion to the Latin Dictionary/Ichnographia|ichnographia]]. == ''Κ.'' == ''κάγκανα'', [[Illustrated Companion to the Latin Dictionary/Coctilis|coctilia]]. ''κάδος'', [[Illustrated Companion to the Latin Dictionary/Cadus|cadus]]. ''Κάδουλος'' or ''-ωλος'', [[Illustrated Companion to the Latin Dictionary/Camillus|Camillus]]. ''καθέδρα'', [[Illustrated Companion to the Latin Dictionary/Cathedra|cathedra]]. ''καθετήρ'', [[Illustrated Companion to the Latin Dictionary/Catheter|catheter]]. ''κάθετος'', [[Illustrated Companion to the Latin Dictionary/Perpendiculum|perpendiculum]]. ''κακκάβη'', [[Illustrated Companion to the Latin Dictionary/Cacabus|caccabus]]. ''κάλαθος'', [[Illustrated Companion to the Latin Dictionary/Calathus|calathus]]. ''καλαμίς'', [[Illustrated Companion to the Latin Dictionary/Calamarius|calamarius]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Calamister|calamister]]. ''κάλαμος'', [[Illustrated Companion to the Latin Dictionary/Calamus|calamus]]. ''καλάπους'', [[Illustrated Companion to the Latin Dictionary/Forma|forma]], 5. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Tentipellium|tentipellium]]. ''κάλπις'', [[Illustrated Companion to the Latin Dictionary/Urna|urna]]. ''κάλυμμα'', [[Illustrated Companion to the Latin Dictionary/Caliptra|calyptra]]. ''κάλλυντρον'', [[Illustrated Companion to the Latin Dictionary/Scopae|scopæ]]. ''καλυπτήρ'', [[Illustrated Companion to the Latin Dictionary/Imbrex|imbrex]]. ''καλύπτρα'', [[Illustrated Companion to the Latin Dictionary/Caliptra|calyptra]]. ''κάλχη'', [[Illustrated Companion to the Latin Dictionary/Voluta|voluta]], 1. ''κάλως'', [[Illustrated Companion to the Latin Dictionary/Rudens|rudens]]. ''κάμαξ'', [[Illustrated Companion to the Latin Dictionary/Hasta|hasta graminea]]. ''καμάρα'', [[Illustrated Companion to the Latin Dictionary/Camara|camara]]. ''κάμινος'', [[Illustrated Companion to the Latin Dictionary/Caminus|caminus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Fornax|fornax]]. ''καμπτήρ'', [[Illustrated Companion to the Latin Dictionary/Meta|meta]], 1. ''κάνεον, κάνης'', [[Illustrated Companion to the Latin Dictionary/Canistrum|canistrum]]. ''κανηφόρος'', [[Illustrated Companion to the Latin Dictionary/Canephora|canephora]]. ''κάνθαρος'', [[Illustrated Companion to the Latin Dictionary/Cantharus|cantharus]]. ''κανθήλια'', [[Illustrated Companion to the Latin Dictionary/Clitellae|clitellæ]]. ''κανοῦν'', [[Illustrated Companion to the Latin Dictionary/Canum|canum]]. ''κανῶν'', [[Illustrated Companion to the Latin Dictionary/Regula|regula]]. ''καπηλεῖον'', [[Illustrated Companion to the Latin Dictionary/Caupona|caupona]], 2. ''καρβάτιναι'', [[Illustrated Companion to the Latin Dictionary/Carbatinae|carbatinæ]]. ''καρδιοφύλαξ'', [[Illustrated Companion to the Latin Dictionary/Pectorale|pectorale]]. ''κάρκαρον'', [[Illustrated Companion to the Latin Dictionary/Carcer|carcer]]. ''κάρπασος'', [[Illustrated Companion to the Latin Dictionary/Carbasus|carbasus]]. ''Καρυάτιδες'', [[Illustrated Companion to the Latin Dictionary/Caryatides|Caryatides]]. ''καρφαμάτιον'', [[Illustrated Companion to the Latin Dictionary/Merga|merga]]. ''καρχήσιον'', [[Illustrated Companion to the Latin Dictionary/Carchesium|carchesium]]. ''κάταγμα'', [[Illustrated Companion to the Latin Dictionary/Tractum|tractum]], 1. ''κατάγραφα'', [[Illustrated Companion to the Latin Dictionary/Catagrapha|catagrapha]]. ''καταῖτυξ'', [[Illustrated Companion to the Latin Dictionary/Cudo|cudo]]. ''κατακλίνομαι'', [[Illustrated Companion to the Latin Dictionary/Accubo|accubo]]. ''καταπέλτης'', [[Illustrated Companion to the Latin Dictionary/Catapulta|catapulta]]. ''καταπελτίκος'', [[Illustrated Companion to the Latin Dictionary/Catapultarius|catapultarius]]. ''καταρῥάκτης'', [[Illustrated Companion to the Latin Dictionary/Cataracta|cataracta]]. ''κατάστρωμα'', [[Illustrated Companion to the Latin Dictionary/Constratum|constratum navis]]. ''κατάφρακτος'', [[Illustrated Companion to the Latin Dictionary/Cataphractus|cataphractus]]. ''κάτοπτρον'', [[Illustrated Companion to the Latin Dictionary/Speculum|speculum]]. ''κατόρυξις'', [[Illustrated Companion to the Latin Dictionary/Humatio|humatio]]. ''κατοχεύς'', [[Illustrated Companion to the Latin Dictionary/Pessulus|pessulus]]. ''κατωμίζω'', [[Illustrated Companion to the Latin Dictionary/Catomidio|catomidio]]. ''καυλός'', [[Illustrated Companion to the Latin Dictionary/Scapus|scapus]], 5. ''καυσία'', [[Illustrated Companion to the Latin Dictionary/Causia|causia]]. ''καυτήρ -ήριον'', [[Illustrated Companion to the Latin Dictionary/Cauter|cauter]], -erium. ''καψιδρώτιον'', [[Illustrated Companion to the Latin Dictionary/Sudarium|sudarium]]. ''κεκρύφαλος'', [[Illustrated Companion to the Latin Dictionary/Reticulum|reticulum]], 2. ''κέλευσμα'', [[Illustrated Companion to the Latin Dictionary/Celeusma|celeusma]]. ''κελευστής'', [[Illustrated Companion to the Latin Dictionary/Hortator|hortator]]. ''κέλης'', [[Illustrated Companion to the Latin Dictionary/Celes|celes]], 1. ''κενοτάφιον'', [[Illustrated Companion to the Latin Dictionary/Cenotaphium|cenotaphium]]. ''κένταυρος'', [[Illustrated Companion to the Latin Dictionary/Centaurus|centaurus]]. ''κέντρον'', [[Illustrated Companion to the Latin Dictionary/Stimulus|stimulus]]. ''κέντρων'', [[Illustrated Companion to the Latin Dictionary/Cento|cento]]. ''κεραμεύς'', [[Illustrated Companion to the Latin Dictionary/Figulus|figulus]]. ''κεράμιον'', [[Illustrated Companion to the Latin Dictionary/Testa|testa]]. ''κέραμον'', [[Illustrated Companion to the Latin Dictionary/Fictile|fictile]]. ''κέραμος'', [[Illustrated Companion to the Latin Dictionary/Tegula|tegula]]. ''κέρας'', [[Illustrated Companion to the Latin Dictionary/Cornu|cornu]]. ''κεραταύλης'', [[Illustrated Companion to the Latin Dictionary/Cornicen|cornicen]]. ''κερκίς'', [[Illustrated Companion to the Latin Dictionary/Pecten|pecten]], 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cuneus|cuneus]], 3. ''κέρκουρος'', [[Illustrated Companion to the Latin Dictionary/Cercurus|cercurus]]. ''κεροῦχοι'', [[Illustrated Companion to the Latin Dictionary/Ceruchi|ceruchi]]. ''κεστός'' (sc. ''ἱμάς''), [[Illustrated Companion to the Latin Dictionary/Cestus|cestus]]. ''κεστροσφενδόνη'', [[Illustrated Companion to the Latin Dictionary/Cestrosphendone|cestrosphendone]]. ''κέστρον'', [[Illustrated Companion to the Latin Dictionary/Cestrum|cestrum]]. ''κήλων, -ώνειον'', [[Illustrated Companion to the Latin Dictionary/Tolleno|tolleno]]. ''κήμός'', [[Illustrated Companion to the Latin Dictionary/Nassa|nassa]]. ''κῆπος'', [[Illustrated Companion to the Latin Dictionary/Hortus|hortus]]. ''κηποτάφιον'', [[Illustrated Companion to the Latin Dictionary/Cepotaphium|cepotaphium]]. ''κηρύκειον'', [[Illustrated Companion to the Latin Dictionary/Caduceus|caduceus]]. ''κήρυξ'', [[Illustrated Companion to the Latin Dictionary/Ceryx|ceryx]]. ''κήρωμα'', [[Illustrated Companion to the Latin Dictionary/Ceroma|ceroma]]. ''καλοβάμων'', [[Illustrated Companion to the Latin Dictionary/Grallator|grallator]]. ''καλοβάτης'', [[Illustrated Companion to the Latin Dictionary/Grallator|grallator]]. ''κάσσυμα'', [[Illustrated Companion to the Latin Dictionary/Fulmenta|fulmenta]]. ''κιβώριον'', [[Illustrated Companion to the Latin Dictionary/Ciborium|ciborium]]. ''κιβώτιον'', [[Illustrated Companion to the Latin Dictionary/Arcula|arcula]]. ''κιβωτός'', [[Illustrated Companion to the Latin Dictionary/Arca|arca]]. ''κιγκλίς'', [[Illustrated Companion to the Latin Dictionary/Cancelli|cancelli]]. ''κίδαρις'', [[Illustrated Companion to the Latin Dictionary/Cidaris|cidaris]]. ''κιθάρα'', [[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]. ''κιθαριστής'', [[Illustrated Companion to the Latin Dictionary/Citharista|citharista]]. ''κιθαριστρία'', [[Illustrated Companion to the Latin Dictionary/Citharistria|citharistria]]. ''κιθαρῳδός'', [[Illustrated Companion to the Latin Dictionary/Citharoedus|citharœdus]]. ''κιλίκιον'', [[Illustrated Companion to the Latin Dictionary/Cilicium|cilicium]]. ''κιλλίβας'', [[Illustrated Companion to the Latin Dictionary/Cilliba|cilliba]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Canteriolus|canteriolus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Vara|vara]], 2. ''κίναιδος'', [[Illustrated Companion to the Latin Dictionary/Cinaedus|cinædus]]. ''κιονόκρανον'', [[Illustrated Companion to the Latin Dictionary/Capitulum|capitulum]]. ''Κίρκος'', [[Illustrated Companion to the Latin Dictionary/Circus|Circus]]. ''κίστη'', [[Illustrated Companion to the Latin Dictionary/Cista|cista]]. ''κιστοφόρος'', [[Illustrated Companion to the Latin Dictionary/Cistophorus|cistophorus]]. ''κίων'', [[Illustrated Companion to the Latin Dictionary/Columna|columna]]. ''κλειδοῦχος'', [[Illustrated Companion to the Latin Dictionary/Claviger|claviger]], 2. ''κλεῖθρον'', [[Illustrated Companion to the Latin Dictionary/Pessulus|pessulus]]. ''κλείς'', [[Illustrated Companion to the Latin Dictionary/Clavis|clavis]]. ''κλεψύδρα'', [[Illustrated Companion to the Latin Dictionary/Clepsydra|clepsydra]]. ''κλιβανίτις'', [[Illustrated Companion to the Latin Dictionary/Clibanicius|clibanicius panis]]. ''κλίβανος'', [[Illustrated Companion to the Latin Dictionary/Clibanus|clibanus]]. ''κλῖμαξ'', [[Illustrated Companion to the Latin Dictionary/Scalae|scalæ]]. ''κλίνη'', [[Illustrated Companion to the Latin Dictionary/Lectica|lectica]]. ''κλινηφόροι'', [[Illustrated Companion to the Latin Dictionary/Lecticarii|lecticarii]]. ''κλινίδιον'', [[Illustrated Companion to the Latin Dictionary/Lectulus|lectulus]]. ''κλινικός'', [[Illustrated Companion to the Latin Dictionary/Clinicus|clinicus]]. ''κλινόπους'', [[Illustrated Companion to the Latin Dictionary/Clinopus|clinopus]]. ''κλισιάς'', [[Illustrated Companion to the Latin Dictionary/Foris|foris]]. ''κλοιοί'', [[Illustrated Companion to the Latin Dictionary/Boiae|boiæ]]. ''κλυστήρ'', [[Illustrated Companion to the Latin Dictionary/Clyster|clyster]]. ''κλώθω'', [[Illustrated Companion to the Latin Dictionary/Neo|neo]]. ''κναφεῖον'', [[Illustrated Companion to the Latin Dictionary/Fullonica|fullonica]]. ''κναφεύς'', [[Illustrated Companion to the Latin Dictionary/Fullo|fullo]]. ''κνέφαλλον'', [[Illustrated Companion to the Latin Dictionary/Tomentum|tomentum]]. ''κνήμη'', [[Illustrated Companion to the Latin Dictionary/Radius|radius]], 3. ''κνημίς'', [[Illustrated Companion to the Latin Dictionary/Ocrea|ocrea]]. ''κνώδαξ'', [[Illustrated Companion to the Latin Dictionary/Cnodax|cnodax]]. ''κνώδων'', [[Illustrated Companion to the Latin Dictionary/Mora|mora]], 1. ''κόγχη'', [[Illustrated Companion to the Latin Dictionary/Concha|concha]]. ''κόθορνος'', [[Illustrated Companion to the Latin Dictionary/Cothurnus|cothurnus]]. ''κοίλη ναῦς'', [[Illustrated Companion to the Latin Dictionary/Cavernae|cavernæ]]. ''κοιλιόδεσμος'', [[Illustrated Companion to the Latin Dictionary/Ventrale|ventrale]]. ''κοίτη'', [[Illustrated Companion to the Latin Dictionary/Cubile|cubile]]. ''κολαπτήρ'', [[Illustrated Companion to the Latin Dictionary/Scalprum|scalprum]]. ''κολεός'', [[Illustrated Companion to the Latin Dictionary/Vagina|vagina]]. ''κόλλυβος'', [[Illustrated Companion to the Latin Dictionary/Collybus|collybus]]. ''κολλύρα'', [[Illustrated Companion to the Latin Dictionary/Collyra|collyra]]. ''κολλυρίς'', [[Illustrated Companion to the Latin Dictionary/Collyris|collyris]]. ''κολλύριον'', [[Illustrated Companion to the Latin Dictionary/Collyrium|collyrium]]. ''κολόβιον'', [[Illustrated Companion to the Latin Dictionary/Colobium|colobium]]. ''κολοκύνθη'', [[Illustrated Companion to the Latin Dictionary/Cucurbita|cucurbita]]. ''κόλπος'', [[Illustrated Companion to the Latin Dictionary/Sinus|sinus]]. ''κολυμβητής'', [[Illustrated Companion to the Latin Dictionary/Urinator|urinator]]. ''κόμη'', [[Illustrated Companion to the Latin Dictionary/Coma|coma]]. ''κομήτης'', [[Illustrated Companion to the Latin Dictionary/Comatus|comatus]]. ''κονίαμα'', [[Illustrated Companion to the Latin Dictionary/Albarium|albarium opus]]. ''κονιατός'', [[Illustrated Companion to the Latin Dictionary/Dealbatus|dealbatus]]. ''κονίστρα'', [[Illustrated Companion to the Latin Dictionary/Conisterium|conisterium]]. ''κοντός'', [[Illustrated Companion to the Latin Dictionary/Contus|contus]]. ''κοντόφοροι'', [[Illustrated Companion to the Latin Dictionary/Contarii|contarii]]. ''κόπανον'', [[Illustrated Companion to the Latin Dictionary/Pilum|pilum]], 1. ''κόπις'', [[Illustrated Companion to the Latin Dictionary/Copis|copis]]. ''κοπρίας'', [[Illustrated Companion to the Latin Dictionary/Coprea|coprea]]. ''κοπτή'', [[Illustrated Companion to the Latin Dictionary/Copta|copta]]. ''κοπτοπλακοῦς'', [[Illustrated Companion to the Latin Dictionary/Coptoplacenta|coptoplacenta]]. ''κόραξ'', [[Illustrated Companion to the Latin Dictionary/Corvus|corvus]]. ''κόρδαξ'', [[Illustrated Companion to the Latin Dictionary/Cordax|cordax]]. ''κόρυμβος'', [[Illustrated Companion to the Latin Dictionary/Corymbus|corymbus]]. ''κορύνη'', [[Illustrated Companion to the Latin Dictionary/Pedum|pedum]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Clava|clava]], 4. ''κορυνήτης'', [[Illustrated Companion to the Latin Dictionary/Claviger|claviger]], 1. ''κόρυς'', [[Illustrated Companion to the Latin Dictionary/Galea|galea]]. ''κορώνη'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 2. ''κορωνίς'', [[Illustrated Companion to the Latin Dictionary/Corona|corona]]. ''κόσκινον'', [[Illustrated Companion to the Latin Dictionary/Cribrum|cribrum]]. ''κότταβος'', [[Illustrated Companion to the Latin Dictionary/Cottabus|cottabus]]. ''κοτύλη'', [[Illustrated Companion to the Latin Dictionary/Cotula|cotyla]]. ''κουρεῖον'', [[Illustrated Companion to the Latin Dictionary/Tonstrina|tonstrina]]. ''κουρεύς'', [[Illustrated Companion to the Latin Dictionary/Tonsor|tonsor]]. ''κουρεύτρια'', [[Illustrated Companion to the Latin Dictionary/Tonstrix|tonstrix]]. ''κούριμος'', [[Illustrated Companion to the Latin Dictionary/Tonsus|tonsus]]. ''κόφινος'', [[Illustrated Companion to the Latin Dictionary/Cophinus|cophinus]]. ''κοχλιάριον'', [[Illustrated Companion to the Latin Dictionary/Cochlear|cochlear]]. ''κοχλίας'', [[Illustrated Companion to the Latin Dictionary/Cochlea|cochlea]]. ''κράβατος'', [[Illustrated Companion to the Latin Dictionary/Grabatus|grabatus]]. ''κράνος'', [[Illustrated Companion to the Latin Dictionary/Galea|galea]]. ''κρατήρ'', [[Illustrated Companion to the Latin Dictionary/Crater|crater]]. ''κρεάγρα'', [[Illustrated Companion to the Latin Dictionary/Creagra|creagra]]. ''κρεουργός'', [[Illustrated Companion to the Latin Dictionary/Lanius|lanius]]. ''κρεωπώλιον'', [[Illustrated Companion to the Latin Dictionary/Laniarium|laniarium]]. ''κρήδεμνον'', [[Illustrated Companion to the Latin Dictionary/Calantica|calantica]]. ''κρηπίς'', [[Illustrated Companion to the Latin Dictionary/Crepida|crepida]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Crepido|crepido]]. ''κριός'', [[Illustrated Companion to the Latin Dictionary/Aries|aries]]. ''κρόκη'', [[Illustrated Companion to the Latin Dictionary/Subtemen|subtemen]]. ''κροκωτόν'', [[Illustrated Companion to the Latin Dictionary/Crocota|crocota]]. ''κροκύς'', [[Illustrated Companion to the Latin Dictionary/Lacinia|lacinia]]. ''κροσσοί'', [[Illustrated Companion to the Latin Dictionary/Fimbria|fimbriæ]]. ''κροτάλιον'', [[Illustrated Companion to the Latin Dictionary/Crotalium|crotalium]]. ''κρόταλον'', [[Illustrated Companion to the Latin Dictionary/Crotalum|crotalum]]. ''κρούπεζαι'', [[Illustrated Companion to the Latin Dictionary/Sculponeae|sculponeæ]]. ''κρουπέζια'', [[Illustrated Companion to the Latin Dictionary/Scabellum|scabellum]], 3. ''κρούσματα'', [[Illustrated Companion to the Latin Dictionary/Crusmata|crusmata]]. ''κρύπτη'', [[Illustrated Companion to the Latin Dictionary/Crypta|crypta]]. ''κρώβυλος'', [[Illustrated Companion to the Latin Dictionary/Crobylus|crobylus]]. ''κτείς'', [[Illustrated Companion to the Latin Dictionary/Pecten|pecten]]. ''κτεριστής'', [[Illustrated Companion to the Latin Dictionary/Libitinarius|libitinarius]]. ''κτηνίατρος'', [[Illustrated Companion to the Latin Dictionary/Mulomedicus|mulomedicus]]. ''κύαθος'', [[Illustrated Companion to the Latin Dictionary/Cyathus|cyathus]]. ''κυβερνήτης'', [[Illustrated Companion to the Latin Dictionary/Gubernator|gubernator]]. ''κυβιστητήρ'', [[Illustrated Companion to the Latin Dictionary/Cernuus|cernuus]]. ''κύβος'', [[Illustrated Companion to the Latin Dictionary/Tessera|tessera]]. ''κύκηθρον'', [[Illustrated Companion to the Latin Dictionary/Rudicula|rudicula]]. ''κυκλάς'', [[Illustrated Companion to the Latin Dictionary/Cyclas|cyclas]]. ''κύκλος'', [[Illustrated Companion to the Latin Dictionary/Circulus|circulus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cortina|cortina]], 2. ''κύκλωμα βυρσότονον'', [[Illustrated Companion to the Latin Dictionary/Tympanum|tympanum]], 1. ''κύλινδρος'', [[Illustrated Companion to the Latin Dictionary/Cylindrus|cylindrus]]. ''κύλιξ'', [[Illustrated Companion to the Latin Dictionary/Calix|calix]]. ''κυμάτιον'', [[Illustrated Companion to the Latin Dictionary/Cymatium|cymatium]]. ''κυμβαλίστρια'', [[Illustrated Companion to the Latin Dictionary/Cymbalistria|cymbalistria]]. ''κύμβαλον'', [[Illustrated Companion to the Latin Dictionary/Cymbalum|cymbalum]]. ''κύμβη'', [[Illustrated Companion to the Latin Dictionary/Cymba|cymba]]. ''κυμβίον'', [[Illustrated Companion to the Latin Dictionary/Cymbium|cymbium]]. ''κυνέν'', [[Illustrated Companion to the Latin Dictionary/Galerus|galerus]]. ''κυνηγέτης'', [[Illustrated Companion to the Latin Dictionary/Venator|venator]], 1. ''κυνηγέτις'', [[Illustrated Companion to the Latin Dictionary/Venatrix|venatrix]]. ''κύρτη'', [[Illustrated Companion to the Latin Dictionary/Nassa|nassa]]. ''κύστις'', [[Illustrated Companion to the Latin Dictionary/Vesica|vesica]]. ''κώδων'', [[Illustrated Companion to the Latin Dictionary/Tintinnabulum|tintinnabulum]]. ''κωμαστής'', [[Illustrated Companion to the Latin Dictionary/Comissator|commissator]]. ''κώμη'', [[Illustrated Companion to the Latin Dictionary/Vicus|vicus]]. ''κῶμος'', [[Illustrated Companion to the Latin Dictionary/Comissatio|commissatio]]. ''κῶνος'', [[Illustrated Companion to the Latin Dictionary/Conus|conus]], [[Illustrated Companion to the Latin Dictionary/Apex|apex]], 2. ''κωνωπεών'', [[Illustrated Companion to the Latin Dictionary/Conopeum|conopeum]]. ''κώπη'', [[Illustrated Companion to the Latin Dictionary/Capulus|capulus]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cupa|cupa]], 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Remus|remus]]. ''κωπηδάτης'', [[Illustrated Companion to the Latin Dictionary/Remex|remex]]. == ''Λ.'' == ''λαβή'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 1. ''λαβύρινθος'', [[Illustrated Companion to the Latin Dictionary/Labyrinthus|labyrinthus]]. ''λάγανον'', [[Illustrated Companion to the Latin Dictionary/Tractum|tractum]], 2. ''λάγηνος'', [[Illustrated Companion to the Latin Dictionary/Lagena|lagena]]. ''λαγοτροφείον'', [[Illustrated Companion to the Latin Dictionary/Leporarium|leporarium]]. ''λαγωβόλον'', [[Illustrated Companion to the Latin Dictionary/Pedum|pedum]]. ''λάκκος'', [[Illustrated Companion to the Latin Dictionary/Lacus|lacus]], 4. ''λαμίαι'', [[Illustrated Companion to the Latin Dictionary/Lamiae|lamiæ]]. ''λαμπάς'', [[Illustrated Companion to the Latin Dictionary/Lampas|lampas]]. ''λαμπτήρ'', [[Illustrated Companion to the Latin Dictionary/Candelabrum|candelabrum]], 3. ''λάσανον'', [[Illustrated Companion to the Latin Dictionary/Lasanum|lasanum]]. ''λατομία'', [[Illustrated Companion to the Latin Dictionary/Lautumia|lautumia]]. ''λάτρις'', [[Illustrated Companion to the Latin Dictionary/Latro|latro]]. ''λέβης'', [[Illustrated Companion to the Latin Dictionary/Lebes|lebes]]. ''λεκάνη'', [[Illustrated Companion to the Latin Dictionary/Patina|patina]]. ''λέκτρον'', [[Illustrated Companion to the Latin Dictionary/Lectus|lectus]]. ''λέμβος'', [[Illustrated Companion to the Latin Dictionary/Lembus|lembus]]. ''λεπαστή'', [[Illustrated Companion to the Latin Dictionary/Lepesta|lepesta]]. ''λεύκωμα'', [[Illustrated Companion to the Latin Dictionary/Album|album]]. ''λημνίσκος'', [[Illustrated Companion to the Latin Dictionary/Lemniscus|lemniscus]]. ''ληνεών'', [[Illustrated Companion to the Latin Dictionary/Torcularium|torcularium]]. ''ληνοβάτης'', [[Illustrated Companion to the Latin Dictionary/Calcator|calcator]]. ''ληνός'', [[Illustrated Companion to the Latin Dictionary/Torcular|torcular]]. ''λιβανωτός'', [[Illustrated Companion to the Latin Dictionary/Tus|tus]]. ''λιβανωτρίς'', [[Illustrated Companion to the Latin Dictionary/Acerra|acerra]]. ''λιβυρνίς'', [[Illustrated Companion to the Latin Dictionary/Liburna|liburna]]. ''λιθοβόλον'', [[Illustrated Companion to the Latin Dictionary/Ballista|ballista]]. ''λιθοξόος'', [[Illustrated Companion to the Latin Dictionary/Lapidarius|lapidarius]]. ''λιθόστρωτον'', [[Illustrated Companion to the Latin Dictionary/Lithostrotum|lithostrotum]]. ''λιθουργός'', [[Illustrated Companion to the Latin Dictionary/Lapidarius|lapidarius]]. ''λίκνον'', [[Illustrated Companion to the Latin Dictionary/Vannus|vannus]]. ''λιμήν'', [[Illustrated Companion to the Latin Dictionary/Portus|portus]]. ''λινοκήρυξ'', [[Illustrated Companion to the Latin Dictionary/Lintearius|lintearius]]. ''λίνον'', [[Illustrated Companion to the Latin Dictionary/Linum|linum]]. ''λογεῖον'', [[Illustrated Companion to the Latin Dictionary/Pulpitum|pulpitum]], 2. ''λόγχη'', [[Illustrated Companion to the Latin Dictionary/Spiculum|spiculum]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lancea|lancea]]. ''λογχόφορος'', [[Illustrated Companion to the Latin Dictionary/Lancearius|lancearius]]. ''λουτρόν'', [[Illustrated Companion to the Latin Dictionary/Lavacrum|lavacrum]]. ''λόφος'', [[Illustrated Companion to the Latin Dictionary/Crista|crista]]. ''λυδίων'', [[Illustrated Companion to the Latin Dictionary/Ludio|ludio]]. ''λύκος'', [[Illustrated Companion to the Latin Dictionary/Lupus|lupus]]. ''λύρη'', [[Illustrated Companion to the Latin Dictionary/Lyra|lyra]]. ''λυριστής'', [[Illustrated Companion to the Latin Dictionary/Lyristes|lyristes]]. ''λύχνος'', [[Illustrated Companion to the Latin Dictionary/Lucerna|lucerna]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lychnus|lychnus]]. ''λυχνοῦχος'', [[Illustrated Companion to the Latin Dictionary/Candelabrum|candelabrum]], 1 & 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lychnuchus|lychnuchus]], 1. == ''Μ.'' == ''μάγειρος'', [[Illustrated Companion to the Latin Dictionary/Coquus|coquus]]. ''μαζονομεῖον'', [[Illustrated Companion to the Latin Dictionary/Mazonomum|mazonomum]]. ''μαίανδρος'', [[Illustrated Companion to the Latin Dictionary/Maeander|mæander]]. ''μάκελλα'', [[Illustrated Companion to the Latin Dictionary/Ligo|ligo]]. ''μάκελλον'', [[Illustrated Companion to the Latin Dictionary/Macellum|macellum]]. ''μάκελον'', [[Illustrated Companion to the Latin Dictionary/Maceria|maceria]]. ''μαλλὸς ἀθλητοῦ'', [[Illustrated Companion to the Latin Dictionary/Cirrus|cirrus in vertice]]. ''μάνδαλος'', [[Illustrated Companion to the Latin Dictionary/Pessulus|pessulus]]. ''μάνδρα'', [[Illustrated Companion to the Latin Dictionary/Mandra|mandra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Funda|funda]], 4. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pala|pala]], 3. ''μάννος'', [[Illustrated Companion to the Latin Dictionary/Monile|monile]]. ''μαρσύπιον'', [[Illustrated Companion to the Latin Dictionary/Marsupium|marsupium]]. ''μαστιγοφόρος'', [[Illustrated Companion to the Latin Dictionary/Mastigophorus|mastigophorus]]. ''μάστιξ'', [[Illustrated Companion to the Latin Dictionary/Flagellum|flagellum]]. ''{{mdash}}{{mdash}} ἀστραγαλωτή'', [[Illustrated Companion to the Latin Dictionary/Flagrum|flagrum talis tessellatum]]. ''ματτύα'', [[Illustrated Companion to the Latin Dictionary/Mattea|mattya]]. ''μάχαιρα'', [[Illustrated Companion to the Latin Dictionary/Machaera|machæra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Culter|culter]]. ''{{mdash}}{{mdash}} διπλῆ'', [[Illustrated Companion to the Latin Dictionary/Forfex|forfex]]. ''μαχαίριον'', [[Illustrated Companion to the Latin Dictionary/Machaerium|machærium]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cultellus|cultellus]]. ''μαχαιρόφορος'', [[Illustrated Companion to the Latin Dictionary/Machaerophorus|machærophorus]]. ''μελανδόχη'', [[Illustrated Companion to the Latin Dictionary/Atramentarium|atramentarium]]. ''μελισσών'', [[Illustrated Companion to the Latin Dictionary/Apiarium|apiarium]]. ''μέσαβον'', [[Illustrated Companion to the Latin Dictionary/Subjugium|subjugium]]. ''μεσάγκυλον'', [[Illustrated Companion to the Latin Dictionary/Ansatus|ansatum telum]]. ''μέσαυλος'', [[Illustrated Companion to the Latin Dictionary/Mesaulos|mesaulos]]. ''μεσοστύλιον'', [[Illustrated Companion to the Latin Dictionary/Intercolumnium|intercolumnium]]. ''μεταβάτης'', [[Illustrated Companion to the Latin Dictionary/Desultor|desultor]]. ''μέταλλον'', [[Illustrated Companion to the Latin Dictionary/Fodina|fodina]]. ''μετόπη'', [[Illustrated Companion to the Latin Dictionary/Metopa|metopa]]. ''μετρητής'', [[Illustrated Companion to the Latin Dictionary/Metreta|metreta]]. ''μήλη'', [[Illustrated Companion to the Latin Dictionary/Specillum|specillum]]. ''μηρός'', [[Illustrated Companion to the Latin Dictionary/Femur|femur]]. ''μηχανή'', [[Illustrated Companion to the Latin Dictionary/Machina|machina]]. ''μίτος'', [[Illustrated Companion to the Latin Dictionary/Licium|licium]]. ''μίτρα'', [[Illustrated Companion to the Latin Dictionary/Mitra|mitra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]], 4. ''μιτρηφόρος'', [[Illustrated Companion to the Latin Dictionary/Mitratus|mitratus]]. ''μιτρίον'', [[Illustrated Companion to the Latin Dictionary/Mitella|mitella]]. ''μνήμα'', [[Illustrated Companion to the Latin Dictionary/Monumentum|monumentum]]. ''μνημεῖον'', [[Illustrated Companion to the Latin Dictionary/Monumentum|monumentum]]. ''μολόχινη'', [[Illustrated Companion to the Latin Dictionary/Molochina|molochina]]. ''μολυβδίς'', [[Illustrated Companion to the Latin Dictionary/Glans|glans]]. ''μόναυλος'', [[Illustrated Companion to the Latin Dictionary/Monaulos|monaulos]]. ''μονήρης'', [[Illustrated Companion to the Latin Dictionary/Moneris|moneris]]. ''μονόγραμμος'', [[Illustrated Companion to the Latin Dictionary/Monogrammos|monogrammos]]. ''μονόκροτος'', [[Illustrated Companion to the Latin Dictionary/Moneris|moneris]]. ''μονόλιθος'', [[Illustrated Companion to the Latin Dictionary/Monolithos|monolithos]]. ''μονομάχοι'', [[Illustrated Companion to the Latin Dictionary/Gladiatores|gladiatores]]. ''μονομαχοτρόφος'', [[Illustrated Companion to the Latin Dictionary/Lanista|lanista]]. ''μονόξυλος'', [[Illustrated Companion to the Latin Dictionary/Monoxylus|monoxylus]]. ''μονόπτερος'', [[Illustrated Companion to the Latin Dictionary/Monopteros|monopteros]]. ''μονοχίτων'', [[Illustrated Companion to the Latin Dictionary/Tunicatus|tunicatus]]. ''μονοχρώματα'', [[Illustrated Companion to the Latin Dictionary/Monochromata|monochromata]]. ''μορμολυκεῖον'', [[Illustrated Companion to the Latin Dictionary/Larva|larva]], 2. ''Μουσεῖον'', [[Illustrated Companion to the Latin Dictionary/Museum|Museum]]. ''μουσεῖον'', [[Illustrated Companion to the Latin Dictionary/Musivum|musivum]]. ''μοχλός'', [[Illustrated Companion to the Latin Dictionary/Vectis|vectis]]. ''μυκτήρ'', [[Illustrated Companion to the Latin Dictionary/Myxa|myxa]]. ''μύλη'', [[Illustrated Companion to the Latin Dictionary/Mola|mola]]. ''μυλώη'', [[Illustrated Companion to the Latin Dictionary/Pistrinum|pistrinum]]. ''μύξα'', [[Illustrated Companion to the Latin Dictionary/Myxa|myxa]]. ''μύρμηξ'', [[Illustrated Companion to the Latin Dictionary/Caestus|cæstus]]. ''μυροπώλης'', [[Illustrated Companion to the Latin Dictionary/Unguentarius|unguentarius]]. ''μυσταγωγός'', [[Illustrated Companion to the Latin Dictionary/Mystagogus|mystagogus]]. ''μύστης'', [[Illustrated Companion to the Latin Dictionary/Mysta|mysta]]. == ''Ν.'' == ''νάβλα'', [[Illustrated Companion to the Latin Dictionary/Nablia|nablia]] and [[Illustrated Companion to the Latin Dictionary/Naulia|naulia]]. ''ναῦλα'', [[Illustrated Companion to the Latin Dictionary/Nablia|nablia]] and [[Illustrated Companion to the Latin Dictionary/Naulia|naulia]]. ''ναῦλον'', [[Illustrated Companion to the Latin Dictionary/Nablia|nablia]] and [[Illustrated Companion to the Latin Dictionary/Naulia|naulia]]. ''νάννοι'', [[Illustrated Companion to the Latin Dictionary/Nani|nani]]. ''ναοφύλαξ'', [[Illustrated Companion to the Latin Dictionary/Aedituus|ædituus]]. ''νάρθηξ'', [[Illustrated Companion to the Latin Dictionary/Ferula|ferula]]. ''νάρθηξ'', [[Illustrated Companion to the Latin Dictionary/Narthecium|narthecium]]. ''ναύαρχος'', [[Illustrated Companion to the Latin Dictionary/Navarchus|navarchus]]. ''ναύκληρος'', [[Illustrated Companion to the Latin Dictionary/Nauclerus|nauclerus]]. ''ναῦλον'', [[Illustrated Companion to the Latin Dictionary/Naulum|naulum]]. ''ναυμαχία'', [[Illustrated Companion to the Latin Dictionary/Naumachia|naumachia]]. ''ναυπήγιον'', [[Illustrated Companion to the Latin Dictionary/Textrinum|textrinum]], 2. ''ναῦς'', [[Illustrated Companion to the Latin Dictionary/Navis|navis]]. ''{{mdash}}{{mdash}} κατάφρακτη'', [[Illustrated Companion to the Latin Dictionary/Navis|navis tecta]]. ''{{mdash}}{{mdash}} μακρά'', [[Illustrated Companion to the Latin Dictionary/Navis|navis longa]]. ''{{mdash}}{{mdash}} στρογγύλη'', [[Illustrated Companion to the Latin Dictionary/Navis|navis oneraria]]. ''ναύσταθμον'', [[Illustrated Companion to the Latin Dictionary/Navale|navale]], 2. ''νεβρίς'', [[Illustrated Companion to the Latin Dictionary/Nebris|nebris]]. ''νεκροκαύστης'', [[Illustrated Companion to the Latin Dictionary/Ustor|ustor]]. ''νευροβάτης'', [[Illustrated Companion to the Latin Dictionary/Neurobata|neurobata]]. ''νεῦρον'', [[Illustrated Companion to the Latin Dictionary/Nervus|nervus]]. ''νευρόσπαστον'', [[Illustrated Companion to the Latin Dictionary/Neurospaston|neurospaston]]. ''νέω'', [[Illustrated Companion to the Latin Dictionary/Neo|neo]]. ''νεωκόρος'', [[Illustrated Companion to the Latin Dictionary/Neocorus|neocorus.]] ''νεώριον'', [[Illustrated Companion to the Latin Dictionary/Navale|navale]], 1. ''νήθω'', [[Illustrated Companion to the Latin Dictionary/Neo|neo]]. ''νικητήριον'', [[Illustrated Companion to the Latin Dictionary/Niceterium|niceterium]]. ''νομεύς'', [[Illustrated Companion to the Latin Dictionary/Pastor|pastor]]. ''Νύμφαιον'', [[Illustrated Companion to the Latin Dictionary/Nymphaeum|Nymphæum]]. ''νύμφη'', [[Illustrated Companion to the Latin Dictionary/Nupta|nupta]]. ''νύσσα'', [[Illustrated Companion to the Latin Dictionary/Meta|meta]], 1. ''νωτοφόρος'', [[Illustrated Companion to the Latin Dictionary/Bajulus|bajulus]]. == ''Ξ.'' == ''ξένια'', [[Illustrated Companion to the Latin Dictionary/Xenia|xenia]]. ''ξενοδοκεῖον'', [[Illustrated Companion to the Latin Dictionary/Caupona|caupona]], 1. ''ξεστός'', [[Illustrated Companion to the Latin Dictionary/Rasus|rasus]]. ''ξιφοθήκη'', [[Illustrated Companion to the Latin Dictionary/Vagina|vagina]]. ''ξίφος'', [[Illustrated Companion to the Latin Dictionary/Gladius|gladius]]. ''{{mdash}}{{mdash}} ἐπικαμπής'', [[Illustrated Companion to the Latin Dictionary/Sica|sica]]. ''ξυλοκοπία'', [[Illustrated Companion to the Latin Dictionary/Fustuarium|fustuarium]]. ''ξυλοπέδη'', [[Illustrated Companion to the Latin Dictionary/Nervus|nervus]], 4. ''ξυρόν'', [[Illustrated Companion to the Latin Dictionary/Novacula|novacula]]. ''ξυστάρχης'', [[Illustrated Companion to the Latin Dictionary/Xystarcha|xystarcha]]. ''ξυστικός'', [[Illustrated Companion to the Latin Dictionary/Xysticus|xysticus]]. ''ξυστίς'', [[Illustrated Companion to the Latin Dictionary/Palla|palla]]. ''ξυστόν'', [[Illustrated Companion to the Latin Dictionary/Hastile|hastile]]. ''ξυστός'' or ''-ον'', [[Illustrated Companion to the Latin Dictionary/Xystus|xystus]], 1. ''ξυστρίς'', [[Illustrated Companion to the Latin Dictionary/Strigilis|strigilis]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Stria|stria]]. == ''Ο.'' == ''ὀβελίσκος'', [[Illustrated Companion to the Latin Dictionary/Obeliscus|obeliscus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Veruculum|veruculum]]. ''ὀβελός'', [[Illustrated Companion to the Latin Dictionary/Veru|veru]], 1. ''ὀβολός'', [[Illustrated Companion to the Latin Dictionary/Obolus|obolus]]. ''ὄγκος'', [[Illustrated Companion to the Latin Dictionary/Superficies|superficies]], 1. ''ὀδοντάγρα'', [[Illustrated Companion to the Latin Dictionary/Dentarpaga|dentarpaga]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Forceps|forceps]], 3. ''ὀδοντόγλυφις'', [[Illustrated Companion to the Latin Dictionary/Dentiscalpium|dentiscalpium]]. ''ὀθόνη'', [[Illustrated Companion to the Latin Dictionary/Linteum|linteum]]. ''ὀθόνιον'', [[Illustrated Companion to the Latin Dictionary/Linteolum|linteolum]]. ''οἴαξ'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 5. ''οἶκος'', [[Illustrated Companion to the Latin Dictionary/Oecus|œcus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Domus|domus]], 2. ''οἰνεών'', [[Illustrated Companion to the Latin Dictionary/Cella|cella vinaria]]. ''οἰνοπώλιον'', [[Illustrated Companion to the Latin Dictionary/Oenopolium|œnopolium]]. ''οἰνοφόρον'', [[Illustrated Companion to the Latin Dictionary/Oenophorum|œnophorum]]. ''οἰνοφόρος'', [[Illustrated Companion to the Latin Dictionary/Oenophorus|œnophorus]]. ''οἰνοχόος'', [[Illustrated Companion to the Latin Dictionary/Pincerna|pincerna]]. ''οἰοπόλος'', [[Illustrated Companion to the Latin Dictionary/Opilio|opilio]]. ''οῖοχίτων'', [[Illustrated Companion to the Latin Dictionary/Tunicatus|tunicatus]]. ''ὀϊστόσ'', [[Illustrated Companion to the Latin Dictionary/Sagitta|sagitta]]. ''οἰωνοσκόπος'', [[Illustrated Companion to the Latin Dictionary/Augur|augur]]. ''ὀκρίβας'', [[Illustrated Companion to the Latin Dictionary/Canteriolus|canteriolus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pulpitum|pulpitum]], 2. ''ὅλμος'', [[Illustrated Companion to the Latin Dictionary/Cortina|cortina]], 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Mortarium|mortarium]], 1. ''ὁμαλιστήρ'', [[Illustrated Companion to the Latin Dictionary/Rutellum|rutellum]]. ''ὄνος'', [[Illustrated Companion to the Latin Dictionary/Catillus|catillus]], 2. ''ὀξίς'', [[Illustrated Companion to the Latin Dictionary/Acetabulum|acetabulum]]. ''ὀξύβαφον'', [[Illustrated Companion to the Latin Dictionary/Acetabulum|acetabulum]]. ''ὀξύκρατον'', [[Illustrated Companion to the Latin Dictionary/Posca|posca]]. ''ὀπαί'', [[Illustrated Companion to the Latin Dictionary/Columbarium|columbaria]], 5. ''ὄπεας'', [[Illustrated Companion to the Latin Dictionary/Subula|subula]]. ''ὀπή'', [[Illustrated Companion to the Latin Dictionary/Opa|opa]]. ''ὀπισθόγραφος'', [[Illustrated Companion to the Latin Dictionary/Opisthographus|opisthographus]]. ''ὀπισθόδομος'', [[Illustrated Companion to the Latin Dictionary/Opisthodomus|opisthodomus]]. ''ὁπλοδιδακτής'', [[Illustrated Companion to the Latin Dictionary/Campidoctor|campidoctor]]. ''ὀμφαλός'', [[Illustrated Companion to the Latin Dictionary/Umbilicus|umbilicus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Umbo|umbo]], 1. ''ὄργανον'', [[Illustrated Companion to the Latin Dictionary/Organum|organum]]. ''ὀρεοκόμος'', [[Illustrated Companion to the Latin Dictionary/Mulio|mulio]], 1. ''ὀρθογραφία'', [[Illustrated Companion to the Latin Dictionary/Orthographia|orthographia]]. ''ὀρθοσταδίας'', [[Illustrated Companion to the Latin Dictionary/Recta|recta]]. ''ὀρθοστάτης'', [[Illustrated Companion to the Latin Dictionary/Orthostata|orthostata]]. ''ὄρκη'', [[Illustrated Companion to the Latin Dictionary/Orca|orca]]. ''ὁρμιευτής'', [[Illustrated Companion to the Latin Dictionary/Hamiota|hamiota]]. ''ὁρμιά'', [[Illustrated Companion to the Latin Dictionary/Linea|linea]], 1. ''ὅρμος'', [[Illustrated Companion to the Latin Dictionary/Portus|portus]]. ''ὀρνιθευτής'', [[Illustrated Companion to the Latin Dictionary/Auceps|auceps]]. ''ὀρνιθών'', [[Illustrated Companion to the Latin Dictionary/Ornithon|ornithon]]. ''ὅρος'', [[Illustrated Companion to the Latin Dictionary/Orbis|orbis olearius]]. ''ὀρύκτης'', [[Illustrated Companion to the Latin Dictionary/Fossor|fossor]]. ''ὀρχηστοπόλος'', [[Illustrated Companion to the Latin Dictionary/Orchestopolarius|orchestopolarius]]. ''ορχησις'', [[Illustrated Companion to the Latin Dictionary/Saltatio|saltatio]]. ''ὀρχηστής'', [[Illustrated Companion to the Latin Dictionary/Saltator|saltator]]. ''ὀρχήστρα'', [[Illustrated Companion to the Latin Dictionary/Orchestra|orchestra]]. ''ὀρχήστρια'', [[Illustrated Companion to the Latin Dictionary/Saltatrix|saltatrix]]. ''ὀστράκιον'', [[Illustrated Companion to the Latin Dictionary/Testa|testa]]. ''οὐγκία'', [[Illustrated Companion to the Latin Dictionary/Uncia|uncia]]. ''οὐδών'', [[Illustrated Companion to the Latin Dictionary/Udo|udo]]. ''οὖλος'', [[Illustrated Companion to the Latin Dictionary/Manipulus|manipulus]]. ''οὐρανός'', [[Illustrated Companion to the Latin Dictionary/Coelum|cœlum]]. ''ὀψοπωλεῖον'', [[Illustrated Companion to the Latin Dictionary/Popina|popina]]. ''ὀψοπώλης'', [[Illustrated Companion to the Latin Dictionary/Macellarius|macellarius]]. == ''Π.'' == ''παγκράτιον'', [[Illustrated Companion to the Latin Dictionary/Pancratium|pancratium]]. ''πάγος'', [[Illustrated Companion to the Latin Dictionary/Pagus|pagus]]. ''παιδαγωγός'', [[Illustrated Companion to the Latin Dictionary/Paedagogus|pædagogos]]. ''παλαίστρα'', [[Illustrated Companion to the Latin Dictionary/Palaestra|palæstra]]. ''παλαιστρικός'', [[Illustrated Companion to the Latin Dictionary/Palaestricus|palæstricus]]. ''παλαιστρίτης'', [[Illustrated Companion to the Latin Dictionary/Palaestrita|palæstrita]]. ''παλάμη'', [[Illustrated Companion to the Latin Dictionary/Palma|palma]], 1. ''παλευτής'', [[Illustrated Companion to the Latin Dictionary/Illix|avis illix]]. ''πάλη'', [[Illustrated Companion to the Latin Dictionary/Lucta|lucta]]. ''παλιγκάπηλος'', [[Illustrated Companion to the Latin Dictionary/Institor|institor]]. ''παλίμψηστος'', [[Illustrated Companion to the Latin Dictionary/Palimpsestus|palimpsestus]]. ''παλλακή'', [[Illustrated Companion to the Latin Dictionary/Pellex|pellex]]. ''παμμάχιον'', [[Illustrated Companion to the Latin Dictionary/Pancratium|pancratium]]. ''πανδοκεῖον'', [[Illustrated Companion to the Latin Dictionary/Caupona|caupona]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Stabulum|stabulum]], 2. ''πανδοῦρα'', [[Illustrated Companion to the Latin Dictionary/Pandura|pandura]]. ''παντόμιμος'', [[Illustrated Companion to the Latin Dictionary/Pantomimus|pantomimus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Saltator|saltator]]. ''παραγναθίς'', [[Illustrated Companion to the Latin Dictionary/Buccula|buccula]]. ''παραζώνιον'', [[Illustrated Companion to the Latin Dictionary/Parazonium|parazonium]]. ''παραπέτασμα'', [[Illustrated Companion to the Latin Dictionary/Velum|velum]], 4. ''παράσημον'', [[Illustrated Companion to the Latin Dictionary/Insigne|insigne]], 2. ''παράσταδες'', [[Illustrated Companion to the Latin Dictionary/Antae|antæ]]. ''παραστάς'', [[Illustrated Companion to the Latin Dictionary/Parastas|parastas]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Postis|postis]]. ''παρατίλτριον'', [[Illustrated Companion to the Latin Dictionary/Alipilus|alipilus]]. ''παρήορος'', [[Illustrated Companion to the Latin Dictionary/Funalis|funalis equus]]. ''πάρμη'', [[Illustrated Companion to the Latin Dictionary/Parma|parma]]. ''παροψίς'', [[Illustrated Companion to the Latin Dictionary/Paropsis|paropsis]]. ''παρυφή'', [[Illustrated Companion to the Latin Dictionary/Limbus|limbus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Clavus|clavus]], 7. ''παρωτίς'', [[Illustrated Companion to the Latin Dictionary/Ancon|ancon]], 2. ''πάσσαλος'', [[Illustrated Companion to the Latin Dictionary/Palus|palus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Paxillus|paxillus]]. ''παστοφόρος'', [[Illustrated Companion to the Latin Dictionary/Pastophorus|pastophorus]]. ''παταγεῖον'', [[Illustrated Companion to the Latin Dictionary/Patagium|patagium]]. ''πέδη'', [[Illustrated Companion to the Latin Dictionary/Pedica|pedica]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Compes|compes]]. ''πέδιλα'', [[Illustrated Companion to the Latin Dictionary/Talaria|talaria]]. ''πελεκίνος'', [[Illustrated Companion to the Latin Dictionary/Securicula|securicula]], 2. ''πέλεκυς'', [[Illustrated Companion to the Latin Dictionary/Securis|securis]]. ''{{mdash}}{{mdash}} δίστομος'', [[Illustrated Companion to the Latin Dictionary/Bipennis|bipennis]]. ''πέλις'', [[Illustrated Companion to the Latin Dictionary/Pelvis|pelvis]]. ''πελταστής'', [[Illustrated Companion to the Latin Dictionary/Peltasta|peltasta]]. ''πέλτη'', [[Illustrated Companion to the Latin Dictionary/Pelta|pelta]]. ''πένταθλον'', [[Illustrated Companion to the Latin Dictionary/Quinquertium|quinquertium]]. ''πεντάσπαστος'', [[Illustrated Companion to the Latin Dictionary/Pentaspastos|pentaspastos]]. ''πεντήρης'', [[Illustrated Companion to the Latin Dictionary/Quinqueremis|quinqueremis]]. ''πέπλον'', [[Illustrated Companion to the Latin Dictionary/Peplum|peplum]]. ''περίβλημα'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]], 3. ''περιβόλαιον'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]], 3. ''περίβολος'', [[Illustrated Companion to the Latin Dictionary/Sacellum|sacellum]]. ''περιβραχιόνιον'', [[Illustrated Companion to the Latin Dictionary/Brachiale|brachiale]]. ''περίδειπνον'', [[Illustrated Companion to the Latin Dictionary/Silicernium|silicernium]]. ''περίζωμα'', [[Illustrated Companion to the Latin Dictionary/Cinctus 1|cinctus]]. ''περιηγητής'', [[Illustrated Companion to the Latin Dictionary/Mystagogus|mystagogus]]. ''περικάρπιον'', [[Illustrated Companion to the Latin Dictionary/Armilla|armilla]], 2. ''περικεφάλαιον'', [[Illustrated Companion to the Latin Dictionary/Galea|galea]]. ''περικνημίς'', [[Illustrated Companion to the Latin Dictionary/Tibiale|tibiale]]. ''περίπτερος'', [[Illustrated Companion to the Latin Dictionary/Peripteros|peripteros]]. ''περιρῥαντήριον'', [[Illustrated Companion to the Latin Dictionary/Labrum|labrum]], 4. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Aspergillum|aspergillum]]. ''περισκελίς'', [[Illustrated Companion to the Latin Dictionary/Periscelis|periscelis]]. ''περιστερεών'', [[Illustrated Companion to the Latin Dictionary/Columbarium|columbarium]]. ''περίστρωμα'', [[Illustrated Companion to the Latin Dictionary/Peristroma|peristroma]]. ''περιστύλιον'', [[Illustrated Companion to the Latin Dictionary/Peristylium|peristylium]]. ''περόνη'', [[Illustrated Companion to the Latin Dictionary/Acus|acus]], 3. ''πεσσός'', [[Illustrated Companion to the Latin Dictionary/Pila 1|pila]]. ''πέτασος'', [[Illustrated Companion to the Latin Dictionary/Petasus|petasus]]. ''πεταυριστής'', [[Illustrated Companion to the Latin Dictionary/Petaurista|petaurista]]. ''πέταυρον'', [[Illustrated Companion to the Latin Dictionary/Petaurum|petaurum]]. ''πήγμα'', [[Illustrated Companion to the Latin Dictionary/Pegma|pegma]]. ''πηδάλιον'', [[Illustrated Companion to the Latin Dictionary/Gubernaculum|gubernaculum]]. ''πήρα'', [[Illustrated Companion to the Latin Dictionary/Pera|pera]]. ''πιθαύλης'', pithaula.<ref group="Note" name="RICH_1849_pithaula"/> ''πιλητός'', [[Illustrated Companion to the Latin Dictionary/Coactilis|coactilis]]. ''πιλίδιον'', [[Illustrated Companion to the Latin Dictionary/Pileolus|pileolus]]. ''πῖλος'', [[Illustrated Companion to the Latin Dictionary/Pileus|pileus]]. ''πιλοφόρος'', [[Illustrated Companion to the Latin Dictionary/Pileatus|pileatus]]. ''πινάκιον'', [[Illustrated Companion to the Latin Dictionary/Tabella|tabella]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Superficies|superficies]], 2. ''πινακοθήκη'', [[Illustrated Companion to the Latin Dictionary/Pinacotheca|pinacotheca]]. ''πίναξ'', [[Illustrated Companion to the Latin Dictionary/Tabula|tabula]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lanx|lanx quadrata]]. ''πίστρις'', [[Illustrated Companion to the Latin Dictionary/Pistris|pistris]]. ''πιττάκιον'', [[Illustrated Companion to the Latin Dictionary/Pittacium|pittacium]]. ''πλαγγών'', [[Illustrated Companion to the Latin Dictionary/Plaguncula|plaguncula]]. ''πλαγίαυλος'', [[Illustrated Companion to the Latin Dictionary/Tibia|tibia obliqua]]. ''πλακοῦς'', [[Illustrated Companion to the Latin Dictionary/Placenta|placenta]]. ''πλάξ'', [[Illustrated Companion to the Latin Dictionary/Tabula|tabula]]. ''πλάστης'', [[Illustrated Companion to the Latin Dictionary/Plastes|plastes]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Fictor|fictor]]. ''πλάστιγξ'', [[Illustrated Companion to the Latin Dictionary/Lanx|lanx]], 3. ''πλατεῖα'', [[Illustrated Companion to the Latin Dictionary/Platea|platea]]. ''πλῆκτρον'', [[Illustrated Companion to the Latin Dictionary/Plectrum|plectrum]]. ''πλήμνη'', [[Illustrated Companion to the Latin Dictionary/Modiolus|modiolus]], 1. ''πλίνθινος'', [[Illustrated Companion to the Latin Dictionary/Latericius|latericius]]. ''πλίνθος'', [[Illustrated Companion to the Latin Dictionary/Plinthus|plinthus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Later|later]]. ''{{mdash}}{{mdash}} ὀπτή'', [[Illustrated Companion to the Latin Dictionary/Later|later coctus]]. ''{{mdash}}{{mdash}} ὠμή'', [[Illustrated Companion to the Latin Dictionary/Later|later crudus]]. ''πλοῖον'', [[Illustrated Companion to the Latin Dictionary/Navigium|navigium]]. ''{{mdash}}{{mdash}} κοντωτόν'', [[Illustrated Companion to the Latin Dictionary/Ratis|ratis]], 2. ''{{mdash}}{{mdash}} σιταγώγόν'', [[Illustrated Companion to the Latin Dictionary/Corbita|corbita]]. ''{{mdash}}{{mdash}} φορτικόν'', [[Illustrated Companion to the Latin Dictionary/Navis|navis oneraria]]. ''πνιγεύς'', [[Illustrated Companion to the Latin Dictionary/Pnigeus|pnigeus]]. ''ποδάγρα'', [[Illustrated Companion to the Latin Dictionary/Pedica|pedica dentata]]. ''ποδανιπτήρ'', [[Illustrated Companion to the Latin Dictionary/Pelluvia|pelluvium]]. ''ποδεῖον'', [[Illustrated Companion to the Latin Dictionary/Fascia|fascia]], 5. ''ποδήρης'', [[Illustrated Companion to the Latin Dictionary/Talaris|talaris]]. ''ποδοστράβη'', [[Illustrated Companion to the Latin Dictionary/Pedica|pedica dentata]]. ''πολύμιτος'', [[Illustrated Companion to the Latin Dictionary/Polymitus|polymitus]]. ''πολύπτυχα'', [[Illustrated Companion to the Latin Dictionary/Polyptycha|polyptycha]]. ''πολύσπαστον'', [[Illustrated Companion to the Latin Dictionary/Polyspaston|polyspaston]]. ''πόπανον'', [[Illustrated Companion to the Latin Dictionary/Popanum|popanum]]. ''πόρπη'', [[Illustrated Companion to the Latin Dictionary/Fibula|fibula]]. ''ποτήρ, -ήριον'', [[Illustrated Companion to the Latin Dictionary/Poculum|poculum]]. ''πούς'', [[Illustrated Companion to the Latin Dictionary/Pes|pes]]. ''πράκτορες'', [[Illustrated Companion to the Latin Dictionary/Coactores|coactores]]. ''πρεσβευτής'', [[Illustrated Companion to the Latin Dictionary/Legatus|legatus]], 2. ''πριόνιον'', [[Illustrated Companion to the Latin Dictionary/Serrula|serrula]]. ''πριστήρ'', [[Illustrated Companion to the Latin Dictionary/Prista|prista]]. ''πρίων'', [[Illustrated Companion to the Latin Dictionary/Serra|serra]]. ''προγευστής'', [[Illustrated Companion to the Latin Dictionary/Praegustator|prægustator]]. ''πρόθυρον'', [[Illustrated Companion to the Latin Dictionary/Vestibulum|vestibulum]]. ''προκοιτών'', [[Illustrated Companion to the Latin Dictionary/Procoeton|procœton]]. ''προκόμιον'', [[Illustrated Companion to the Latin Dictionary/Capronae|capronæ]]. ''προμετωπίδιον'', [[Illustrated Companion to the Latin Dictionary/Frontale|frontale]], 3. ''πρόναος'', [[Illustrated Companion to the Latin Dictionary/Pronaus|pronaus]]. ''πρόπλασμα'', [[Illustrated Companion to the Latin Dictionary/Proplasma|proplasma]]. ''προπνιγεῖον'', [[Illustrated Companion to the Latin Dictionary/Praefurnium|præfurnium]]. ''προσγναθίδιον'', [[Illustrated Companion to the Latin Dictionary/Focale|focale]]. ''προσκεφάλαιον'', [[Illustrated Companion to the Latin Dictionary/Cervical|cervical]]. ''προσκήνιον'', [[Illustrated Companion to the Latin Dictionary/Proscenium|proscenium]]. ''προσκύνησις'', [[Illustrated Companion to the Latin Dictionary/Adoratio|adoratio]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Adulatio|adulatio]]. ''πρόστυπον'', [[Illustrated Companion to the Latin Dictionary/Prostypum|prostypum]]. ''πρόσωπον'' or ''-εῖον'', [[Illustrated Companion to the Latin Dictionary/Persona|persona]]. ''προτομή'', [[Illustrated Companion to the Latin Dictionary/Thorax|thorax]], 2. ''πρότυπον'', [[Illustrated Companion to the Latin Dictionary/Protypum|protypum]]. ''πρόχοος'', [[Illustrated Companion to the Latin Dictionary/Gutturnium|gutturnium]]. ''πρύμνα'', [[Illustrated Companion to the Latin Dictionary/Puppis|puppis]]. ''πρῷρα'', [[Illustrated Companion to the Latin Dictionary/Prora|prora]]. ''πρῳράτης'', [[Illustrated Companion to the Latin Dictionary/Proreta|proreta]]. ''πτερόν'', [[Illustrated Companion to the Latin Dictionary/Pinna|pinna]]. ''πτερόπους'', [[Illustrated Companion to the Latin Dictionary/Alipes|alipes]]. ''πτήρυξ'', [[Illustrated Companion to the Latin Dictionary/Mora|mora]], 1. ''πτέρωμα'', [[Illustrated Companion to the Latin Dictionary/Pteroma|pteroma]]. ''πτερωτός'', [[Illustrated Companion to the Latin Dictionary/Pterotus|pterotus]]. ''πτύον'', [[Illustrated Companion to the Latin Dictionary/Pala|pala]], 2. ''πτωχός'', [[Illustrated Companion to the Latin Dictionary/Mendicus|mendicus]]. ''πυελίς'', [[Illustrated Companion to the Latin Dictionary/Funda|funda]], 4. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pala|pala]], 3. ''πυετία'', [[Illustrated Companion to the Latin Dictionary/Coagulum|coagulum]]. ''πυκνόστυλος'', [[Illustrated Companion to the Latin Dictionary/Pycnostylos|pycnostylos]]. ''πύκτης'', [[Illustrated Companion to the Latin Dictionary/Pugil|pugil]]. ''πύλη'', [[Illustrated Companion to the Latin Dictionary/Porta|porta]]. ''πυλίς'', [[Illustrated Companion to the Latin Dictionary/Portula|portula]]. ''πυξίς'', [[Illustrated Companion to the Latin Dictionary/Pyxis|pyxis]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Modiolus|modiolus]], 4. ''πύξος'', [[Illustrated Companion to the Latin Dictionary/Buxum|buxum]]. ''πυρά'', [[Illustrated Companion to the Latin Dictionary/Pyra|pyra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Rogus|rogus]]. ''πυράγρα'', [[Illustrated Companion to the Latin Dictionary/Forceps|forceps]]. ''πυραμίς'', [[Illustrated Companion to the Latin Dictionary/Pyramis|pyramis]]. ''πύργος'', [[Illustrated Companion to the Latin Dictionary/Turris|turris]]. ''πυριαιτήριον'', [[Illustrated Companion to the Latin Dictionary/Laconicum|laconicum]]. ''πυρρίχη'', [[Illustrated Companion to the Latin Dictionary/Pyrrhicha|pyrrhicha]]. ''πωγωνίας'', [[Illustrated Companion to the Latin Dictionary/Barbatus|barbatus]]. ''πώμα'', [[Illustrated Companion to the Latin Dictionary/Operculum|operculum]]. == ''Ρ.'' == ''ῥαβδίον'', [[Illustrated Companion to the Latin Dictionary/Penicillum|penicillum]]. ''ῥάβδοι'', [[Illustrated Companion to the Latin Dictionary/Fascis|fasces]]. ''ῥάβδος'', [[Illustrated Companion to the Latin Dictionary/Radius|radius]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Virga|virga]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Hastile|hastile]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Stria|stria]]. ''ῥαβδοῦχος'', [[Illustrated Companion to the Latin Dictionary/Lictor|lictor]]. ''ῥαβδωσις'', [[Illustrated Companion to the Latin Dictionary/Striatura|striatura]]. ''ῥαβδωτός'', [[Illustrated Companion to the Latin Dictionary/Striatus|striatus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Virgatus|virgatus]]. ''ῥάπτης'', [[Illustrated Companion to the Latin Dictionary/Sutor|sutor]]. ''ῥαφίς'', [[Illustrated Companion to the Latin Dictionary/Acus|acus]], 1. ''ῥιζάγρα'', [[Illustrated Companion to the Latin Dictionary/Forceps|forceps]], 2. ''ῥίνη'', [[Illustrated Companion to the Latin Dictionary/Lima|lima]]. ''ῥιπίς'', [[Illustrated Companion to the Latin Dictionary/Flabellum|flabellum]]. ''ῥίσκος'', [[Illustrated Companion to the Latin Dictionary/Riscus|riscus]]. ''ῥόμβος'', [[Illustrated Companion to the Latin Dictionary/Rhombus|rhombus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Turbo|turbo]], 1. ''ῥομφαία'', [[Illustrated Companion to the Latin Dictionary/Rhompaea|rhomphæa]]. ''ῥόπαλον'', [[Illustrated Companion to the Latin Dictionary/Clava|clava]]. ''ῥόπτρον'', [[Illustrated Companion to the Latin Dictionary/Ansa|ansa]], 2. ''{{mdash}}{{mdash}} βυρσοπαγές'', [[Illustrated Companion to the Latin Dictionary/Symphonia|symphonia]], 2. ''ῥύγχος'', [[Illustrated Companion to the Latin Dictionary/Rostrum|rostrum]]. ''ῥυκάνη'', [[Illustrated Companion to the Latin Dictionary/Runcina|runcina]]. ''ῥῦμα'', [[Illustrated Companion to the Latin Dictionary/Remulcum|remulcus]]. ''ῥυμός'', [[Illustrated Companion to the Latin Dictionary/Temo|temo]], 1. ''ῥυπαρογράφος'', [[Illustrated Companion to the Latin Dictionary/Rhyparographus|rhyparographus]]. ''ῥυταγωγεύς'', [[Illustrated Companion to the Latin Dictionary/Habena|habena]], 2. ''ῥυτίς'', [[Illustrated Companion to the Latin Dictionary/Ruga|ruga]]. ''ῥυτόν'', [[Illustrated Companion to the Latin Dictionary/Rhytium|rhytium]]. == ''Σ.'' == ''σάβανον'', [[Illustrated Companion to the Latin Dictionary/Sabanum|sabanum]]. ''σαγήνη'', [[Illustrated Companion to the Latin Dictionary/Sagena|sagena]]. ''σάγμα'', [[Illustrated Companion to the Latin Dictionary/Sagma|sagma]]. ''σάγος'', [[Illustrated Companion to the Latin Dictionary/Sagum|sagum]]. ''σακκίον'', [[Illustrated Companion to the Latin Dictionary/Sacculus|sacculus]]. ''σακκοπήρα'', [[Illustrated Companion to the Latin Dictionary/Sacciperium|sacciperium]]. ''σάκκος'', [[Illustrated Companion to the Latin Dictionary/Saccus|saccus]]. ''Σαλίοι'', [[Illustrated Companion to the Latin Dictionary/Salii|Salii]]. ''σαλπιγκτής'', [[Illustrated Companion to the Latin Dictionary/Tubicen|tubicen]]. ''σάλπιγξ'', [[Illustrated Companion to the Latin Dictionary/Tuba|tuba]]. ''{{mdash}}{{mdash}} στρογγύλη'', [[Illustrated Companion to the Latin Dictionary/Cornu|cornu]], 6. ''σαμβύκη'', [[Illustrated Companion to the Latin Dictionary/Sambuca|sambuca]]. ''σαμβυκίστρια'', [[Illustrated Companion to the Latin Dictionary/Sambucina|sambucina]]. ''σανδάλιον'', [[Illustrated Companion to the Latin Dictionary/Sandalium|sandalium]]. ''σανίδιον'', [[Illustrated Companion to the Latin Dictionary/Tabella|tabella]]. ''σανίς'', [[Illustrated Companion to the Latin Dictionary/Tabula|tabula]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Foris|foris]]. ''σάπων'', [[Illustrated Companion to the Latin Dictionary/Sapo|sapo]]. ''σαράβαλλα'', [[Illustrated Companion to the Latin Dictionary/Saraballa|saraballa]]. ''σάραπις'', [[Illustrated Companion to the Latin Dictionary/Sarapis|sarapis]]. ''σάρισσα'', [[Illustrated Companion to the Latin Dictionary/Sarissa|sarissa]]. ''σαρισσοφόρος'', [[Illustrated Companion to the Latin Dictionary/Sarissophorus|sarissophorus]]. ''σαρκοφάγος'', [[Illustrated Companion to the Latin Dictionary/Sarcophagus|sarcophagus]]. ''σάρωθρον'', [[Illustrated Companion to the Latin Dictionary/Scopae|scopæ]]. ''σαύνιον'', [[Illustrated Companion to the Latin Dictionary/Veru|veru]], 2. ''σειραφόρος'', [[Illustrated Companion to the Latin Dictionary/Funalis|funalis equus]]. ''σεῖστρον'', [[Illustrated Companion to the Latin Dictionary/Sistrum|sistrum]]. ''σέλματα, τὰ'', [[Illustrated Companion to the Latin Dictionary/Transtrum|transtra]]. ''σηκός'', [[Illustrated Companion to the Latin Dictionary/Cella|cella]], 7. ''σήκωμα'', [[Illustrated Companion to the Latin Dictionary/Aequipondium|æquipondium]]. ''σημαιοφόρος'', [[Illustrated Companion to the Latin Dictionary/Signifer|signifer]]. ''σημεῖον'', [[Illustrated Companion to the Latin Dictionary/Signum|signum]]. ''σιβύνη'', [[Illustrated Companion to the Latin Dictionary/Sibina|sibyna]]. ''σικιννιστής'', [[Illustrated Companion to the Latin Dictionary/Sicinnista|sicinnista]]. ''σικύα'', [[Illustrated Companion to the Latin Dictionary/Cucurbita|cucurbita]]. ''σίλλυβος'', [[Illustrated Companion to the Latin Dictionary/Index|index]], 1. ''σίμβλος'', [[Illustrated Companion to the Latin Dictionary/Alveare|alveare]]. ''σινδών'', [[Illustrated Companion to the Latin Dictionary/Sindon|sindon]]. ''σίραιον'', [[Illustrated Companion to the Latin Dictionary/Sapa|sapa]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Defrutum|defrutum]]. ''σιτευτής'', [[Illustrated Companion to the Latin Dictionary/Fartor|fartor]]. ''σίφων'', [[Illustrated Companion to the Latin Dictionary/Sipho|sipho]]. ''σκαλίς'', [[Illustrated Companion to the Latin Dictionary/Sarculum|sarculum]]. ''σκαλμός'', [[Illustrated Companion to the Latin Dictionary/Scalmus|scalmus]]. ''σκάμμα'', [[Illustrated Companion to the Latin Dictionary/Scamma|scamma]]. ''σκᾶπος'', [[Illustrated Companion to the Latin Dictionary/Scapus|scapus]]. ''σκάφη'', [[Illustrated Companion to the Latin Dictionary/Scapha|scapha]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cunabula|cunabula]]. ''σκάφιον'', [[Illustrated Companion to the Latin Dictionary/Scaphium|scaphium]]. ''σκεπαρνίζω'', [[Illustrated Companion to the Latin Dictionary/Ascio|ascio]]. ''σκέπαρνον'', [[Illustrated Companion to the Latin Dictionary/Ascia|ascia]], 1. ''σκεύη, τά'', [[Illustrated Companion to the Latin Dictionary/Impedimentum|impedimenta]]. ''σκηνή'', [[Illustrated Companion to the Latin Dictionary/Scena 1|scena]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Tentorium|tentorium]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Diaeta|diæta]], 2. ''σκηνογραφία'', [[Illustrated Companion to the Latin Dictionary/Scenographia|scenographia]]. ''σκηπτούχος'', [[Illustrated Companion to the Latin Dictionary/Sceptuchus|sceptuchus]]. ''σκήπτρον'', [[Illustrated Companion to the Latin Dictionary/Sceptrum|sceptrum]]. ''σκιάδειον'', [[Illustrated Companion to the Latin Dictionary/Umbella|umbella]]. ''σκιάθηρον'', [[Illustrated Companion to the Latin Dictionary/Solarium|solarium]], 1. ''σκιμπόδιον'', [[Illustrated Companion to the Latin Dictionary/Scimpodium|scimpodium]]. ''σκίπων'', [[Illustrated Companion to the Latin Dictionary/Scipio|scipio]]. ''σκοπιά'', [[Illustrated Companion to the Latin Dictionary/Specula|specula]]. ''σκοτία'', [[Illustrated Companion to the Latin Dictionary/Scotia|scotia]]. ''σκυτάλη'', [[Illustrated Companion to the Latin Dictionary/Scytala|scytale]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Scutula|scutula]]. ''σκυτεῖον'', [[Illustrated Companion to the Latin Dictionary/Sutrina|sutrina]]. ''σκύφος'', [[Illustrated Companion to the Latin Dictionary/Scyphus|scyphus]]. ''συῆνος'', [[Illustrated Companion to the Latin Dictionary/Alveare|alveare]]. ''σμηνών'', [[Illustrated Companion to the Latin Dictionary/Alvearium|alvearium]]. ''σμίλη'', [[Illustrated Companion to the Latin Dictionary/Scalprum|scalprum]]. ''σμιλίον'', [[Illustrated Companion to the Latin Dictionary/Scalpellum|scalpellum]]. ''σμινύη'', [[Illustrated Companion to the Latin Dictionary/Bidens|bidens]]. ''σόβη'', [[Illustrated Companion to the Latin Dictionary/Muscarium|muscarium]], 1. ''σπαθάλιον'', [[Illustrated Companion to the Latin Dictionary/Spathalium|spathalium]]. ''σπάθη'', [[Illustrated Companion to the Latin Dictionary/Spatha|spatha]]. ''σπάργανα'', [[Illustrated Companion to the Latin Dictionary/Crepundia|crepundia]]. ''σπεῖρα'', [[Illustrated Companion to the Latin Dictionary/Spira|spira]]. ''σπεῖραι βόειαι'', [[Illustrated Companion to the Latin Dictionary/Caestus|cæstus]]. ''σπέος'', [[Illustrated Companion to the Latin Dictionary/Specus|specus]]. ''σπλαγχνοσκόπος'', [[Illustrated Companion to the Latin Dictionary/Extispex|extispex]]. ''σπλήνιον'', [[Illustrated Companion to the Latin Dictionary/Spleniatus|splenium]]. ''σπονδαύλης'', [[Illustrated Companion to the Latin Dictionary/Spondaules|spondaules]]. ''σπυρίδιον'', [[Illustrated Companion to the Latin Dictionary/Sportella|sportella]], [[Illustrated Companion to the Latin Dictionary/Sportula|sportula]]. ''στάθμη'', [[Illustrated Companion to the Latin Dictionary/Linea|linea]], 3. ''σταθμοί'', [[Illustrated Companion to the Latin Dictionary/Mansiones|mansiones]]. ''σταθμός'', [[Illustrated Companion to the Latin Dictionary/Stabulum|stabulum]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pondus|pondus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Libra|libra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Postis|postis]]. ''σταλίς'', [[Illustrated Companion to the Latin Dictionary/Vara|vara]], 1. ''σταδιεύς, -οδρόμος'', [[Illustrated Companion to the Latin Dictionary/Cursor|cursor]], 1. ''στάδιον'', [[Illustrated Companion to the Latin Dictionary/Stadium|stadium]]. ''στέμφυλα'', [[Illustrated Companion to the Latin Dictionary/Fraces|fraces]]. ''στενωπός'', [[Illustrated Companion to the Latin Dictionary/Angiportus|angiportus]]. ''στεφανηπλόκος'', [[Illustrated Companion to the Latin Dictionary/Coronarius|coronarius]]. ''στεφανηφόρος'', [[Illustrated Companion to the Latin Dictionary/Coronatus|coronatus]]. ''στεφανοπώλης'', [[Illustrated Companion to the Latin Dictionary/Coronarius|coronarius]]. ''στέφανος'', [[Illustrated Companion to the Latin Dictionary/Corona|corona]]. ''στήλη'', [[Illustrated Companion to the Latin Dictionary/Cippus|cippus]]. ''στηλίδιον'', [[Illustrated Companion to the Latin Dictionary/Columella|columella]], 2. ''στήμων'', [[Illustrated Companion to the Latin Dictionary/Stamen|stamen]]. ''στῆριγξ, -ιγμα'', [[Illustrated Companion to the Latin Dictionary/Furca|furca]], 4. ''στίγμα'', [[Illustrated Companion to the Latin Dictionary/Stigma|stigma]]. ''στλεγγίς'', [[Illustrated Companion to the Latin Dictionary/Strigilis|strigilis]], 1. ''στέγαστρον'', [[Illustrated Companion to the Latin Dictionary/Segestre|segestre]]. ''στέγη'', [[Illustrated Companion to the Latin Dictionary/Constratum|constratum navis]]. ''στέμμα'', [[Illustrated Companion to the Latin Dictionary/Stemma|stemma]]. ''στοά'', [[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]. ''στολή'', [[Illustrated Companion to the Latin Dictionary/Stola|stola]], 2. ''στρατηγεῖον'', [[Illustrated Companion to the Latin Dictionary/Praetorium|prætorium]]. ''στρατηγὸς ἑξαπέλεκυς'', [[Illustrated Companion to the Latin Dictionary/Praetor|prætor]]. ''στρεβλωτήριον'', [[Illustrated Companion to the Latin Dictionary/Tormentum|tormentum]], 2. ''στρεπτός'', [[Illustrated Companion to the Latin Dictionary/Torquis|torquis]]. ''στρεπτοφόρος'', [[Illustrated Companion to the Latin Dictionary/Torquatus|torquatus]]. ''στρόμβος'', [[Illustrated Companion to the Latin Dictionary/Turbo|turbo]], 1. ''στροφεύς'', [[Illustrated Companion to the Latin Dictionary/Cardo|cardo]]. ''στρόφιγξ'', [[Illustrated Companion to the Latin Dictionary/Cardo|cardo]]. ''στρόφιγξ'', [[Illustrated Companion to the Latin Dictionary/Scapus|scapus cardinalis]]. ''στρόφιον'', [[Illustrated Companion to the Latin Dictionary/Strophium|strophium]]. ''στρῶμα'', [[Illustrated Companion to the Latin Dictionary/Stragulum|stragulum]], 1. ''στρωμνή'', [[Illustrated Companion to the Latin Dictionary/Culcita|culcita]]. ''στυλίς'', [[Illustrated Companion to the Latin Dictionary/Columella|columella]]. ''στυλοβάτης'', [[Illustrated Companion to the Latin Dictionary/Stylobata|stylobata]]. ''στύλος'', [[Illustrated Companion to the Latin Dictionary/Columna|columna]]. ''στύπος'', [[Illustrated Companion to the Latin Dictionary/Stipes|stipes]]. ''συβώτης'', [[Illustrated Companion to the Latin Dictionary/Porcarius|porcarius]]. ''συγκύπτης'', [[Illustrated Companion to the Latin Dictionary/Capreolus|capreolus]], 2. ''σύμβολον'', [[Illustrated Companion to the Latin Dictionary/Tessera|tessera hospitalis]]. ''συμποσίαρχος'', [[Illustrated Companion to the Latin Dictionary/Magister|magister]], 4. ''συμπόσιον'', [[Illustrated Companion to the Latin Dictionary/Symposium|symposium]]. ''σύνδειπνον'', [[Illustrated Companion to the Latin Dictionary/Convivium|convivium]]. ''σύνθεσις'', [[Illustrated Companion to the Latin Dictionary/Synthesis|synthesis]]. ''σύνθημα'', [[Illustrated Companion to the Latin Dictionary/Tessera|tessera militaris]]. ''συνωρίς'', [[Illustrated Companion to the Latin Dictionary/Biga|biga]]. ''σύριγξ'', [[Illustrated Companion to the Latin Dictionary/Arundo|arundo]], 6; [[Illustrated Companion to the Latin Dictionary/Fistula|fistula]], 2. ''σύρμα'', [[Illustrated Companion to the Latin Dictionary/Syrma|syrma]]. ''συσκηνία'', [[Illustrated Companion to the Latin Dictionary/Contubernium|contubernium]]. ''σύσκηνοι'', [[Illustrated Companion to the Latin Dictionary/Contubernales|contubernales]]. ''συστάται'', [[Illustrated Companion to the Latin Dictionary/Canterius|canterii]]. ''σύστολος'', [[Illustrated Companion to the Latin Dictionary/Systylos|systylos]]. ''σφαῖρα'', [[Illustrated Companion to the Latin Dictionary/Pila 2|pila]]. ''σφαιριστήριον'', [[Illustrated Companion to the Latin Dictionary/Sphaeristerium|sphæristerium]]. ''σφαιρωτήρ'', [[Illustrated Companion to the Latin Dictionary/Corrigia|corrigia]]. ''σφενδόνη'', [[Illustrated Companion to the Latin Dictionary/Funda|funda]], 1 and 4. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Pala|pala]], 3. ''σφενδονήται'', [[Illustrated Companion to the Latin Dictionary/Funditores|funditores]]. ''σφιγκτήρ'', [[Illustrated Companion to the Latin Dictionary/Spinther|spinther]]. ''σφραγίς'', [[Illustrated Companion to the Latin Dictionary/Anulus|anulus]]. ''σφῦρα'', [[Illustrated Companion to the Latin Dictionary/Malleus|malleus]]. ''σχεδία'', [[Illustrated Companion to the Latin Dictionary/Ratis|ratis]], 1. ''σχίδη'', [[Illustrated Companion to the Latin Dictionary/Scheda|scheda]]. ''σχίδαξ'', [[Illustrated Companion to the Latin Dictionary/Scandula|scandula]]. ''σχοινίον ἐπίγειον'', [[Illustrated Companion to the Latin Dictionary/Retinaculum|retinaculum]]. ''σχοινοβάτης'', [[Illustrated Companion to the Latin Dictionary/Funambulus|funambulus]]. ''σχολή'', [[Illustrated Companion to the Latin Dictionary/Schola|schola]]. ''σωλήν'', [[Illustrated Companion to the Latin Dictionary/Fistula|fistula]], 1. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Canalis|canalis]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Imbrex|imbrex]]. == ''Τ.'' == ''ταινία'', [[Illustrated Companion to the Latin Dictionary/Taenia|tænia]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Fascia|fascia]], 9. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]], 1. ''τάλαντον'', [[Illustrated Companion to the Latin Dictionary/Libra|libra]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lanx|lanx]], 3. ''ταλαρίς'', [[Illustrated Companion to the Latin Dictionary/Quasillus|quasillus]]. ''τάλαρος'', [[Illustrated Companion to the Latin Dictionary/Qualus|qualus]]. ''τάπης'', [[Illustrated Companion to the Latin Dictionary/Tapes|tapes]]. ''ταριχοπώλης'', [[Illustrated Companion to the Latin Dictionary/Salsamentarius|salsamentarius]]. ''ταρῥίον'', [[Illustrated Companion to the Latin Dictionary/Craticula|craticula]]. ''ταρσός'', [[Illustrated Companion to the Latin Dictionary/Crates|crates]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Palmula|palmula]]. ''τάφος'', [[Illustrated Companion to the Latin Dictionary/Funus|funus]]. ''τέθριππον ἅρμα'', [[Illustrated Companion to the Latin Dictionary/Quadriga|quadriga]]. ''τεθωρακισμένος'', [[Illustrated Companion to the Latin Dictionary/Loricatus|loricatus]]. ''τεῖχος'', [[Illustrated Companion to the Latin Dictionary/Murus|murus]]. ''τέκτων'', [[Illustrated Companion to the Latin Dictionary/Faber|faber]]. ''τελαμών'', [[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]. ''τελώνης'', [[Illustrated Companion to the Latin Dictionary/Publicanus|publicanus]]. ''τεμάχιον'', [[Illustrated Companion to the Latin Dictionary/Tomaculum|tomaculum]]. ''τέρατρον'', [[Illustrated Companion to the Latin Dictionary/Terebra|terebra]]. ''τετράδραχμον'', [[Illustrated Companion to the Latin Dictionary/Tetradrachmum|tetradrachmum]]. ''τετράδωρος'', [[Illustrated Companion to the Latin Dictionary/Tetradoros|tetradorus]]. ''τετράθυρος'', [[Illustrated Companion to the Latin Dictionary/Quadriforis|quadriforis]]. ''τετραόδιον'', [[Illustrated Companion to the Latin Dictionary/Quadrivium|quadrivium]]. ''τετρήρης'', [[Illustrated Companion to the Latin Dictionary/Quadriremis|quadriremis]]. ''τήβεννα'', [[Illustrated Companion to the Latin Dictionary/Toga|toga]]. ''τήγανον'', [[Illustrated Companion to the Latin Dictionary/Sartago|sartago]]. ''τηλία'', [[Illustrated Companion to the Latin Dictionary/Incerniculum|incerniculum]]. ''τιάρα'', [[Illustrated Companion to the Latin Dictionary/Tiara|tiara]]. ''τιθασσευτής'', [[Illustrated Companion to the Latin Dictionary/Mansuetarius|mansuetarius]]. ''τιμητής'', [[Illustrated Companion to the Latin Dictionary/Censor|censor]]. ''τοῖχος'', [[Illustrated Companion to the Latin Dictionary/Paries|paries]]. ''τολύπη'', [[Illustrated Companion to the Latin Dictionary/Glomus|glomus]]. ''τόξευμα'', [[Illustrated Companion to the Latin Dictionary/Sagitta|sagitta]]. ''τοζεύω'', [[Illustrated Companion to the Latin Dictionary/Sagitto|sagitto]]. ''τόξον'', [[Illustrated Companion to the Latin Dictionary/Arcus|arcus]], 1, 2, 3. ''τόρευμα'', [[Illustrated Companion to the Latin Dictionary/Toreuma|toreuma]]. ''τόρνος'', [[Illustrated Companion to the Latin Dictionary/Tornus|tornus]]. ''τορυνή'', [[Illustrated Companion to the Latin Dictionary/Trua|trua]]. ''τράπεζα'', [[Illustrated Companion to the Latin Dictionary/Mensa|mensa]]. ''τραπεζίτης'', [[Illustrated Companion to the Latin Dictionary/Mensarii|mensarius]]. ''τραπεζοποιός'', [[Illustrated Companion to the Latin Dictionary/Structor|structor]]. ''τραπεζοφόρον'', [[Illustrated Companion to the Latin Dictionary/Trapezophorum|trapezophorum]]. ''τράπηξ'', [[Illustrated Companion to the Latin Dictionary/Trabs|trabs]]. ''τρίαινα'', [[Illustrated Companion to the Latin Dictionary/Fuscina|fuscina]]. ''τρίβολα, τὰ'', [[Illustrated Companion to the Latin Dictionary/Tribulum|tribulum]]. ''τρίβολος'', [[Illustrated Companion to the Latin Dictionary/Tribulus|tribulus]]. ''τρίβων'', [[Illustrated Companion to the Latin Dictionary/Tribon|tribon]]. ''τρίγλυφος'', [[Illustrated Companion to the Latin Dictionary/Triglyphus|triglyphus]]. ''τρίγωνον'', [[Illustrated Companion to the Latin Dictionary/Trigonum|trigonum]]. ''τριήρης'', [[Illustrated Companion to the Latin Dictionary/Triremis|triremis]]. ''τρίκλινον'', [[Illustrated Companion to the Latin Dictionary/Triclinium|triclinium]]. ''τρίμιτος'', [[Illustrated Companion to the Latin Dictionary/Trilix|trilix]]. ''τρίοδος'', [[Illustrated Companion to the Latin Dictionary/Trivium|trivium]]. ''τριόδους'', [[Illustrated Companion to the Latin Dictionary/Tridens|tridens]]. ''τριπτήρ'', [[Illustrated Companion to the Latin Dictionary/Orbis|orbis olearius]]. ''τρίσπαστος'', [[Illustrated Companion to the Latin Dictionary/Trispastos|trispastos]]. ''τριττύα'', [[Illustrated Companion to the Latin Dictionary/Suovetaurilia|suovetaurilia]]. ''τρόπαιον'', [[Illustrated Companion to the Latin Dictionary/Tropaeum|tropæum]]. ''τρόπις'', [[Illustrated Companion to the Latin Dictionary/Carina|carina]]. ''τροπός, -ωτήρ'', [[Illustrated Companion to the Latin Dictionary/Struppus|struppus]]. ''τρουλλίον'', [[Illustrated Companion to the Latin Dictionary/Trulla|trulla]], 1. ''τροχιλέα'', [[Illustrated Companion to the Latin Dictionary/Trochlea|trochlea]]. ''τροχίλος'', [[Illustrated Companion to the Latin Dictionary/Scotia|scotia]]. ''τροχίσκος'', [[Illustrated Companion to the Latin Dictionary/Pastillus|pastillus]]. ''τροχοπέδη'', [[Illustrated Companion to the Latin Dictionary/Sufflamen|sufflamen]]. ''τροχός'', [[Illustrated Companion to the Latin Dictionary/Trochus|trochus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Rota|rota]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Orbis|orbis]], 4. ''τρύβλιον'', [[Illustrated Companion to the Latin Dictionary/Trulla|trulla]], 2. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Tryblium|tryblium]]. ''τρυγητήρ'', [[Illustrated Companion to the Latin Dictionary/Vindemiator|vindemiator]]. ''τρύγητος'', [[Illustrated Companion to the Latin Dictionary/Vindemia|vindemia]]. ''τρυήλα'', [[Illustrated Companion to the Latin Dictionary/Trua|trua]]. ''τρύξ'', [[Illustrated Companion to the Latin Dictionary/Mustum|mustum]]. ''τρυπάνιον'', [[Illustrated Companion to the Latin Dictionary/Terebra|terebra]], 3. ''τρυπάνον'', [[Illustrated Companion to the Latin Dictionary/Terebra|terebra]], 4. ''τρυπήματα'', [[Illustrated Companion to the Latin Dictionary/Columbarium|columbaria]], 4. ''τρυτάνη'', [[Illustrated Companion to the Latin Dictionary/Trutina|trutina]]. ''τύκος'' or ''-χος'', [[Illustrated Companion to the Latin Dictionary/Ascia|ascia]], 2. ''τύλη'', [[Illustrated Companion to the Latin Dictionary/Culcita|culcita]]. ''τυμβαύλης'', [[Illustrated Companion to the Latin Dictionary/Siticen|siticen]]. ''τύμβος'', [[Illustrated Companion to the Latin Dictionary/Tumulus|tumulus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Bustum|bustum]]. ''τυμπανιστής'', [[Illustrated Companion to the Latin Dictionary/Tympanista|tympanista]]. ''τυμπανίστρια'', [[Illustrated Companion to the Latin Dictionary/Tympanistria|tympanistria]]. ''τύμπανον'', [[Illustrated Companion to the Latin Dictionary/Tympanum|tympanum]]. ''τύπος'', [[Illustrated Companion to the Latin Dictionary/Forma|forma]]. ''τυρός'', [[Illustrated Companion to the Latin Dictionary/Caseus|caseus]]. ''τύρσις'', [[Illustrated Companion to the Latin Dictionary/Turris|turris]]. == ''Υ.'' == ''ὑάλινος'', [[Illustrated Companion to the Latin Dictionary/Vitreus|vitreus]], 1. ''ὑαλοειδής'', [[Illustrated Companion to the Latin Dictionary/Vitreus|vitreus]], 2. ''ὑδραγωγεῖον'', [[Illustrated Companion to the Latin Dictionary/Aquaeductus|aquæductus]]. ''ὑδραλέτης'', [[Illustrated Companion to the Latin Dictionary/Hydraletes|hydraletes]]. ''ὕδραυλος'', [[Illustrated Companion to the Latin Dictionary/Hydraulus|hydraulus]]. ''ὑδρία'', [[Illustrated Companion to the Latin Dictionary/Hydria|hydria]]. ''ὑδροφόρος'', [[Illustrated Companion to the Latin Dictionary/Aquarius|aquarius]]. ''ὕννις'', [[Illustrated Companion to the Latin Dictionary/Vomer|vomer]]. ''ὑπαγκώνιον'', [[Illustrated Companion to the Latin Dictionary/Cubital|cubital]]. ''ὕπαιθρος'', [[Illustrated Companion to the Latin Dictionary/Hypaethros|hypyæthros]]. ''ὕπαρχος'', [[Illustrated Companion to the Latin Dictionary/Legatus|legatus]], 1. ''ὕπατος'', [[Illustrated Companion to the Latin Dictionary/Consul|consul]]. ''ύπαυχένιον'', [[Illustrated Companion to the Latin Dictionary/Cervical|cervical]]. ''ὑπέραι'', [[Illustrated Companion to the Latin Dictionary/Opiferae|opiferæ]]. ''ὑπέρθυρον'', [[Illustrated Companion to the Latin Dictionary/Hyperthyrum|hyperthyrum]]. ''ὑπέρον'', [[Illustrated Companion to the Latin Dictionary/Pistillum|pistillum]]. ''ὑπερῷον'', [[Illustrated Companion to the Latin Dictionary/Coenaculum|cœnaculum]]. ''ὑπόγειον'', [[Illustrated Companion to the Latin Dictionary/Hypogeum|hypogeum]]. ''ὑπογραφεύς'', [[Illustrated Companion to the Latin Dictionary/Amanuensis|amanuensis]]. ''ὑπόδημα κοῖλον'', [[Illustrated Companion to the Latin Dictionary/Calceus|calceus]]. ''ὑποδημάτιον'', [[Illustrated Companion to the Latin Dictionary/Calceolus|calceolus]]. ''ὑπόζωμα'', [[Illustrated Companion to the Latin Dictionary/Tormentum|tormentum]], 3. ''ύποζώνιον'', [[Illustrated Companion to the Latin Dictionary/Succingulum|succingulum]]. ''ὑποζώστος'', [[Illustrated Companion to the Latin Dictionary/Succinctus|succinctus]]. ''ὑπόκαυσις'', [[Illustrated Companion to the Latin Dictionary/Hypocausis|hypocausis]]. ''ὑπόκαυστον'', [[Illustrated Companion to the Latin Dictionary/Hypocaustum|hypocaustum]]. ''ὑπόνομος'', [[Illustrated Companion to the Latin Dictionary/Cloaca|cloaca]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Cuniculus|cuniculus]]. ''ύποπόδιον'', [[Illustrated Companion to the Latin Dictionary/Scabellum|scabellum]], 2. ''ὑποτραχήλιον'', [[Illustrated Companion to the Latin Dictionary/Hypotrachelium|hypotrachelium]]. ''ὑπουρίς'', [[Illustrated Companion to the Latin Dictionary/Postilena|postilena]]. ''ὕρχα'', [[Illustrated Companion to the Latin Dictionary/Orca|orca]]. ''ὑσσός'', [[Illustrated Companion to the Latin Dictionary/Pilum|pilum]], 2. ''ὑφάντης'', [[Illustrated Companion to the Latin Dictionary/Textor|textor]]. ''ὑψίζωνος'', [[Illustrated Companion to the Latin Dictionary/Alticinctus|alticinctus]]. == ''Φ.'' == ''φαικάσιον'', [[Illustrated Companion to the Latin Dictionary/Phaecasium|phæcasium]]. ''φαινόλης'', [[Illustrated Companion to the Latin Dictionary/Paenula|pænula]]. ''φάλαγξ'', [[Illustrated Companion to the Latin Dictionary/Phalanga|phalanga]]. ''φάλαραι'', [[Illustrated Companion to the Latin Dictionary/Phalerae|phaleræ]]. ''φανός'', [[Illustrated Companion to the Latin Dictionary/Fax|fax]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Laterna|laterna]]. ''φαρέτρα'', [[Illustrated Companion to the Latin Dictionary/Pharetra|pharetra]]. ''φαρμακοπώλης'', [[Illustrated Companion to the Latin Dictionary/Pharmacopola|pharmacopola]]. ''φᾶρος'', [[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]. ''φάρος'', [[Illustrated Companion to the Latin Dictionary/Pharos|pharos]]. ''φάσηλος'', [[Illustrated Companion to the Latin Dictionary/Faselus|faselus]]. ''φάσκαλος'' or ''-ωλος'', [[Illustrated Companion to the Latin Dictionary/Pasceolus|pasceolus]]. ''φάτνη'', [[Illustrated Companion to the Latin Dictionary/Patena|patena]]. ''φατνώμα'', [[Illustrated Companion to the Latin Dictionary/Lacunar|lacunar]], 1. ''φατνωτός'', [[Illustrated Companion to the Latin Dictionary/Laqueatus|laqueatus]]. ''φάκελος'', [[Illustrated Companion to the Latin Dictionary/Fascis|fascis]]. ''φέρετρον'', [[Illustrated Companion to the Latin Dictionary/Feretrum|feretrum]]. ''φετιάλεις'', [[Illustrated Companion to the Latin Dictionary/Fetiales|fetiales]]. ''φιάλη'', [[Illustrated Companion to the Latin Dictionary/Patera|patera]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Lacunar|lacunar]], 1. ''φιλύρα'', [[Illustrated Companion to the Latin Dictionary/Philyra|philyra]]. ''φιμός'', [[Illustrated Companion to the Latin Dictionary/Fritillus|fritillus]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Fiscella|fiscella]], 2. ''φοίνιξ'', [[Illustrated Companion to the Latin Dictionary/Palma|palma]], 2. ''φορβειά'', [[Illustrated Companion to the Latin Dictionary/Capistrum|capistrum]]. ''φορειαφόροι'', [[Illustrated Companion to the Latin Dictionary/Lecticarii|lecticarii]]. ''φορεῖον'', [[Illustrated Companion to the Latin Dictionary/Lectica|lectica]]. ''{{mdash}}{{mdash}} κατάστεγον'', [[Illustrated Companion to the Latin Dictionary/Sella|sella gestatoria]]. ''φορτηγός'', [[Illustrated Companion to the Latin Dictionary/Bajulus|bajulus]]. ''φρέαρ'', [[Illustrated Companion to the Latin Dictionary/Puteus|puteus]]. ''φρύγανον'', [[Illustrated Companion to the Latin Dictionary/Cremium|cremium]]. ''φῦκος'', [[Illustrated Companion to the Latin Dictionary/Fucus|fucus]]. ''φῦρα'', [[Illustrated Companion to the Latin Dictionary/Follis|follis]], 4. ''φύσκη'', [[Illustrated Companion to the Latin Dictionary/Botulus|botulus]]. ''φωνασκός'', [[Illustrated Companion to the Latin Dictionary/Phonascus|phonascus]]. == ''Χ.'' == ''χαλινός'', [[Illustrated Companion to the Latin Dictionary/Frenum|frenum]]. ''{{mdash}}{{mdash}}'', [[Illustrated Companion to the Latin Dictionary/Oreae|oreæ]]. ''Χαλκιδικόν'', [[Illustrated Companion to the Latin Dictionary/Chalcidicum|Chalcidicum]]. ''χαμουλκός'', [[Illustrated Companion to the Latin Dictionary/Chamulchus|chamulchus]]. ''χαρακτήρ'', [[Illustrated Companion to the Latin Dictionary/Character|character]]. ''χαράκωμα'', [[Illustrated Companion to the Latin Dictionary/Vallum|vallum]]. ''χάραξ'', [[Illustrated Companion to the Latin Dictionary/Vallus|vallus]]. ''Χαρίσια'', [[Illustrated Companion to the Latin Dictionary/Charistia|Charistia]]. ''χειμάδια'', [[Illustrated Companion to the Latin Dictionary/Hiberna|hiberna]]. ''χειραμάξιον'', [[Illustrated Companion to the Latin Dictionary/Chiramaxium|chiramaxium]]. ''χειριδωτός'' (sc. ''χιτών''), [[Illustrated Companion to the Latin Dictionary/Chiridota|chiridota]]. ''χειρίς'', [[Illustrated Companion to the Latin Dictionary/Manica|manica]]. ''χειρόμακτρον'', [[Illustrated Companion to the Latin Dictionary/Mantele|mantele]]. ''χειρομύλη'', [[Illustrated Companion to the Latin Dictionary/Mola|mola manuaria]]. ''χειρόνιπτρον'', [[Illustrated Companion to the Latin Dictionary/Malluvia|malluvium]]. ''χειρονομία'', [[Illustrated Companion to the Latin Dictionary/Chironomia|chironomia]]. ''χειρονόμος'', [[Illustrated Companion to the Latin Dictionary/Chironomos|chironomos]]. ''χειρουργός'', [[Illustrated Companion to the Latin Dictionary/Chirurgus|chirurgus]]. ''χεῖρ σιδηρᾶ'', [[Illustrated Companion to the Latin Dictionary/Manus ferrea|manus ferrea]]. ''χέλυς, -ώνη'', [[Illustrated Companion to the Latin Dictionary/Testudo|testudo]]. ''χελώνιον'', [[Illustrated Companion to the Latin Dictionary/Chelonium|chelonium]]. ''χέρνιβον'', [[Illustrated Companion to the Latin Dictionary/Labrum|labrum]], 4. ''χηλή'', [[Illustrated Companion to the Latin Dictionary/Chele|chele]]. ''χηνίσκος'', [[Illustrated Companion to the Latin Dictionary/Cheniscus|cheniscus]]. ''χιλίαρχοι'', [[Illustrated Companion to the Latin Dictionary/Tribunus|tribuni militares]]. ''χιτών'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]]. ''{{mdash}}{{mdash}} ἀμφιμάσχαλος'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 1. ''{{mdash}}{{mdash}} ἑτερομάσχαλος'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 2. ''{{mdash}}{{mdash}} καρπωτός'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 6. ''{{mdash}}{{mdash}} ποδήρης'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 7. ''{{mdash}}{{mdash}} σχιστός'', [[Illustrated Companion to the Latin Dictionary/Tunica|tunica]], 5. ''χιτώνιον'', [[Illustrated Companion to the Latin Dictionary/Tunicula|tunicula]]. ''χιτωνίσκος'', [[Illustrated Companion to the Latin Dictionary/Tunicula|tunicula]]. ''χλαῖνα'', [[Illustrated Companion to the Latin Dictionary/Laena|læna]]. ''χλαμυδώτος'', [[Illustrated Companion to the Latin Dictionary/Chlamydatus|chlamydatus]]. ''χλαμύς'', [[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]]. ''χλιδών'', [[Illustrated Companion to the Latin Dictionary/Armilla|armilla]]. ''χνόη'', [[Illustrated Companion to the Latin Dictionary/Modiolus|modiolus]], 1. ''χοινίκη'', [[Illustrated Companion to the Latin Dictionary/Modiolus|modiolus]], 1 and 5. ''χοραύλης'', [[Illustrated Companion to the Latin Dictionary/Choraules|choraules]]. ''χορεία'', [[Illustrated Companion to the Latin Dictionary/Chorea|chorea]]. ''χόρευσις'', [[Illustrated Companion to the Latin Dictionary/Saltatio|saltatio]]. ''χορήγιον'', [[Illustrated Companion to the Latin Dictionary/Choragium|choragium]]. ''χορηγός'', [[Illustrated Companion to the Latin Dictionary/Choragus|choragus]], 2. ''χόρτος'', [[Illustrated Companion to the Latin Dictionary/Chors|chors]]. ''χρυσένδετα'', [[Illustrated Companion to the Latin Dictionary/Chrysendeta|chrysendeta]]. ''χύτρα'', [[Illustrated Companion to the Latin Dictionary/Chytra|chytra]]. ''χυτρόπους'', [[Illustrated Companion to the Latin Dictionary/Chytropus|chytropus]]. ''χῶμα'', [[Illustrated Companion to the Latin Dictionary/Agger|agger]]. ''χώνη'', [[Illustrated Companion to the Latin Dictionary/Infundibulum|infundibulum]]. == ''Ψ.'' == ''ψαλίς'', [[Illustrated Companion to the Latin Dictionary/Forfex|forfex]]. ''ψαλτήριον'', [[Illustrated Companion to the Latin Dictionary/Psalterium|psalterium]]. ''ψάλτρια'', [[Illustrated Companion to the Latin Dictionary/Psaltria|psaltria]]. ''ψέλλιον'', [[Illustrated Companion to the Latin Dictionary/Armilla|armilla]]. ''ψευδισόδομον'', [[Illustrated Companion to the Latin Dictionary/Pseudisodomum|pseudisodomum]]. ''πσευδοδίπτερος'', [[Illustrated Companion to the Latin Dictionary/Pseudodipteros|pseudodipteros]]. ''ψευδόθυρον'', [[Illustrated Companion to the Latin Dictionary/Pseudothyrum|pseudothyrum]]. ''ψευδοπερίπτερος'', [[Illustrated Companion to the Latin Dictionary/Pseudoperipteros|pseudoperipteros]]. ''ψῆφος'', [[Illustrated Companion to the Latin Dictionary/Calculus|calculus]]. ''ψίαθον'', [[Illustrated Companion to the Latin Dictionary/Matta|matta]]. ''ψίλωθρον'', [[Illustrated Companion to the Latin Dictionary/Psilothrum|psilothrum]]. == ''Ω.'' == ''ᾠδεῖον'', [[Illustrated Companion to the Latin Dictionary/Odeum|odeum]]. ''ὡρεῖον'', [[Illustrated Companion to the Latin Dictionary/Horreum|horreum]]. ''ὡρολόγιον'', [[Illustrated Companion to the Latin Dictionary/Horologium|horologium]]. ''ὠτεγχύτης'', [[Illustrated Companion to the Latin Dictionary/Strigilis|strigilis]], 2. ''ὠτογλυφίς'', [[Illustrated Companion to the Latin Dictionary/Auriscalpium|auriscalpium]]. == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="RICH_1849_pithaula">No lemma ''Pithaula'' in the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''.</ref> }} [[Category:Illustrated Companion to the Latin Dictionary|*]] [[Category:RICH-2K/Project pages]] svkpns2jb3qffj8cxy8tftc1c6o1ey1 Illustrated Companion to the Latin Dictionary/Cardinalis 0 311708 2683460 2671328 2024-11-11T15:25:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683460 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARDINA'LIS'''. See [[Illustrated Companion to the Latin Dictionary/Scapus|SCAPUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] qk1qsi942djzksvo5agq9553vmuuf31 Illustrated Companion to the Latin Dictionary/Cardinatus 0 311709 2683461 2671329 2024-11-11T15:25:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683461 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARDINA'TUS'''. See [[Illustrated Companion to the Latin Dictionary/Cardo|CARDO]] 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] n15s0fhk7j08hrfghzd32zmxkz2dccf Illustrated Companion to the Latin Dictionary/Cardo 0 311710 2683462 2671330 2024-11-11T15:25:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683462 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARDO'''. A ''pivot'' and ''socket'', forming an apparatus by means of which the doors of the ancients were fixed in their places, and made to revolve in opening and shutting; thus answering the same purpose as the hinges more commonly in use amongst us, though the contrivance was entirely different in its character. (See [[Illustrated Companion to the Latin Dictionary/Ginglymus|GINGLYMUS]].) The Greeks distinguished each of these parts by distinct names, using {{lang|grc|στρόφιγξ}} for the ''pivot'', and {{lang|grc|στροφεύς}} for the ''socket'' in which the pivot worked; but the Latin writers commonly include the whole apparatus under the term ''cardo'', though they sometimes apply it to each of the parts separately, and sometimes to the whole style of the [[Illustrated Companion to the Latin Dictionary/Foris|door-leaf]] (''[[Illustrated Companion to the Latin Dictionary/Scapus|scapus cardinalis]]''), that formed the axle by which the contrivance acted. (Plin. ''H. N.'' xvi. 77. ''ib.'' 84. Id. xxxvi. 24. n. 8. Plaut. ''Asin.'' ii. 3. 38. Virg. ''Aen.'' ii. 480. Apul. ''Met.'' i. p. 9.) The figures in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Cardo 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 120.jpg|annexed engraving |caption=Cardo/1.1}} will explain the nature of these objects, and the manner in which they were applied. The two top ones on the right hand exhibit a pair of bronze shoes from Egyptian originals in the British Museum, which were fastened on to the top and bottom of a door-leaf, to act as pivots ({{lang|grc|στρόφιγγες}}), for the wooden axles were cased with bronze to bear the wear and tear (Virg. ''Cir.'' 222. ''aeratus cardo''); the two lower ones on the same side are two boxes which were let into the [[Illustrated Companion to the Latin Dictionary/Limen|sill]] and lintel of the door case to act as sockets ({{lang|grc|στροφεῖς}}), in which the pivots turned; the left-hand one, which is Egyptian, and of very hard stone, is now in the British Museum, and was actually used with the pivot shoe drawn immediately above it: the right-hand one is of bronze, and was found in the sill of a door at Pompeii; the teeth or flutings round the sides are too keep it firm in its place, and prevent it from turning in its setting with the working of the door; the left-hand figure is an Egyptian door from Wilkinson, and shows the manner in which the apparatus was attached and worked. Compare the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Antepagmentum|ANTEPAGMENTUM]]. 2. The pin or pivot at each extremity of an axle in machinery, by means of which the axle revolves in the sockets which receive them, as in a wheel-barrow, roller, and similar contrivances. Vitruv. x. 14. 1. 3. A ''tenon'' in carpentry; i. e. the head of a timber cut into a particular form for the purpose of fitting into a cavity of the same size and shape in another piece, and so forming a joint (Vitruv. x. 14. 2.); hence ''cardo securiculatus'', a tenon in the form of an axe, or as we call it "dove-tailed." Vitruv. x. 10. 3. <gallery> File:Cardo 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 120.jpg|Cardo/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Doors]] i550rbw3hutwm8p01ucx015ck2snuva Illustrated Companion to the Latin Dictionary/Carenum 0 311711 2683463 2671331 2024-11-11T15:25:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683463 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARE'NUM'''. The ''must'' of new wine inspissated by boiling down to two-thirds of its original quantity. Pallad. ''Oct.'' 18. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Manufacture of Oil and Wine]] 8xj4i86a5hnxpujwq1c6sb9lh69meo5 Illustrated Companion to the Latin Dictionary/Carina 0 311712 2683464 2671332 2024-11-11T15:25:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683464 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARI'NA''' ({{lang|grc|τρόπις}}). The ''keel'', or lowest piece of timber in the framework of a ship, running the whole length from stem to stern, and serving as a foundation for the entire fabric (Cic. ''de Orat.'' iii. 46.); including also the false keel or "keelson." Liv. xxii. 20. Caes. ''B. G.'' iii. 13. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Parts and Ornaments of Vessels]] 9ck93j0v2097lc0mn27n7o9ms97okqi Illustrated Companion to the Latin Dictionary/Carnarium 0 311713 2683465 2671333 2024-11-11T15:26:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683465 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARNA'RIUM'''. A frame suspended from the ceiling, and furnished with hooks and nails, for the purpose of hanging up cured provisions dried fruits, herbs, &c., similar to those still used in our kitchens. (Plaut. ''Capt.'' iv. 4. 6. Pet. ''Sat.'' 135. 4. Id. 136. 1. Plin. ''H. N.'' xviii. 60.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Carnarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 121.jpg|illustration |caption=Carnarium/1.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, in which it is suspended from the ceiling of a tavern, and shows sausages, vegetables, and such things hanging by strings or in nets. 2. In a more general sense, a ''safe'' or ''larder'' for the preservation of fresh viands. Plaut. ''Curc.'' ii. 3. 45. Plin. ''H. N.'' xix. 19. n. 3. <gallery> File:Carnarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 121.jpg|Carnarium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] [[Category:Classed Index/Provision Dealers]] b939firjc8hbpj7c6yyxvznjft3hwa6 Illustrated Companion to the Latin Dictionary/Carnifex 0 311714 2683466 2671334 2024-11-11T15:26:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683466 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAR'NIFEX'''. The public executioner, who inflicted torture and scourging upon criminals, and executed the condemned by strangling them with a rope. Plaut. ''Capt.'' v. 4. 22. Suet. ''Nero'', 54. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] fs06mjm7rzd3tb6z0pjunj4hu9juk27 Illustrated Companion to the Latin Dictionary/Carnificina 0 311715 2683467 2671335 2024-11-11T15:26:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683467 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARNIFICI'NA'''. The place in which criminals were tortured and executed (Liv. ii. 23. Suet. ''Tib.'' 62.); viz. an underground dungeon beneath all the other cells of the [[Illustrated Companion to the Latin Dictionary/Carcer|gaol]]. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Carnificina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 121.jpg|illustration |caption=Carnificina/1.1}} represents the interior of the ''carnificina'' in the state prisons at Rome, constructed by Servius Tullius, after whom it was called the Tullianum, and the identical spot in which the friends and accomplices of Catiline were executed by order of Cicero. The criminal was let down into it by a rope through the aperture in the ceiling, and his body dragged up again by an iron hook (''[[Illustrated Companion to the Latin Dictionary/Uncus|uncus]]'') after the execution. The small door-way on the left hand, though ancient, does not belong to the original construction; it gives admission to a low subterranean gallery, now filled with rubbish, but which takes a direction towards the Tiber, and was, perhaps, intended for carrying the dead bodies to the river, when they were not dragged out of the prison for exposure on the Gemonian stairs. <gallery> File:Carnificina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 121.jpg|Carnificina/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] of9mhi4eqb0700h9ofh8zgldpvq90mk Illustrated Companion to the Latin Dictionary/Carpentum 0 311716 2683468 2671336 2024-11-11T15:26:34Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683468 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARPEN'TUM'''. A two-wheeled carriage, with an awning over it, and curtains by which it might be closed in front (Prop. iv. 8. 23. Apul. ''Met.'' x. p. 224.); capable of containing two or three persons, usually drawn by a pair of mules (Lamprid. ''Heliog.'' 4.), and used by the Roman matrons and ladies of distinction from remote antiquity. (Ov. ''Fast.'' i. 619. Liv. v. 25.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Carpentum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|illustration |caption=Carpentum/1.1}}, which belongs to the earliest times is copied from an Etruscan [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] (Micali, ''Italia avanti i Romani'', tav. 27.), and represents a bride and bridegroom, or a married pair, as Livy describes Lucumo and his wife on their arrival at Rome (''sedens carpento cum uxore''. Liv. i. 34.). 2. ''Carpentum funebre'' or ''pompaticum''. A state ''carpentum'' or carriage, in which the urn containing the ashes of the great, or their statues, were carried in the funeral procession. (Suet. ''Cal.'' 15. Id. ''Claud.'' 11. Isidor. ''Orig.'' xx. 12. 3.) These were likewise covered carriages, constructed upon the same principle as the preceding, but more showy and imposing in character; as may be seen by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Carpentum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|example |caption=Carpentum/2.1}}, from a medal struck in commemoration of one of the Roman empresses, its use being further implied by the form, which, it will be observed, is made in imitation of a tomb. 3. A cart employed for agricultural purposes, and apparently of very common and general use; for the same word is frequently applied in the sense of ''cart-load'', as of dung, &c., to indicate a certain quantity, which every one would immediately recognise, as in the English phrase, "a load." (Pallad. x. 1. Veget. ''Mul. Med.'' iv. 3. ''Praef.'') It was probably built like the first of the two specimens, but of coarser workmanship, and without the awning. <gallery> File:Carpentum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|Carpentum/1.1 File:Carpentum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|Carpentum/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carriages]] nly9s1ijdino2ujccoyvpl7gqy52wnh Illustrated Companion to the Latin Dictionary/Carptor 0 311717 2683469 2671337 2024-11-11T15:26:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683469 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARPTOR'''. The ''carver''; a slave whose duty it was to carve the dishes at grand entertainments before they were handed round to the guests. Juv. ''Sat.'' ix. 110. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Attendants]] [[Category:Classed Index/Domestic Slaves]] bm7v2xz3ymow5j5mv8h1nd5yuozh4eo Illustrated Companion to the Latin Dictionary/Carrago 0 311718 2683470 2671338 2024-11-11T15:26:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683470 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARRA'GO'''. A species of fortification adopted by many of the barbarous nations with whom the Romans came into collision. It was effected by drawing up their waggons and war-chariots into a circle round the positions which they occupied. Amm. Marc. xxxi. 7. 7. Trebell. ''Gallien.'' 13. Veget. ''Mil.'' iii. 10. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Fortification]] tt5wtomata7wj7h7m4e7zr0t4g86juu Illustrated Companion to the Latin Dictionary/Carroballista 0 311719 2683471 2671339 2024-11-11T15:27:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683471 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARROBALLIS'TA'''. A ''[[Illustrated Companion to the Latin Dictionary/Ballista|ballista]]'' mounted upon a carriage, and drawn by horses or mules for the convenience of transport from place to place, or to different points in the scene of action. (Veget. ''Mil.'' iii. 24. Id. ii. 25.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Carroballista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|illustration |caption=Carroballista/1.1}} represents an engine of this description, as it is expressed on the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Antonine; but it is too imperfect in point of detail, to give an adequate idea of the constructive principle upon which such machines acted. <gallery> File:Carroballista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 122.jpg|Carroballista/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Machines and Engines of War]] 6we3l0ylvtcf4t8ysq2nrrvrmkthx2s Illustrated Companion to the Latin Dictionary/Carrucarius 0 311720 2683472 2671340 2024-11-11T15:27:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683472 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARRUCA'RIUS'''. Belonging to a ''[[Illustrated Companion to the Latin Dictionary/Carruca|carruca]]''; an epithet applied to the coachman who drove it (Capitol. ''Maxim. jun.'' 4.), and to the horses or mules which drew it. (Ulp. ''Dig.'' 21. 1. 38.) See the [[Illustrated Companion to the Latin Dictionary/Carruca|preceding word]] and illustration. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ome7ngmwd66n1cms2q0uyt1c59qgtwa Illustrated Companion to the Latin Dictionary/Carruca 0 311721 2683473 2671341 2024-11-11T15:27:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683473 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARRU'CA''' or '''CARRU'CHA'''. A particular kind of carriage introduced at Rome under the Empire (at least mention of it first occurs in Pliny, and it subsequently becomes common in Suetonius, Martial, and others). Its precise form and character is a matter of mere conjecture; but it is clearly distinguished from the ''[[Illustrated Companion to the Latin Dictionary/Covinus|covinus]]'' and ''[[Illustrated Companion to the Latin Dictionary/Esseda|essedum]]'' by Martial (''Ep.'' xii. 24.), and from the ''[[Illustrated Companion to the Latin Dictionary/Rheda|rheda]]'' by Lampridius. (''Alex. Sev.'' 43.) It was at all times a vehicle of costly description, and highly ornamented; at first, by carvings in bronze and ivory (Aurel. ''Vopisc.'' 46.), and afterwards by chasings in silver and gold. (Plin. ''H. N.'' xxxiii. 40. Mart. ''Ep.'' iii. 62.) This description agrees so far with the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Carruca 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|annexed engraving |caption=Carruca/1.1}}, representing the carriage of the [[Illustrated Companion to the Latin Dictionary/Praefecti|praefect]] of Rome from the Notitia Imperii, and in which the metal ornaments are very apparent. It may, therefore, by a plausible conjecture, be regarded as affording a type of these conveyances, but the Latin writers certainly make use of the term at times in a general sense, without intending thereby to designate any particular build (as in Suet. ''Nero'', 30. and Mart. ''Ep.'' iii. 47., where the same vehicle is indiscriminately termed ''carruca'' and ''rheda''), and the word retained this usage in after times, for it contains the elements of the Italian ''carrozza'', and our ''carriage'', both of which are general expressions. 2. ''Carruca dormitoria''. A close ''carruca'' (Scaevol. ''Dig.'' 34. 2. 11.); the ''carruca undique contecta'' of Isidorus, ''Orig.'' xx. 12. 3. <gallery> File:Carruca 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|Carruca/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carriages]] hqspntfe5od969wv60bpdb4eocss7uf Illustrated Companion to the Latin Dictionary/Carrus 0 311722 2683474 2671342 2024-11-11T15:27:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683474 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARRUS'''. A small two-wheeled cart with boarded sides all round, used chiefly in the Roman armies for a commissariat and baggage waggon, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Carrus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|example |caption=Carrus/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan, on which such vehicles are frequently represented. The name is of Celtic origin, as was the vehicle itself, having been extensively employed by the ancient Britons, Gauls, Helvetii, &c. Sisenn. ''ap.'' Non. ''s. v.'' p. 125. Liv. x. 28. Caes. ''B. G.'' i. 3. <gallery> File:Carrus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|Carrus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carts]] pixqlstz4payxja6vvbrmezyso55k9e Illustrated Companion to the Latin Dictionary/Cartibulum 0 311723 2683475 2671343 2024-11-11T15:27:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683475 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARTIB'ULUM'''. A particular kind of table, made of stone or marble, with an oblong square slab for the top, and supported by a single central pedestal, or after the manner of those now called ''console tables'' by our upholsterers. It was not used as a dining-table, but as an ornamental slab or sideboard for holding the plate and vases belonging to the household, and used to stand on one side of the ''[[Illustrated Companion to the Latin Dictionary/Atrium|atrium]]'' with the vessels arranged upon it. (Varro, ''L. L.'' v. 125.) This account from Varro is accurately illustrated by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Cartibulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|engraving |caption=Cartibulum/1.1}}, which represents a marble table of the kind, as it was discovered on the margin of the ''[[Illustrated Companion to the Latin Dictionary/Impluvium|impluvium]]'' in the house of the Nereids at Pompeii. Behind it is a fountain, and underneath it there is a sort of sink, divided into two compartments, into which the drainings or residue from the vessels were emptied before they were put upon the table. <gallery> File:Cartibulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 123.jpg|Cartibulum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Tables]] q7uync3n0ji4vtmdud8uxwybxkjhkjm Illustrated Companion to the Latin Dictionary/Caryatides 0 311724 2683476 2671344 2024-11-11T15:28:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683476 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CARYAT'IDES''' ({{lang|grc|Καρυάτιδες}}). Female figures employed instead of [[Illustrated Companion to the Latin Dictionary/Columna|columns]] by the ancient architects to support an entablature, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Caryatides 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 124.jpg|annexed engraving |caption=Caryatides/1.1}}, which represents the [[Illustrated Companion to the Latin Dictionary/Porticus|portico]] attached to the [[Illustrated Companion to the Latin Dictionary/Templum|temple]] of Pandrosos at Athens. Vitruv. i. 1. 5. <gallery> File:Caryatides 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 124.jpg|Caryatides/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Column]] k3fkajufk487vnvga7zn2tb8gayjpiz Illustrated Companion to the Latin Dictionary/Casa 0 311725 2683477 2671345 2024-11-11T15:28:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683477 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASA'''. Generally ''a cottage''; understood in the same latitude of meaning which we apply to that word in our own language; for instance:{{mdash}} 1. A cottage proper (Vitruv. ii. 1. 3. and 5. Pet. ''Sat.'' 115. 6.); the first regular effort in building of the pastoral ages, and which continued afterwards as the constant model for the residence of a village population. Of this description was the thatched cottage of Romulus on the Capitoline hill (''casa Romuli'', Vitruv. ii. 1. Pet. ''Fragm.'' 21. 6.), and those of the aboriginal inhabitants of Latium, of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Casa 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 124.jpg|illustration |caption=Casa/1.1}} here introduced may be regarded as an authentic and highly curious example. It is copied from an earthenware vase, now preserved amongst the Egyptian and other antiquities in the British Museum, but originally employed as a sepulchral urn, which was discovered in the year 1817 amongst several others in the form of [[Illustrated Companion to the Latin Dictionary/Templum|temples]], [[Illustrated Companion to the Latin Dictionary/Galea|helmets]], &c., at Marino, near the ancient Alba Longa, imbedded in a sort of white earth ''under'' a thick stratum of volcanic lava (the Italian ''peperino''), which flowed from the Alban mount before its eruptions became extinct; previously to which period these vases must in consequence have been deposited there, an irresistible proof of their great antiquity. Visconti, ''Lettera al Sigr. Giuseppe Carnevali, sopra alcuni Vasi sepolcrali rinvenuti nella vicinanza della antica Alba Longa.'' Roma. 1817. 2. A ''small country-house'' (Mart. ''Ep.'' vi. 43.); built, as we should say, in cottage fashion, upon a far less grand or magnificent scale than the regular ''villa'' or country mansion, as represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Casa 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 125.jpg|annexed engraving |caption=Casa/2.1}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, which affords a good idea of the small Roman country-house, with its courtyard, outbuildings, and live stock. When Martial (''Ep.'' xii. 66.) used the words ''[[Illustrated Companion to the Latin Dictionary/Domus|domus]]'' and ''casa'' as convertible terms, it is purposely and pointedly, in order to insinuate that the ''domus'' or town-house was but a poor and ill-built one; i. e. no better than a ''casa'' or cottage. 3. A bower or rustic arbour, made of osiers and branches, and sometimes covered with vines, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Casa 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 125.jpg|example |caption=Casa/3.1}} from the ancient [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] of Praeneste. Tribull. ii. 1. 24. 4. A sort of wigwam or hut which the soldiery sometimes formed with branches of trees, as a substitute for a [[Illustrated Companion to the Latin Dictionary/Tentorium|tent]]. Veget. ''Mil.'' ii. 10. <gallery> File:Casa 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 124.jpg|Casa/1.1 File:Casa 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 125.jpg|Casa/2.1 File:Casa 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 125.jpg|Casa/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] [[Category:Classed Index/The Garden]] 3bmcpxy7a4f5p0l72c74zowk1y8s7ve Illustrated Companion to the Latin Dictionary/Caseus 0 311726 2683478 2671346 2024-11-11T15:28:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683478 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CA'SEUS''' ({{lang|grc|τυρός}}). ''Cheese'' (Varro, ''L. L.'' v. 108.); which the ancients made from the milk of cows, sheep, and goats (Varro, ''R. R.'' ii. 11.), and eat in a fresh state, like cream cheese, or dried and hardened. (Id. ''ib.'') It was also pressed and made into ornamental shapes by boxwood moulds (Columell. vii. 8. 7.). Pliny (''H. N.'' xi. 97.) enumerates the different places where the best cheeses were made. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ptwh6aludyg893bg2vt6zyu82h0hdaq Illustrated Companion to the Latin Dictionary/Cassidarius 0 311727 2683479 2682910 2024-11-11T15:28:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683479 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASSIDA'RIUS'''. An armourer who makes metal helmets. Inscript. ''ap.'' Muret. 959. 5. 2. An office whose duty it was to take charge of the [[Illustrated Companion to the Latin Dictionary/Cassis (helmet)|metal helmets]] in the Imperial armoury. Inscript ''ap.'' Reines. 8. 70. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 9q7voopgxqnsvzdjwgnw5uud692t8sm Illustrated Companion to the Latin Dictionary/Cassida 0 311728 2683480 2682915 2024-11-11T15:28:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683480 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASS'IDA'''. Same as [[Illustrated Companion to the Latin Dictionary/Cassis (helmet)|CASSIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 66w958jws0qnkeqtx16tw6nk68eu2tr Illustrated Companion to the Latin Dictionary/Cassis (helmet) 0 311729 2683481 2671349 2024-11-11T15:28:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683481 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAS'SIS''', ''-idis'' ({{lang|grc|κόρυς}}). A casque or helmet made of metal, as contradistinguished from [[Illustrated Companion to the Latin Dictionary/Galea|GALEA]], a helmet of leather (Isidor. ''Orig.'' xviii. 14. compare Tac. ''Germ.'' 6.); but this distinction is not always observed (Ov. ''Met.'' viii. 25., where both names are given to the same helmet); and as the latter is the more common name, the different kinds and forms are described and illustrated under [[Illustrated Companion to the Latin Dictionary/Galea|that word]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Defensive Armour]] nx8jpfa77wfxdzrdu1a053g6syfcc8j Illustrated Companion to the Latin Dictionary/Cassis (net) 0 311730 2683482 2671350 2024-11-11T15:29:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683482 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASSIS''', ''-is'' ({{lang|grc|ἄρκυς}}). One of the nets employed by the ancients in hunting wild animals, such as boars and deer. (Isidor. ''Orig.'' xix. 5. 4. Ov. ''A. Am.'' i. 392. Mart. ''Ep.'' iii. 58.) It was a sort of purse or tunnel net, the mouth of which was kept open by branches of trees, and so deceived the animal who was driven into it, when it was immediately closed by a running rope (''[[Illustrated Companion to the Latin Dictionary/Epidromus|epidromus]]'') round the neck. Yates, ''Textrin. Antiq.'' p. 422. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Hunting]] 1zb35p32ebgc6oxv5invm93a67bzxeu Illustrated Companion to the Latin Dictionary/Castellarius 0 311731 2683483 2671351 2024-11-11T15:29:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683483 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASTELLA'RIUS'''. An officer who had the charge of superintending the public reservoir (''[[Illustrated Companion to the Latin Dictionary/Castellum|castellum]]'') of an [[Illustrated Companion to the Latin Dictionary/Aquaeductus|aqueduct]]. Front. ''Aq.'' 117. Inscript. ''ap.'' Grut. 601. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] pk9qb74dzzfuzbua9zx2t8fu9c8gs58 Illustrated Companion to the Latin Dictionary/Castellum 0 311732 2683484 2671352 2024-11-11T15:29:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683484 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASTEL'LUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Castrum|CASTRUM]]. A small fortified place or fortress in which a body of soldiers was stationed, either in the open country to protect the agricultural population from the incursions of hostile tribes, or on the frontiers, to guard the boundaries of the state, or in any other position which commanded the main [[Illustrated Companion to the Latin Dictionary/Via|road]] and lines of intercommunication. (Sisenn. ''ap.'' Non. ''s.'' Festinatim. p. 514. Cic. ''Fam.'' xi. 4. Id. ''Phil.'' v. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Castellum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 126.jpg|illustration |caption=Castellum/1.1}} represents one of these fortified posts with its garrison, from the Vatican Virgil. 2. A small fortified town; so called because many of the forts, originally intended as mere military posts, grew into towns and villages from the neighbouring population flocking to them, and building their cottages about the fort, for the sake of protection; just as the baronial castles of the feudal ages formed a nucleus for many of the town in modern Europe. Curt. v. 3. 3. The reservoir of an [[Illustrated Companion to the Latin Dictionary/Aquaeductus|aqueduct]]; formed at its city termination, or at any part of the line, were a head of water was required for the supply of the locality; and into which the main pipes were inserted for the purpose of distributing the water through the various districts of a city. (Vitruv. viii. 6. 1. Plin. ''H. N.'' xxxvi. 24. n. 9. Frontin. ''Aq.'' 35.) In ordinary situations, these were plain brick or stone towers containing a deep cistern or reservoir within them, but at the termination of the duct when it reached the city walls, the ''castellum'' was designed with a regard to ornament as well as use, having a grand architectural façade of one or more stories, decorated with [[Illustrated Companion to the Latin Dictionary/Columna|columns]] and statues, and forming with its waste water a noble fountain which poured its jets through many openings into an ample basin below (Vitruv. ''l. c.''); as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Castellum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 126.jpg|illustration |caption=Castellum/3.1}} here inserted, which is a restoration of the ''castellum'' belonging to the Julian aqueduct, still remaining, though in a dilapidated state at Rome, near the church of S. Eusebio; but the details here introduced are authorized by an old drawing of the structure executed in the 16th century, when the principal ornaments were still in their original situations, and the whole in a much more perfect condition than at present. 4. ''Castellum privatum''. A reservoir built at the expense of a certain number of private individuals living in the same district, and who had obtained a grant of water from the public duct, which was thus collected into one head from the main reservoir, and thence distributed amongst themselves by private pipes. Frontin. 106. compare 27. 5. ''Castellum domesticum''. A cistern which each person constructed on his own property to receive the water allotted to him from the public reservoir. Frontin. 6. A cistern or receptacle, into which the water raised by a water-wheel was discharged from the scoops, buckets, or troughs (''[[Illustrated Companion to the Latin Dictionary/Modiolus|modioli]]'') which collected it. (Vitruv. x. 4. 3.) See [[Illustrated Companion to the Latin Dictionary/Rota|ROTA AQUARIA]] <gallery> File:Castellum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 126.jpg|Castellum/1.1 File:Castellum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 126.jpg|Castellum/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Aqueducts]] [[Category:Classed Index/Fortification]] eemxbp6n67gt96o1jtmpumlr0e5p4gv Illustrated Companion to the Latin Dictionary/Casteria 0 311733 2683485 2671353 2024-11-11T15:29:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683485 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASTER'IA'''. A place in which the oars, rudders, and moveable gear of a vessel were laid up, when the ship was not in commission; or, as others think, a particular compartment in the vessel itself, to which the rowers retired to rest themselves when relieved from duty. Non. ''s. v.'' p. 85. Plaut. ''Asin.'' iii. i. 16. Scheffer, ''Mil. Nav.'' ii. 5. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Port, etc.]] odzwwrheypc0ft7jtlmmcwao42726on Illustrated Companion to the Latin Dictionary/Castra 0 311734 2683486 2671354 2024-11-11T15:29:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683486 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASTRA'''. Plural of [[Illustrated Companion to the Latin Dictionary/Castrum|CASTRUM]]. An encampment, or fortified camp. The arrangement of a Roman camp was one of remarkable system and skill. Its general form was square, and the entire position was surrounded by a ditch (''fossa''), and an embankment (''[[Illustrated Companion to the Latin Dictionary/Agger|agger]]'') on the inside of it, the top of which was defended by a strong fencing of palisades (''[[Illustrated Companion to the Latin Dictionary/Vallum|vallum]]''). Each of the four sides was furnished with a wide [[Illustrated Companion to the Latin Dictionary/Porta|gate]] for ingress and egress; the one furthest removed from the enemy's position ({{Illustrated Companion to the Latin Dictionary/Inscription|text=A}}) was styled ''porta decumana''; that immediately in front of it ({{Illustrated Companion to the Latin Dictionary/Inscription|text=B}}) ''porta praetoria''; the one on the right hand ({{Illustrated Companion to the Latin Dictionary/Inscription|text=C}}), ''porta principalis dextra''; the other on the left ({{Illustrated Companion to the Latin Dictionary/Inscription|text=D}}), ''porta principalis sinistra''. The whole of the interior was divided into seven streets or gangways, of which the broadest one, running in a direct line between the two side gates, and immediately in front of the general's [[Illustrated Companion to the Latin Dictionary/Tentorium|tent]] (''[[Illustrated Companion to the Latin Dictionary/Praetorium|praetorium]]''), was 100 feet wide, and called ''Via Principalis''. In advance of this, but parallel to it, was another street, called ''Via Quintana'', 50 feet wide, which divided the whole of the upper part of the camp into two equal divisions; and these were again subdivided by five other streets of the same width, intersecting the ''Via Quintana'' at right angles. The tents and quarters of the troops were then arranged as follows:{{mdash}}1. The ''[[Illustrated Companion to the Latin Dictionary/Praetorium|praetorium]]'', or general's tent. 2. The ''quaestorium'', a space allotted to the quaestor, and the commissariat stores under his charge. 3. The ''[[Illustrated Companion to the Latin Dictionary/Forum|forum]]'', a sort of market place. 4. 4. The tents of the select horse and volunteers. 5. 5. The tents of the select foot and volunteers. 6. 6. The ''[[Illustrated Companion to the Latin Dictionary/Eques|Equites]] Extraordinarii'', or extraordinary cavalry furnished by the allies. 7. 7. The ''Pedites Extraordinarii'', or extraordinary infantry furnished by the allies. 8. 8. Places reserved for occasional auxiliaries. 9. 9. The tents of the [[Illustrated Companion to the Latin Dictionary/Tribunus|tribunes]], and of the ''praefecti sociorum'', or generals who commanded the allies. This completes the upper portion of the camp. The centre of the lower portion was allotted to the two Roman [[Illustrated Companion to the Latin Dictionary/Legio|legions]] which constituted a consular army, flanked on each side by the right and left wings, composed of allied troops. The manner in which these were respectively quartered will be at once understood by the names of each, which are written in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Castra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 127.jpg|engraving |caption=Castra/1.1}} over their respective positions. Finally, the whole of the interior was surrounded by an open space, 200 feet wide, between the ''agger'' and the tents, which protected them from fire or missiles, and facilitated the movements of the troops within. The plan, drawn out after the description of Polybius, when the Roman armies were divided by [[Illustrated Companion to the Latin Dictionary/Manipulus|maniples]], is inserted in order to illustrate the general method upon which a Roman camp was constructed, and not as an authentic design from any ancient monument. Some of the minor details were necessarily altered after the custom of dividing the legions into [[Illustrated Companion to the Latin Dictionary/Cohors|cohorts]], instead of maniples, had obtained; but the general plan and principal features of the interior distribution, remained the same. 2. ''Castra Praetoriana''. The permanent camp on the skirts of the city of Rome, in which the [[Illustrated Companion to the Latin Dictionary/Praetoriani|Praetorian]] guards were stationed. (Suet. ''Claud.'' 21. Tac. ''Ann.'' iv. 2.) A portion of the high brick wall which enclosed it, with one of the gates, is still to be seen standing near the Porta Pia, where it forms a part of the present city walls, into the general circuit of which it was taken when they were extended by Aurelian. 3. ''Castra navalia'' or ''nautica''. A naval encampment; i. e. a line of fortification formed round the ships of a fleet, to protect them from the enemy, when they were drawn up ashore. Caes. ''B. G.'' v. 22. Nepos, ''Alcib.'' 8. <gallery> File:Castra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 127.jpg|Castra/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Camp and Tents]] ozm3umhvorunbkhkm0mypwviv9c177i Illustrated Companion to the Latin Dictionary/Castrum 0 311735 2683487 2671355 2024-11-11T15:30:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683487 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CASTRUM'''. An augmentative of [[Illustrated Companion to the Latin Dictionary/Casa|CASA]], meaning in its primary sense a large or strongly-built hut, and thence a fort or fortress; though the diminutive [[Illustrated Companion to the Latin Dictionary/Castellum|CASTELLUM]] was retained in more common use. Nepos, ''Alcib.'' 9. Virg. ''Aen.'' vi. 776. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] sbu24m6wdagsmmogd6rm1irbx5humto Illustrated Companion to the Latin Dictionary/Castula 0 311736 2683489 2671356 2024-11-11T15:30:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683489 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAS'TULA'''. A woman's ''petticoat''; worn next the skin, and fastened under the breast, which it left exposed. (Varro, ''de Vit. Pop. Rom. ap.'' Non. ''s. v.'' Caltula, p. 584.) In early works of art, it is often represented as the only under garment or sole article of the attire, similar to the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Castula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 128.jpg|engraving |caption=Castula/1.1}}, from a bas-relief on an Etruscan tomb; but the Roman women mostly wore a tunic or some other article of dress over the breast and shoulders, so that the two covered the person as much as an upper and under [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]]; in which case the upper part of the petticoat, as well as the bosom, is concealed under the skirts of the outer covering. In this manner it is worn by Silvia in the Vatican Virgil (p. 146.), and by a female figure amongst the Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]]. ''Mus. Borb.'' xiv. 2. compare xii. 57., where the ''castula'' is put on ''over'' a long-sleeved tunic, but fastened over the shoulders and round the waist in the same manner as above. <gallery> File:Castula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 128.jpg|Castula/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Cinctures]] 5oc20my843h5rcg8c28gqqp8nl82mc9 Illustrated Companion to the Latin Dictionary/Casula 0 311737 2683490 2671357 2024-11-11T15:30:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683490 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CA'SULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Casa|CASA]]. Any very small cottage or humble dwelling in general; but, more especially, a temporary hut or cabin of a conical form, which sheep and goat herds erected on the lands where their flocks pastured; and agricultural peasants in the fields for their shelter at harvest time. (Plin. ''H. N.'' xxxv. 37. Juv. ''Sat.'' xi. 153.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Casula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 128.jpg|example |caption=Casula/1.1}} is from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] representing a rustic scene; and the illustration introduced in [[Illustrated Companion to the Latin Dictionary/Caprarius|CAPRARIUS]] shows a goat-herd's hut of similar character. The second meaning belonging to this word is also an evidence of the first. 2. A hooded cloak or capote; such as was worn by the country people, and universally given to Telesphorus, the attendant of Aesculapius, as he is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Casula 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|annexed example |caption=Casula/2.1}}, from an engraved gem. When the hood is drawn over the head, as here, the whole garment presents an appearance very similar to the cabin last described, and from this resemblance the term originated, being probably a sort of nick-name, or familiar word amongst the lower orders. Isidor. ''Orig.'' xix. 24. 17. <gallery> File:Casula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 128.jpg|Casula/1.1 File:Casula 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|Casula/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] [[Category:Classed Index/The Houses]] lvujza2st6zom33b8yae28p4ohpdkum Illustrated Companion to the Latin Dictionary/Cataclista 0 311738 2683492 2671358 2024-11-11T15:30:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683492 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATACLIS'TA''' sc. ''vestis'' (Apul. ''Met.'' xi. 245.; but neither the reading nor the meaning of the word is free from uncertainty.) A term which some have interpreted to mean a dress kept shut up in the wardrobe, and only taken out to be worn upon great occasions as a holiday dress (Salmas. ''ad'' Tertull. ''de Pall.'' 3.); others, with more apparent reason, a garment without any opening, but fitting tight and close to the person, like those commonly seen on Egyptian statues. Visconti, ''Mus. Pio-Clem.'' vi. 14. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Outward Apparel]] 966twmnbtuzqo274vltzbqww4mshbf6 Illustrated Companion to the Latin Dictionary/Catadromus 0 311739 2683493 2671359 2024-11-11T15:30:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683493 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAD'ROMUS'''. A rope extended in a slanting position from the ground to some elevated point in a [[Illustrated Companion to the Latin Dictionary/Theatrum|theatre]], upon which rope-dancers ascended and descended; a feat which, however extraordinary it may appear, is also recorded to have been performed in the Roman [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatre]] by an elephant with a rider on its back. (Suet. ''Nero'' 11. compare ''Galb.'' 6. and Plin. ''H. N.'' viii. 2.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catadromus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|illustration |caption=Catadromus/1.1}} is from a medal of Caracalla; the slanting ropes and the dancers on them are clearly indicated, while the baskets and palm branches on the top represent the prizes for those who succeed in reaching up to them. <gallery> File:Catadromus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|Catadromus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] bmllj7o40lcv1pbo5muihnfs00qjw18 Illustrated Companion to the Latin Dictionary/Catagrapha 0 311740 2683494 2671360 2024-11-11T15:30:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683494 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAG'RAPHA''' ({{lang|grc|τà κατάγραφα}}). [[Illustrated Companion to the Latin Dictionary/Pictura|Paintings]] in which the figures are drawn in perspective, or, as the artists have it, ''fore-shortened'', so that, although the whole figure is represented, only a portion of it is seen by the spectator (Plin. ''H. N.'' xxxv. 34.); a practice now considered as indicating great skill on the part of the artist, but which the ancient [[Illustrated Companion to the Latin Dictionary/Pictor|painters]] seldom had recourse to. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catagrapha 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|illustration |caption=Catagrapha/1.1}} here introduced is from a Pompeian picture, which represents Agamemnon conducting Chryseis on board the vessel which was to convey her to her father. The figure of Agamemnon is slightly foreshortened in its upper portion; but, slight as that is, it is the closest approximation towards such a mode of treatment discoverable in the whole of the works executed by the artists of Pompeii. Even in the celebrated [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] which represents the battle of Issus, the largest pictorial composition, and richest in number of figures, which has descended to us, the whole of them are represented in full front or side views, and in postures nearly erect, though in the most energetic action. But, with the exception of some arms and legs, and one horse which has his back turned to the spectator, there is no attempt at fore-shortening the ''figure'' in the sense now understood, whereby an entire figure is portrayed upon the canvass, within a space which otherwise would only admit a part of it. Even the three men who are wounded, and upon the ground, have their bodies presented in profile, and at full length, their legs and arms only being slightly foreshortened. The same observations are equally applicable to the designs on fictile vases. <gallery> File:Catagrapha 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 129.jpg|Catagrapha/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Painting]] dei7w3o7ktkf8cgc1823o7meap9sf6w Illustrated Companion to the Latin Dictionary/Cataphractarius 0 311741 2683495 2671361 2024-11-11T15:31:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683495 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPHRACTA'RIUS'''. Same as [[Illustrated Companion to the Latin Dictionary/Cataphractus|CATAPHRACTUS]]. Lamprid. ''Alex. Sev.'' 56. Ammian. xvi. 2. 5. ''ib.'' 10. 8. and 12. 63. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] d76jn428d80jb4en7vs7cdr0viqfxiv Illustrated Companion to the Latin Dictionary/Cataphracta 0 311742 2683496 2671362 2024-11-11T15:31:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683496 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPHRAC'TA''' ({{lang|grc|καταφράκτης}}). A term employed by Vegetius to designate generally any kind of breast-plate worn by the Roman infantry from the earliest period until the reign of the Emperor Gratianus. Veget. ''Mil.'' i. 20. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Defensive Armour]] bbrleh836wbklobt5capttv0160f3i5 Illustrated Companion to the Latin Dictionary/Cataphractus 0 311743 2683497 2682920 2024-11-11T15:31:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683497 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPHRAC'TUS''' ({{lang|grc|κατάφρακτος}}). A heavy-armed cavalry-soldier (Sallust ''ap.'' Non. ''s. v.'' p. 556.), whose horse, as well as himself, was covered with a complete suit of armour (Serv. ''ad'' Virg. ''Aen.'' xi. 770.), like the scaled back of a crocodile (Ammian. xxii. 15, 16); more especially characteristic of some foreign nations; the Parthians (Prop. iii. 12. 12.), Persians (Liv. xxxvii. 40.), and Sarmatians (Tac. ''Hist.'' i. 79.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cataphractus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 130.jpg|illustration |caption=Cataphractus/1.1}} representing a Sarmatian cataphract, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. 2. Sisenna (''ap.'' Non. ''l. c.'') applies the same term to an infantry soldier, by which it is to be understood that he is armed cap-a-pie in heavy body armour, consisting of [[Illustrated Companion to the Latin Dictionary/Cassis (helmet)|helmet]], [[Illustrated Companion to the Latin Dictionary/Lorica|cuirass]], cuisses, or thigh pieces, and [[Illustrated Companion to the Latin Dictionary/Ocrea|greaves]], as seen in the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Ocreatus|OCREATUS]]. <gallery> File:Cataphractus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 130.jpg|Cataphractus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Troops]] c6u2tt7qs5nwg50wxqxapg4d88rw544 Illustrated Companion to the Latin Dictionary/Catapirates 0 311744 2683498 2671364 2024-11-11T15:31:41Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683498 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPIRA'TES''' ({{lang|grc|βολίς}}). The ''lead'' which sailors use for taking soundings. It had tallow fixed to the bottom, in the same way as now, for the purpose of ascertaining the nature of the ground, whether of sand, rock, pebbles, or shells, and if fit for anchorage or not. (Lucil. ''Sat.'' p. 82. 11. ed Gerlach. Isidor. ''Orig.'' xix. 4. 10.) In the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catapirates 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 130.jpg|illustration |caption=Catapirates/1.1}}, from a marble bas-relief, of which there is a cast in the British Museum, it is represented as hanging from the head of a vessel. <gallery> File:Catapirates 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 130.jpg|Catapirates/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Ship's Gear]] 8wmjb8k9w0in0j0yf60ogjpgnbfmlmu Illustrated Companion to the Latin Dictionary/Catapultarius 0 311745 2683499 2671365 2024-11-11T15:31:52Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683499 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPULTA'RIUS''' ({{lang|grc|καταπελτικός}}). Any thing used with, or belonging to, a catapult; hence ''pilum catapultarium'' (Plaut. ''Curc.'' iii. 5. 11.), a dart of large and heavy description, made for the purpose of being projected from the ''[[Illustrated Companion to the Latin Dictionary/Catapulta|catapulta]]''. (Compare Polyb. xi. 11. 3.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catapultarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|illustration |caption=Catapultarius/1.1}} is taken from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan, and also affords an insight into the manner of using and working these engines. <gallery> File:Catapultarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|Catapultarius/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Machines and Engines of War]] fh63bhly2sudev77lgloa6ng2pzs9gt Illustrated Companion to the Latin Dictionary/Catapulta 0 311746 2683500 2671367 2024-11-11T15:32:03Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683500 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAPUL'TA''' ({{lang|grc|καταπέλτης}}). A military engine constructed principally for discharging darts and spears of great substance and weight (Paulus ''ex'' Fest. ''s.'' [[Illustrated Companion to the Latin Dictionary/Trifax|Trifax]]); whence it is sometimes put for the missile which it discharges. (Titin. ''ap.'' Non. ''s. v.'' p. 552. Plaut. ''Pers.'' i. 1. 27.) This machine is described in detail by Vitruvius (x. 15.), and it appears no less than six times on the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan, from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed representation |imagelink=Media:Catapulta 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|annexed representation |caption=Catapulta/1.1}} is taken; but the details are not sufficiently circumstantial in any one of them to illustrate satisfactorily the words of Vitruvius, or to show the precise manner in which it acted, beyond the general fact that it projected the missile by the force of its rebound, when the cross bar was drawn back from one of the sides, and then allowed to fly again with a recoil. It was also employed in the same manner as the ''[[Illustrated Companion to the Latin Dictionary/Ballista|ballista]]'', for projecting large blocks of stone (Caes. ''B. C.'' ii. 9.); for which purpose the arch in in the centre seems intended, in order to let the mass pass; and it was also placed at times upon a carriage, and transported by horses or mules, like the ''[[Illustrated Companion to the Latin Dictionary/Carroballista|carro-ballista]]'', as proved by the [[Illustrated Companion to the Latin Dictionary/Catapultarius|next wood-cut]]. <gallery> File:Catapulta 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|Catapulta/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Machines and Engines of War]] e6pszt2pufb0dzcflky5fmzk1nxw1jc Illustrated Companion to the Latin Dictionary/Cataracta 0 311747 2683501 2671370 2024-11-11T15:32:14Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683501 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATARAC'TA''' or '''CATARAC'TES''' ({{lang|grc|καταρράκτης}}). A ''cataract, cascade'', or sudden fall of water from a higher to a lower level, like the falls of Tivoli or Terni. Plin. ''H. N.'' v. 10. Vitruv. viii. 2. 6. 2. A ''sluice, flood-gate'', or ''lock'' in a river, either for the purpose of moderating the rapidity of the current (Plin. ''Ep.'' x. 69.), or for shutting in the water, so as to preserve a good depth in the stream. (Rutil. i. 481.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cataracta 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|illustration |caption=Cataracta/2.1}} is copied from one of the bas-reliefs on the [[Illustrated Companion to the Latin Dictionary/Arcus|arch]] of Septimius Severus. It will be observed, that the Roman artist, in accordance with the practice of his school, has omitted to insert the flood-gate, contenting himself with carving the uprights by which it was kept in its place, and made to slide up and down. 3. A ''portcullis'', suspended over the entrance of a city or fortified place, so that it could be let down or drawn up by iron rings and chains at pleasure. (Liv. xxvii. 28. Veget. ''Mil.'' iv. 4.) In one of the ancient gate-ways still remaining at Rome, another at Tivoli, and also at Pompeii, the grooves in which the portcullis worked are plainly aparent; and the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example here introduced |imagelink=Media:Cataracta 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|example here introduced |caption=Cataracta/3.1}}, from an ancient fresco [[Illustrated Companion to the Latin Dictionary/Pictura|painting]], where it defends the entrance to a bridge, exhibits the chains and ring by which it was worked, precisely as mentioned by Vegetius. The grating which closed the entrance does not appear in the original, which may be the effect of age; or, perhaps, it was not a regular portcullis, but only a movable bar raised and lowered at certain hours to close the passage against travellers or cattle; but in either case, it is sufficient to exhibit the character of such contrivances amongst the ancients. <gallery> File:Cataracta 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|Cataracta/2.1 File:Cataracta 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 131.jpg|Cataracta/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Water-courses]] [[Category:Classed Index/Fortification]] nnyehistym4fzxasircwrh7np8t5apy Illustrated Companion to the Latin Dictionary/Catascopium 0 311748 2683502 2671371 2024-11-11T15:32:25Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683502 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATASCOP'IUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Catascopus|CATASCOPUS]]. A small vessel employed as a spy-ship, to keep a watch or look-out. Aul. Gell. x. 25. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] 3dnuz1a0vdylil6rquvzol8ek0p9feo Illustrated Companion to the Latin Dictionary/Catascopus 0 311749 2683503 2671372 2024-11-11T15:32:36Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683503 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAS'COPUS''' ({{lang|grc|κατάσκοπος}}). A spy or scout. Hirt. ''Bell. Afr.'' 26. 2. A vessel employed as a spy-ship. Caes. ''B. G.'' iv. 26. Isidor. ''Orig.'' xix. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dje7tjdydvz5twqr92ghfcsxjsjm78g Illustrated Companion to the Latin Dictionary/Catasta 0 311750 2683504 2671373 2024-11-11T15:32:47Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683504 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATAS'TA'''. An elevated wooden frame or platform upon which slaves were placed when exposed for sale in the slave market, in order that the purchaser might examine them, to discover their points or defects. (Tibull. ii. 3. 60. Pers. vi. 77. Suet. ''Gramm.'' 13.) From an expression of Statius (''Sylv.'' ii. 1. 72. ''turbo catastae''), it would appear that the machine was made to revolve, like the stands used for statues, that the purchaser might have an opportunity of inspecting the structure of the figure exposed all round. 2. ''Catasta arcana''. An apparatus of similar description, on which the most valuable and beautiful slaves were shown, not in the public market, but privately in the depôts of the dealers. Mart. ''Ep.'' ix. 60. 5. 3. An iron bed or grating under which a fire was kindled, and on which criminals were sometimes laid to be tortured, and some of the early martyrs roasted alive. Prudent. {{lang|grc|''Περὶ στεφ.''}} i. 56. Id. ii. 399. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] [[Category:Classed Index/Domestic Slaves]] led6byb8xr7stj6xj2c3px5bwv3klnq Illustrated Companion to the Latin Dictionary/Cateja 0 311751 2683506 2671374 2024-11-11T15:32:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683506 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATE'JA'''. A missile employed in warfare by the Germans, Gauls, Hirpini, &c. It was a [[Illustrated Companion to the Latin Dictionary/Hasta|spear]] of considerable length and slender shaft, having a long cord attached to it, like the harpoon, so that it could be recovered by the person who had launched it. Virg. ''Aen.'' vii. 742. Serv. ''ad l.'' Sil. iii. 277. Isidor. ''Orig.'' xviii. 7. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Spears and Missiles]] p5i5nxlvmsto6hch1w1mwpnam8fcd2d Illustrated Companion to the Latin Dictionary/Catella 0 311752 2683507 2671375 2024-11-11T15:33:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683507 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATELLA''' ({{lang|grc|ἁλυσίδιον}}). A diminutive of [[Illustrated Companion to the Latin Dictionary/Catena|CATENA]]; but generally used to indicate the smaller and finer sort of chains made by jewellers in gold or silver, and used for trinkets, or any of the various purposes to which similar articles are applied in our own days. (Hor. ''Ep.'' i. 17. 55. Liv. xxxix. 31. Cato, ''R. R.'' 135.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Catella 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 132.jpg|example |caption=Catella/1.1}} here introduced, from a Pompeian original, exhibits a small bronze chain of a pattern very commonly found; but the excavations made at different times in that city and other parts of Italy have produced a great variety of other designs, affording specimens of all the patterns now made, as well as some others, which cannot be imitated by modern workmen. <gallery> File:Catella 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 132.jpg|Catella/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ornaments for the Person]] evg1q0ldcobihglpw5wfqkw7zyvgb20 Illustrated Companion to the Latin Dictionary/Catellus 0 311753 2683508 2671376 2024-11-11T15:33:20Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683508 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATELLUS'''. A diminutive of [[Illustrated Companion to the Latin Dictionary/Catena|CATENA]]; a small chain made use of for the confinement of slaves, but whether of any special character, it is difficult to determine. From the passage of Plautus where the word occurs (''Curc.'' v. 3. 13.), it may be surmised that the ''catellus'' was something like what is now called a "''clog''," which is attached to the legs of animals to prevent them from straying, and which might have been fastened as a punishment, to the leg of a slave; the term thus originating in a pun upon the word ''[[Illustrated Companion to the Latin Dictionary/Canis|canis]]'' (Becker, ''Quaest. Plautin.'' p. 63. Lips. 1837.), the clog and chain having a sort of affinity to a dog with its chain. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] fwso6lvtxyh39iibeedi24i82zagkkn Illustrated Companion to the Latin Dictionary/Catenarius 0 311754 2683509 2671377 2024-11-11T15:33:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683509 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATENA'RIUS''', sc. CANIS. A yard or watch dog, chained up to protect the premises from strangers. The Romans kept dogs in this way at the entrance of their houses by the side of the porter's cell, with the notice, {{Illustrated Companion to the Latin Dictionary/Inscription|text=CAVE CANEM}} {{mdash}} "Beware of the dog," written up (Pet. ''Sat.'' 19. 1. Id. 72. 7. Seneca, ''Ira'', 3. 37.); as is shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Catenarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|annexed illustration |caption=Catenarius/1.1}}, from a [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]], which forms the pavement of the ''[[Illustrated Companion to the Latin Dictionary/Prothyrum|prothyrum]]'' in the house of the "tragic poet," as it is called, at Pompeii. <gallery> File:Catenarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|Catenarius/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Classed Index-category missing]] a8owhbveivgjqem6v1bocjv2o7gjk1a Illustrated Companion to the Latin Dictionary/Catenatus 0 311755 2683510 2671378 2024-11-11T15:33:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683510 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATENA'TUS''' ({{lang|grc|ἁλυσίδετος}}). Shackled, fettered, or ''in chains'', like a slave, criminal, or captive. (Flor. iii. 19. 3. Suet. ''Tib.'' 64. Hor. ''Epod.'' vii. 8.) The word does not imply that the person so confined was chained ''up'', or bound ''to'', another object, which is expressed by ''alligatus''; but merely that he was bound with chains in a manner to impede the freedom of his motions, and prevent an escape by flight. See the illustrations ''s.'' [[Illustrated Companion to the Latin Dictionary/Catulus|CATULUS]] and [[Illustrated Companion to the Latin Dictionary/Compeditus|COMPEDITUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] erhfqpfwsnhzykk9d32720s2kqqdhg4 Illustrated Companion to the Latin Dictionary/Catena 0 311756 2683511 2671379 2024-11-11T15:33:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683511 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATE'NA''' ({{lang|grc|ἅλυσις}}). A ''chain'', formed by a series of iron links interlacing with each other. (Cic. Virg. Hor. Ov. &c.) The chains of the ancients were made exactly like our own, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catena 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|illustration |caption=Catena/1.1}}, which represents some of the links of an ancient chain now preserved as a sacred relic in the Church of S. Pietro in Vinculis at Rome, and which gave its title to the church; for it is there said to be the identical one with which St. Peter was chained in the ''[[Illustrated Companion to the Latin Dictionary/Tullianum|Tullianum]]'', or Servian prison. See Cancellieri, ''Carcere Tulliano'', where all the evidence upon which this tradition depends is stated at length. 2. A chain of gold or silver worn by women as an ornament round the body, or over the shoulder and sides, like a ''[[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]'' (Plin. ''H. N.'' xxxiii. 12.) Ornaments of this description are frequently depicted in the Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]], from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catena 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|illustration |caption=Catena/2.1}} is taken; and always placed, as here, upon the naked body of goddesses, bacchanals, dancing girls, and persons of that description. <gallery> File:Catena 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|Catena/1.1 File:Catena 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 133.jpg|Catena/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ornaments for the Person]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 5htpepahskhrolb05ksfykez3b57ph3 Illustrated Companion to the Latin Dictionary/Catervarii 0 311757 2683512 2671380 2024-11-11T15:34:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683512 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATERVA'RII'''. [[Illustrated Companion to the Latin Dictionary/Gladiatores|Gladiators]] and combatants who fought in companies or bodies, and not in single pairs, which was the more usual manner. Suet. ''Aug.'' 45. Compare ''Cal.'' 30. ''gregatim dimicantes''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Gladiators]] tfcedgy707369l68ivxrm05bjt11b0s Illustrated Companion to the Latin Dictionary/Cathedra 0 311758 2683513 2671381 2024-11-11T15:34:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683513 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATHED'RA''' ({{lang|grc|καθέδρα}}). A chair with a back to it, but without arms, such as was used more especially by females (Hor. ''Sat.'' i. 10. 91. Mart. ''Ep.'' iii. 63.); hence when assigned to males, it frequently implies a notion that they were of idle, luxurious, or effeminate habits. (Juv. ''Sat.'' ix. 52. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cathedra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|illustration |caption=Cathedra/1.1}} represents Leda's chair, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. 2. ''Cathedra supina''. A chair with a long deep [[Illustrated Companion to the Latin Dictionary/Sedes|seat]] (hence ''cathedra longa''. Juv. ''Sat.'' ix. 52.), and reclining back (whence ''supina''. Plin. ''H. N.'' xvi. 68.), such as we might call an easy or lounging chair. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cathedra 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|example |caption=Cathedra/2.1}} is from a Greek fictile vase, and represents one of the masters who taught the young men their exercises in the [[Illustrated Companion to the Latin Dictionary/Gymnasium|gymnasium]] ({{lang|grc|παιδοτρίβης}}). A marble in the [[Illustrated Companion to the Latin Dictionary/Capitolium|Capitol]] at Rome shows the empress Agrippina sitting in one of a similar character. 3. ''Cathedra strata''. A chair covered with a cushion, as seen in the first engraving. Juv. ''l. c.'' 4. The chair in which philosophers, rhetoricians, &c., sat to deliver their lectures; ''a professor's chair'' (Juv. ''Sat.'' vii. 203. Mart. ''Ep.'' 1. 77.), of which the last illustration probably affords the type. 5. A sedan chair (Juv. ''Sat.'' i. 65.); for [[Illustrated Companion to the Latin Dictionary/Sella|SELLA]], which see. 6. More recently, the chair in which the bishops of the early Christian Church sat during divine service (Sidon. ''in conc. post Epist.'' 9. 1. 7.); from which the principal church of a diocese was called the "cathedral;" i. e. in which the bishop's chair is placed. <gallery> File:Cathedra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|Cathedra/1.1 File:Cathedra 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|Cathedra/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Chairs]] rrtqerza3oqbhu6fgc04052aggfx13a Illustrated Companion to the Latin Dictionary/Catheter 0 311759 2683514 2671382 2024-11-11T15:34:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683514 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATH'ETER''' ({{lang|grc|καθετήρ}}). Properly, a Greek word, for which the Romans used ''[[Illustrated Companion to the Latin Dictionary/Fistula|fistula aenea]]'' (Celsus, vii. 26. 1.); a ''catheter'', or [[Illustrated Companion to the Latin Dictionary/Chirurgus|surgical]] instrument employed in drawing off the water, when suppressed, from the bladder, into which it is inserted. Cael. Aurel. ''Tard.'' ii. 1. n. 13.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Catheter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|example |caption=Catheter/1.1}} is from an original, nine inches long, discovered at Pompeii. <gallery> File:Catheter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 134.jpg|Catheter/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Surgical Implements, etc.]] ckmf9sxpzozjh5tv8ak0anff4fdo8a6 Illustrated Companion to the Latin Dictionary/Catillus 0 311760 2683515 2671383 2024-11-11T15:34:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683515 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATILLUS''' or '''CATILLUM'''. A small dish of the same form and character as the ''[[Illustrated Companion to the Latin Dictionary/Catinum|catinus]]'', but of less capacity, and possibly of inferior manufacture. Columell. xii. 57. 1. Val. Max. iv. 3. 5. 2. ({{lang|grc|ὄνος}}). The upper or outer of the two stones in a [[Illustrated Companion to the Latin Dictionary/Mola|mill]] for grinding corn (Paul. ''Dig.'' 33. 7. 18. § 5.), which served as a hopper or bowl into which the corn was poured; whence the name. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Catillus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|annexed illustration |caption=Catillus/2.1}} represents a Roman mill now remaining at Pompeii, with a section on the left hand. The upper part or basin is the ''catillus'', into which the unground corn was put; it was then turned round by slaves or animals, and as it turned, the ears of corn gradually subsided through a hole at its bottom on to the conical or bell-shaped stone underneath (see the section), between which and the inner surface of its cap, they were ground into flour. 3. An ornament employed in decorating the [[Illustrated Companion to the Latin Dictionary/Vagina|scabbard]] of a sword (Plin. ''H. N.'' xxxiii. 54.), which is supposed to have been in the form of a round silver plate or stud, similar to those seen on the sheath of the sword inserted under [[Illustrated Companion to the Latin Dictionary/Capulus|CAPULUS]]; but the reading of the passage, as well as the meaning of it, if correct, is uncertain. <gallery> File:Catillus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|Catillus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] auos9em75axflmiefrm2bbcmomshfa2 Illustrated Companion to the Latin Dictionary/Catinum 0 311761 2683516 2671384 2024-11-11T15:34:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683516 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAT'INUM''' or '''CAT'INUS'''. A deep sort of dish, in which vegetables, fish, and poultry were brought to table. (Hor. ''Sat.'' i. 6. 115. ''Ib.'' ii. 4. 77. ''Ib.'' i. 3. 92.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catinum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|illustration |caption=Catinum/1.1}}, which is copied from a series of ancient fresco [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]] discovered near the church of St. John in Lateran, at Rome (Cassini, ''Pitture Antichi'', tav. 4.), representing a number of slaves bringing in different dishes at a feast, shows the ''catinus'', with a fowl and fish in it, precisely as described by Horace in the last two passages cited. 2. A deep earthenware dish, in which some kinds of cakes, pies, or puddings were cooked, and served up to table in the same; like our ''pie-dish''. Varro, ''R. R.'' 84. 3. A deep dish made of earthenware, glass, or more precious materials, in which pastiles of incense were carried to the sacrifice (Suet. ''Galb.'' 18. Apul. ''Apol.'' p. 434.), and thence taken out to be dropped upon a small burning fire-basket. (See the illustration to [[Illustrated Companion to the Latin Dictionary/Focus|FOCUS TURICREMUS]].) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catinum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|illustration |caption=Catinum/3.1}} represents a curious and valuable dish of agate, which was brought from Cesarea in Palestine in the year 1101, and is now preserved as a sacred relic in the sacristy of the cathedral at Genoa, where it goes by the name of the ''sagro catino''. It is devoutly believed in that city that our Saviour partook of the paschal lamb with his disciples out of this identical dish; but the smallness of its size, and the value of its material, sufficiently prove that it was never made to contain food, though it might have been, reasonably enough, employed for the purpose assigned. 4. An earthenware crucible for melting metals. (Plin. ''H. N.'' xxxiii. 21.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustrations |imagelink=Media:Catinum 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|illustrations |caption=Catinum/4.1}} represent two originals, one of red, the other of white clay, which were found in an ancient Roman pottery at Castor in Northamptonshire. Artis. ''Durobriv.'' pl. 38. 5. A particular member of the forcing pump invented by Ctesibius. (Vitruv. x. 12.) See the conjectural diagram in [[Illustrated Companion to the Latin Dictionary/Ctesibica machina|CTESIBICA MACHINA]], in which the ''Catinum'' is marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=A}}. <gallery> File:Catinum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|Catinum/1.1 File:Catinum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|Catinum/3.1 File:Catinum 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 135.jpg|Catinum/4.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Plates and Dishes]] [[Category:Classed Index/Implements of Worship and Sacrifice]] os8yft5paxjk7psy3p24htdothk3irv Illustrated Companion to the Latin Dictionary/Catomidio 0 311762 2683517 2671385 2024-11-11T15:34:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683517 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CATOMID'IO''' ({{lang|grc|κατωμίζω}}). To "hoist" one upon the shoulders of another, for the purpose of inflicting a flogging; a mode of punishment which, amongst the Romans, was applied to grown-up persons, as well as boys. (Pet. ''Sat.'' 132. 2. compare Apul. ''Met.'' ix. p. 196. Spart. ''Hadr.'' 18.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catomidio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 136.jpg|illustration |caption=Catomidio/1.1}} represents the whole process as taking place in a school-room at Herculaneum, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] discovered in that city. <gallery> File:Catomidio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 136.jpg|Catomidio/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] 6ov661ym1ra6baxqmzma3mw5j8ujfn3 Illustrated Companion to the Latin Dictionary/Catulus 0 311763 2683518 2671387 2024-11-11T15:35:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683518 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAT'ULUS'''. A chain attached to an iron collar (''[[Illustrated Companion to the Latin Dictionary/Collare|collare]]'') round the neck, like a dog's chain by which runaway slaves, when recaptured, were brought back to their masters. (Lucil. ''Sat.'' xxix. 15. ed. Gerlach. ''Cum manicis, catulo, collarique'', with [[Illustrated Companion to the Latin Dictionary/Manica|manacles]], leading chain, and neck [[Illustrated Companion to the Latin Dictionary/Collare|collar]].) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Catulus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 136.jpg|illustration |caption=Catulus/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Antonine, representing a barbarian captive, shows both the collar and chain attached to it, as mentioned by Lucilius. <gallery> File:Catulus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 136.jpg|Catulus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 6gveei0kff6rkdlhpkgu6ojkw94aryb Illustrated Companion to the Latin Dictionary/Caudex 0 311765 2683519 2671389 2024-11-11T15:35:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683519 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUDEX'''. See [[Illustrated Companion to the Latin Dictionary/Codex|CODEX]], which is the more usual spelling. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] eh81m80ntxm4sbviygnaam1m4bm22gy Illustrated Companion to the Latin Dictionary/Caudicarius 0 311766 2683520 2671390 2024-11-11T15:35:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683520 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUDICA'RIUS''' or '''CODICA'RIUS'''. ''Naves caudicariae''. Large boats employed upon the Tiber, and made of coarse planking roughly joined (Varro, ''de Vit. Pop. Rom. ap.'' Non. ''s. v.'' p. 535. Festus. ''s. v.''.; probably so constructed, because the rapidity of the current rendered it difficult to remount the stream; and they could thus be broken up or taken to pieces, without much loss, upon reaching the mouth of the river or their place of destination, as was the usual practice upon the Rhone before the introduction of steam navigation. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] mkmdkgkuh3hyrzfddkp0vaszmlbgs2b Illustrated Companion to the Latin Dictionary/Caudicius 0 311767 2683521 2671391 2024-11-11T15:35:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683521 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUDIC'IUS''', sc. ''[[Illustrated Companion to the Latin Dictionary/Lembus|lembus]]''. A vessel of similar character as the [[Illustrated Companion to the Latin Dictionary/Caudicarius|preceding]], employed upon the Moselle. Auson. ''Mosell.'' 197. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] 4nqm209fk5ae5464a0zn4e1i1f5jw5h Illustrated Companion to the Latin Dictionary/Caula 0 311768 2683522 2671392 2024-11-11T15:35:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683522 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAULA'''. A general name for any place surrounded with fences, so as to form an enclosure, as a ''sheepfold'', &c. Festus, ''s. v.'' Virg. ''Aen.'' ix. 61. Serv. ''ad l.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0z8jofwc9srazvhvgasqmn5eziuhody Illustrated Companion to the Latin Dictionary/Cauliculi 0 311769 2683523 2671393 2024-11-11T15:36:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683523 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAULIC'ULI'''. In architecture, the eight smaller leaves or stalks in a Corinthian capital which spring out of the four larger or principal ones, by which the eight [[Illustrated Companion to the Latin Dictionary/Voluta|volutes]] of the capital are sustained. (Vitruv. iv. 1. 12. Gwilt, ''Glossary of Architrecture'', ''s. v.'') They are easily distinguished upon any Corinthian capitals. See [[Illustrated Companion to the Latin Dictionary/Capitulum|CAPITULUM]] 6.; but in consequence of the very diminished size of the drawing, it is difficult to make them sufficiently prominent. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Column]] hewjmpzs6ch2h4tacnofe0854bagobt Illustrated Companion to the Latin Dictionary/Caupona 0 311770 2683524 2671394 2024-11-11T15:36:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683524 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUPO'NA''' ({{lang|grc|ξενοδοκειον, πανδοκεῖον}}). An ''inn'', for the accommodation of travellers, where they could be furnished with temporary board and lodging. (Hor. ''Ep.'' 1. 11. 12. Aul. Gell. vii. 11. 1.) The old-fashioned country inn, or road-side house, affords the nearest parallel in our language to the ancient ''caupona'', which has no resemblance to the more imposing establishments or ''hotels'', in which people of wealth amongst us take up their residence for long periods together. It was opened for the convenience of the poorer and trading classes, and those who travelled upon business, not for pleasure; for most other persons had private connections, or were furnished with introductions, which would ensure them a hospitable entertainment in some friend's house wherever they went; and such is still the custom in modern Italy, where the traveller who diverges from the beaten track, is obliged to have recourse to private hospitality, in consequence of the wretched nature of the places called inns. 2. ({{lang|grc|καπηλεῖον}}). In the large towns, the ''caupona'' was a place where wine and other refreshments, but wine more especially, was sold and drunk on the premises (Cic. ''Pis.'' 22. compare Mart. ''Ep.'' i. 27. ''ib.'' 57.); and thus it had a closer resemblance to our ''tavern, gin'', or ''beer'' shop; the chief object of which is to retail spirits and liquors, though some also supply eatables. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Caupona 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|illustration |caption=Caupona/2.1}} represents the interior of a wine shop, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] on the walls of one of these establishments at Pompeii; but in the original, a frame for dried and salted provisions is also suspended from the ceiling, which has been omitted, from inadvertance, in the engraving; it is, however, given under the word [[Illustrated Companion to the Latin Dictionary/Carnarium|CARNARIUM]]. 3. ({{lang|grc|καπηλίς}}). A female who keeps one of these places of entertainment. Lucil. ''Sat.'' iii. 33. Gerlach. Apul. ''Met.'' i. p. 6. and 15. <gallery> File:Caupona 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|Caupona/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Inns and Public-Houses]] gq7533z76jabyo4jh9qh5vnnrmyukwo Illustrated Companion to the Latin Dictionary/Cauponius 0 311771 2683525 2671395 2024-11-11T15:36:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683525 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUPO'NIUS''', sc. ''puer''. The ''waiter'' or ''pot-boy'' at a [[Illustrated Companion to the Latin Dictionary/Caupona|tavern]], or a wine shop (Plaut. ''Poen.'' v. 5. 19.); see on the right hand in the [[Illustrated Companion to the Latin Dictionary/Caupona|preceding wood-cut]], the figure who is bringing in the wine. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] bvool6jkkpaae8evu62f9xohjvz9zvz Illustrated Companion to the Latin Dictionary/Cauponula 0 311772 2683526 2671396 2024-11-11T15:36:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683526 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUPO'NULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Caupona|CAUPONA]]; a low, poor, and common wine-shop. Cic. ''Phil.'' ii. 31. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] hwrwqw7h0ymasy0dkt31pyaccie3fnj Illustrated Companion to the Latin Dictionary/Caupo 0 311773 2683527 2671397 2024-11-11T15:36:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683527 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAUPO'''. The master or keeper of a [[Illustrated Companion to the Latin Dictionary/Caupona|caupona]]; i. e. 1. An ''innkeeper'' ({{lang|grc|ξενοδόκος}}), who receives travellers in his house, and furnishes them with food and lodging (Cic. ''Div.'' i. 27); 2. a ''publican'' ({{lang|grc|κάπηλος}}), who furnished strangers with drink or food, but not with lodgings. Mart. ''Ep.'' i. 27. ''ib.'' i. 57., and see the [[Illustrated Companion to the Latin Dictionary/Caupona|next word]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] abnaotantlf4yk77nsukqjsckzx3r80 Illustrated Companion to the Latin Dictionary/Caupulus 0 311774 2683528 2671398 2024-11-11T15:36:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683528 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAU'PULUS''' or '''CAU'POLUS'''. A particular kind of boat (Aul. Gell. x. 25. 3.), the peculiar characteristics of which are unknown; but said to belong to the same class as the ''[[Illustrated Companion to the Latin Dictionary/Lembus|lembo]]'' and ''[[Illustrated Companion to the Latin Dictionary/Cymba|cymba]]''. Isidor. ''Orig.'' xix. i. 25. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] 1l3g8cocl07xfetnq52o9tdmek155tx Illustrated Companion to the Latin Dictionary/Causia 0 311775 2683529 2671399 2024-11-11T15:37:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683529 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAU'SIA''' ({{lang|grc|καυσία}}). A high-crowned, and broad-rimmed felted hat invented by the Macedonians (Val. Max. v. 1. 4.); from whom it descended to the Romans, and was especially worn by their fishermen and sailors. (Plaut. ''Mil.'' iv. 4. 42. Id. ''Pers.'' i. 3. 75.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Causia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|example |caption=Causia/1.1}} is from a fictile vase; but it resembles exactly the hat worn by Alexander, on a medal. <gallery> File:Causia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|Causia/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Coverings for the Head]] mwxpslj2lbm1ojyecv7ldjgt58691oa Illustrated Companion to the Latin Dictionary/Cauter 0 311776 2683530 2671400 2024-11-11T15:37:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683530 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAU'TER''' and '''CAUTE'RIUM''' ({{lang|grc|καυτήρ, καυτήριον}}). A ''cautery'' or ''branding iron'', used by [[Illustrated Companion to the Latin Dictionary/Chirurgus|surgeons]], veterinaries, and others, for branding cattle, affixing a [[Illustrated Companion to the Latin Dictionary/Stigma|stigma]] upon slaves, and similar purposes. (Pallad. i. 43. 3. Veget. ''Vet.'' i. 28.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cauter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|example |caption=Cauter/1.1}} represents an original, four inches long, which was discovered in a surgeon's house at Pompeii. 2. An instrument employed for burning in the colours of an [[Illustrated Companion to the Latin Dictionary/Encaustica|encaustic painting]]; but as that art, as it was practised amongst the ancients, is now lost, it is impossible to determine the exact character of the instrument, or the precise manner in which it was used. Mart. ''Dig.'' 33. 7. 17. Tertull. ''adv. Hermog.'' 1. <gallery> File:Cauter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 137.jpg|Cauter/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Surgical Implements, etc.]] 7d23zu8epm0jxd0hu4pdfpqq7yaxqc5 Illustrated Companion to the Latin Dictionary/Cavaedium 0 311777 2683531 2671401 2024-11-11T15:37:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683531 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAVAE'DIUM''' or '''CAVUM AEDIUM'''. Literally, the void or hollow part of a [[Illustrated Companion to the Latin Dictionary/Domus|house]]. To understand the real meaning of this word, it is to be observed that in early times, or for houses of small dimensions, the ancient style of building was a very simple one, and consisted in disposing all the habitable apartments round four sides of a quadrangle, which thus left a space or court-yard in the centre, without any roof, and entirely open to the sky, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cavaedium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 138.jpg|annexed example |caption=Cavaedium/1.1}}, from the Vatican Virgil. This hollow space received the primitive name of ''cavum aedium'', so truly descriptive of it; and formed, with the suites of apartments all round it, the entire house. But as the Romans increased in wealth, and began to build upon a more magnificent scale, adopting the style and plans of other nations, they converted this open court into an apartment suitable to the uses of their families, by covering in the sides of it with a roof supported upon [[Illustrated Companion to the Latin Dictionary/Columna|columns]] of one story high, and leaving only an opening in the centre (''[[Illustrated Companion to the Latin Dictionary/Compluvium|compluvium]]'') for the admission of light and air. This practice they learnt from the Etruscans (''ab Atriatibus Tuscis''. Varro, ''L. L.'' v. 161.), and, therefore, when the ''cavum aedium'' was so constructed, they designated it by the name of ''[[Illustrated Companion to the Latin Dictionary/Atrium|atrium]]'', after the people from whom they had borrowed the design. By referring to the ground-plans which illustrate the article [[Illustrated Companion to the Latin Dictionary/Domus|DOMUS]], it will be perceived that the ''atrium'' is in reality nothing more than the hollow part of the house, with a covered gallery or [[Illustrated Companion to the Latin Dictionary/Porticus|portico]] round its sides; and thus the two words sometimes appear to be used as convertible terms, and at others, with so much uncertainty as to bear an interpretation which would refer them to two separate and distinct members of the edifice; and, in reality, in great houses, or in country villas which covered a large space of ground, and comprised many distinct members, with their own appurtenances attached to each, we find that both a ''cavaedium'' and ''atrium'' were comprised in the general plan. This was the case in Pliny's villa (''Ep.'' ii. 17.), in which we are to understand that the first was an open court-yard, without any roof and side galleries (whence it is expressly said to be light and cheerful, ''hilare''); the other, a regular ''atrium'', partially covered in, according to the Etruscan, or foreign fashion. There can be no doubt that such is the real difference between the ''cavaedium'' and ''atrium''; but when the two words are not applied in a strictly distinctive sense, as in the passage of Pliny above cited, both the one and the other may be commonly used to designate the same member of a house, without reference to any particular position or mode of fitting up, both of them in reality being situate in the hollow, or shell of the house; and, consequently, Vitruvius, as an architect, employs the term ''cavaedium'' (vi. 5.) for the style which more strictly and accurately resembles an ''atrium''. (See [[Illustrated Companion to the Latin Dictionary/Atrium|that word]], and the illustrations there introduced; which will show the different ways of arranging a ''cavaedium'', when taken in its more general meaning.) <gallery> File:Cavaedium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 138.jpg|Cavaedium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] 78dw3kfxisx530di671pyn39a89rrp1 Illustrated Companion to the Latin Dictionary/Cavea 0 311778 2683532 2671402 2024-11-11T15:37:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683532 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CA'VEA'''. An artificial cage or den for wild beasts, made with open bars of wood or iron (Hor. ''A. P.'' 473.), in which they were transported from place to place (Claud. ''Cons. Stilich.'' ii. 322{{mdash}}5.); exposed to public view, as in a menagerie (Plin. ''H. N.'' viii. 25.); and sometimes brought into the [[Illustrated Companion to the Latin Dictionary/Arena|arena]] of an [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatre]], to be let loose upon the victims condemned to fight with them, in order to render their attack more ferocious than would be the case if they were emitted from an underground den into the sudden glare of open day. Vopisc. ''Prob.'' 19. 2. A ''bird cage'', made of wicker-work, or sometimes of gold wire (Pet. ''Sat.'' 28. 9.), in which singing birds were domesticated, and kept in private houses; or the call bird carried out by the fowler (''[[Illustrated Companion to the Latin Dictionary/Auceps|auceps]]'') for his sport. The passage from Petronius, quoted above, speaks of a magpie, suspended in his cage over a door, which was taught to utter salutations to all who entered. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cavea 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|example |caption=Cavea/2.1}} is from a fictile vase in Boldetti, ''Cimiterj'', p. 154. 3. The ''coop'' or cage in which the sacred chickens were kept and carried to the places where the auspices were taken, by observing the manner in which they fed. (Cic. ''N. D.'' ii. 3. Id. ''Div.'' ii. 33.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cavea 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|illustration |caption=Cavea/3.1}} represents one of these cages, with the cickens feeding, and the handle, by which it was carried, from a Roman bas-relief. 4. Poetically, a bee-hive. Virg. ''G.'' iv. 58. See [[Illustrated Companion to the Latin Dictionary/Alveare|ALVEARE]]. 5. A conical frame of laths or wicker-work, made use of by fullers and dyers for airing, drying, and bleaching cloth. (Apul. ''Met.'' ix. p. 193.) This frame was placed over a fire-pan, or a pot with sulphur kindled in it, the use of which is well known for bleaching, and the cloth was then spread over the frame, which confined the heat, and excluded the air. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cavea 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|example |caption=Cavea/5.1}} here given is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] in the fuller's establishment (''[[Illustrated Companion to the Latin Dictionary/Fullonica|fullonica]]'') at Pompeii. In the original, a man carries it on his head, and the pot of sulphur in his hand; but it has been drawn here standing on the ground, with the vessel of sulphur placed underneath it, precisely in the same way as it is now commonly employed in Italy for airing clothes, in order to show more clearly the mode of use. 6. A circular fence constructed round the stems of young trees to preserve them from being damaged by cattle. Columell. v. 6. 21. 7. That portion of the interior of a theatre, or amphitheatre (Apul. ''Met.'' x. p. 227.), which contained the [[Illustrated Companion to the Latin Dictionary/Sedes|seats]] where the spectators sat, and which was formed by a number of concentric tiers of steps, either excavated out of the solid rock on the side of a hill, or supported upon stories of [[Illustrated Companion to the Latin Dictionary/Arcus|arches]] constructed in the shell of the building. According to the size of the edifice, these tiers of seats were divided into one, two, or three distinct flights, separated from one another by a wall (''[[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]'') of sufficient height to intercept communication between them, and then the several divisions were distinguished by the names of ''ima, summa, media cavea'', i. e. the lower, upper, or middle tier; the lowest one being the post of honour, where the ''[[Illustrated Companion to the Latin Dictionary/Eques|equites]]'' sat. (Plaut. ''Amph. Prol.'' 66. Cic. ''Am.'' 7. Id. ''Senect.'' 14.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cavea 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|illustration |caption=Cavea/7.1}} affords a view of the interior, or ''cavea'', of the amphitheatre at Pompeii, as it now remains; and shows the general plan of arrangement. See also the articles and illustrations to [[Illustrated Companion to the Latin Dictionary/Theatrum|THEATRUM]] and [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|AMPHITHEATRUM]]. <gallery> File:Cavea 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|Cavea/2.1 File:Cavea 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|Cavea/3.1 File:Cavea 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|Cavea/5.1 File:Cavea 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 139.jpg|Cavea/7.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Miscellaneous Domestic Furniture and Utensils]] [[Category:Classed Index/The Amphitheatre and its Component Parts]] [[Category:Classed Index/Fowling]] [[Category:Classed Index/Fulling]] [[Category:Classed Index/Implements of Worship and Sacrifice]] lpysxjqureh031rmc88rpom8zzosicl Illustrated Companion to the Latin Dictionary/Cavernae 0 311779 2683533 2671403 2024-11-11T15:37:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683533 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CAVER'NAE''' ({{lang|grc|κοίλη}} or {{lang|grc|κοίλη ναῦς}}). The hold of a ship, and the cabins it contains. Cic. ''Orat.'' iii. 46. Lucan. ix. 110. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Parts and Ornaments of Vessels]] rk1mi8rukhwmrh1opeqwg0osdziit21 Illustrated Companion to the Latin Dictionary/Celeres 0 311780 2683534 2671404 2024-11-11T15:38:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683534 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CEL'ERES'''. The old and original name by which the [[Illustrated Companion to the Latin Dictionary/Eques|equestrian order]] at Rome was designated upon its first institution by Romulus, consisting of a body of 300 mounted men, selected from the 300 patrician or burgher families, and thus forming the nucleus of the Roman cavalry. Liv. i. 15. Plin. ''H. N.'' xxxiii. 9. Festus. ''s. v.'' Niebur, ''Hist. Rom.'' vol. i. p. 325. transl. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] o4aozb23s9vq9p6x3jdm31383equ8y4 Illustrated Companion to the Latin Dictionary/Celes 0 311781 2683535 2671405 2024-11-11T15:38:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683535 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CEL'ES''' ({{lang|grc|κέλης}}). A horse for riding, in contradistinction to a carriage or draught horse; but more particularly a race-horse, ridden in the Greek [[Illustrated Companion to the Latin Dictionary/Hippodromus|Hippodrome]], or the Roman [[Illustrated Companion to the Latin Dictionary/Circus|Circus]] (Plin. ''H. N.'' xxxiv. 10.), one of which is shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Celes 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 140.jpg|illustration |caption=Celes/1.1}}, from a stucco [[Illustrated Companion to the Latin Dictionary/Zophorus|frieze]], representing Cupids racing, in the [[Illustrated Companion to the Latin Dictionary/Balineae|baths]] of Pompeii. 2. A boat or vessel of a particular class, in which each [[Illustrated Companion to the Latin Dictionary/Remex|rower]] handled a single [[Illustrated Companion to the Latin Dictionary/Remus|oar]] on his own side, in contradistinction to those in which each man worked a pair, and those in which more than one man laboured at the same oar. The larger descriptions had many oarsmen, and were sometimes fitted with a [[Illustrated Companion to the Latin Dictionary/Malus|mast]] and [[Illustrated Companion to the Latin Dictionary/Velum|sail]], but had no deck, and in consequence of their fleetness were much used by pirates. (Plin. ''H. N.'' vi. 57. Aul. Gell. x. 25. Herod. vii. 94. Thucyd. iv. 9. Scheffer, ''Mil. Nav.'' p. 68.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Celes 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 140.jpg|illustration |caption=Celes/2.1}} here given is from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan, and clearly represents a vessel rowed in the manner described, and therefore belonging to this class. <gallery> File:Celes 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 140.jpg|Celes/1.1 File:Celes 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 140.jpg|Celes/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Horse]] [[Category:Classed Index/The Racecourse and Races]] [[Category:Classed Index/Ships and Boats]] cjkp7livykm7wgmg7nnwtfsijkb6j8m Illustrated Companion to the Latin Dictionary/Celetizontes 0 311782 2683536 2671406 2024-11-11T15:38:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683536 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELETIZON'TES''' ({{lang|grc|κελητίζοντες}}). ''Jockeys'', who rode the race-horses in the Greek [[Illustrated Companion to the Latin Dictionary/Hippodromus|Hippodrome]] (Plin. ''H. N.'' xxxiv. 19. n. 14), as shown in the [[Illustrated Companion to the Latin Dictionary/Celes|last wood-cut but one]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Racecourse and Races]] psph9t6mhiv0hpsnhhajmayodokj1jy Illustrated Companion to the Latin Dictionary/Celeusma 0 311783 2683537 2671407 2024-11-11T15:38:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683537 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELEUS'MA''' ({{lang|grc|κέλευσμα}}). The chaunt or cry given out by the cockswain (''[[Illustrated Companion to the Latin Dictionary/Hortator|hortator]]'', ''[[Illustrated Companion to the Latin Dictionary/Pausarius|pausarius]]'', {{lang|grc|κελευστής}}) to the [[Illustrated Companion to the Latin Dictionary/Remex|rowers]] of the Greek and Roman vessels, in order to aid them in keeping the stroke, and encourage them at their work. (Mart. ''Ep.'' iii. 67. Rutil. i. 370.) The chaunt was sometimes taken up, and sung in chorus by the rowers, and sometimes played upon musical instruments. Auson. ''in Div. Verr.'' 17. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Oarage and Rowers]] 9qc0nizturbwbxyfosfxstwati6rqcy Illustrated Companion to the Latin Dictionary/Cellarius 0 311784 2683538 2671408 2024-11-11T15:38:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683538 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELLA'RIUS'''. A slave belonging to the class of ''[[Illustrated Companion to the Latin Dictionary/Ordinarii|ordinarii]]'', who had charge of the pantry, store-room, and wine cellar (''cella penaria et vinaria''), and whose duty it was to give out the daily rations of meat and drink to the household. Plaut. ''Capt.'' iv. 2. 116. Columell. xi. 1. 19. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] 4zrqi2pcdtwbjxi6anx3gkajfo0vam7 Illustrated Companion to the Latin Dictionary/Cellatio 0 311785 2683539 2671409 2024-11-11T15:38:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683539 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELLA'TIO'''. A suite or set of small rooms, as in the illustration to [[Illustrated Companion to the Latin Dictionary/Cella|CELLA]] 4., which might be applied for any of the ordinary purposes of life, as store-rooms, sleeping-rooms for slaves and inferior dependants, &c. Pet. ''Sat.'' 77. 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Houses]] jsfgvuikx2ru5ikrcur3a58ipihixd0 Illustrated Companion to the Latin Dictionary/Cella 0 311786 2683540 2671410 2024-11-11T15:39:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683540 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELLA'''. A ''cellar''; employed as a general term, denoting a magazine or store-room upon the ''ground-floor'', in which produce of any description was kept; the different kinds of cellars being distinguished by an epithet indicating the nature of the articles contained therein; for example,{{mdash}} 1. ''Cella vinaria'' ({{lang|grc|οἰνεών}}). A wine cellar, forming one of the principal appurtenances to a vineyard. It was a magazine where the produce of the year's vintage was deposited in large earthenware vessels (''[[Illustrated Companion to the Latin Dictionary/Dolium|dolia]]'', ''[[Illustrated Companion to the Latin Dictionary/Seria|seriae]]'', &c.), or in wooden barrels (''[[Illustrated Companion to the Latin Dictionary/Cupa|cupae]]''), after it had been removed from the vats of the press room (''[[Illustrated Companion to the Latin Dictionary/Torcularium|torcularium]]''), where it was made and kept in bulk until sold or bottled; i. e. put into ''[[Illustrated Companion to the Latin Dictionary/Amphora|amphorae]]'', for the purpose of being removed into the ''[[Illustrated Companion to the Latin Dictionary/Apotheca|apotheca]]'' at the top of the house, where it was kept to ripen. (Varro, ''R. R.'' i. 13. 1. Colum. xii. 18. 3. and 4. Pallad. i. 18. Cic. ''Senect.'' 16.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cella 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 141.jpg|illustration |caption=Cella/1.1}}, which is copied from a bas-relief discovered at Augsburgh in the year 1601, shows one of these magazines for wine in the wood, the usual manner of keeping it in the less genial climates (Plin. ''H. N.'' xiv. 27.); and the next example, though not properly a wine grower's cellar, will serve to convey an idea of the plan on which the stores were arranged and disposed when the wine was kept in vessels of earthenware, which was the more usual practice. 2. A wine-merchant's or tavern-keeper's cellar, upon the ''ground''-floor, in which they also kept their wine in bulk, to be drawn off for private sale, or to be supplied in draught to the poorer customers who frequented their houses, and which was thence termed draught wine (''vinum doliare''), or, out of the wood (''de cupa''). (Cic. ''Pis.'' 27.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustrations |imagelink=Media:Cella 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 141.jpg|illustrations |caption=Cella/2.1}} represent a section and ground-plan of a portion of one of these wine-stores, which was discovered in the year 1789, under the walls of Rome. It is divided into three compartments: the first, which is approached by a few steps, consists of a small chamber, ornamented with arabesques and a [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] pavement, but contained nothing when excavated; the second one, which leads out of it, is of the same size, but entirely devoid of ornament, and without any pavement, the floor consisting of a bed of sand, in the centre of which a single row of the largest description of ''dolia'' was found imbedded (''defossa'') two-thirds of their height in the soil; the last of the three is a narrow gallery, six feet high, and eighteen long (of which a portion only is represented in the engraving, but it extends about four times the length of the part here drawn), and like the preceding one is covered at bottom with a deep bed of sand, in which a great number of earthenware vessels, of different forms and sizes, were partially imbedded, like the preceding ones, but ranged in a double row along the walls on both sides, so as to leave a free passage down the middle, as shown by the lowest of the two engravings, which represents the ground-plan of the cellars. 3. ''Cella olearia''. A magazine or cellar attached to an olive ground, in which the oil when made was kept in large earthenware vessels, until disposed of to the oil merchants. Cato, ''R. R.'' iii. 2. Varro, ''R. R.'' i. 11. 2. Columell. i. 6. 9. 4. Any one of a number of small rooms clustered together, such as were constructed for the dormitories of household slaves (Cic. ''Phil.'' ii. 27.); for travellers' sleeping rooms at inns and public houses (Pet. ''Sat.'' 9. 3. and 7.); or the vaults occupied by public prostitutes. (Juv. ''Sat.'' vi. 128. Pet. ''Sat.'' viii. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cella 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|illustration |caption=Cella/4.1}} represents part of a long line of ''cellae'' now remaining amidst the ruins of a Roman villa at Mola di Gaeta; the fronts were originally bricked in, with only an entrance-door in the centre to admit the occupant, and so much of light and air as could be supplied through such an aperture. 5. In like manner, the different chambers which contained the necessary conveniences for hot and cold bathing in a set of [[Illustrated Companion to the Latin Dictionary/Balineae|baths]], were called ''cellae''; because, in fact, they consisted of a number of rooms leading one into another, like the cells of a honey-comb, as is very clearly shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Cella 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|annexed illustration |caption=Cella/5.1}}, from a fresco [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] which decorated an apartment in the [[Illustrated Companion to the Latin Dictionary/Thermae|Thermae]] of Titus at Rome; thus the room containing the warm baths was the ''cella caldaria'', or ''[[Illustrated Companion to the Latin Dictionary/Caldarium|caldarium]]''; the tepid chamber, ''cella tepidaria'', or ''[[Illustrated Companion to the Latin Dictionary/Tepidarium|tepidarium]]''; the one which held the cold bath, ''cella frigidaria'', or ''[[Illustrated Companion to the Latin Dictionary/Frigidarium|frigidarium]]''. Plin. ''Ep.'' v. 6. 25. and 26. Pallad. i. 40. 6. The niches or cells in a dovecote and poultry-house, which are clustered in a similar manner. Columell. viii. 8. 3. Id. viii. 14. 9. 7. ({{lang|grc|σηκός}}) The interior of a [[Illustrated Companion to the Latin Dictionary/Templum|temple]]; i. e. the part enclosed within the four side-walls, but not including the [[Illustrated Companion to the Latin Dictionary/Porticus|portico]] and [[Illustrated Companion to the Latin Dictionary/Peristylium|peristyle]], if there is any. (Cic. ''Phil.'' iii. 12.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cella 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|illustration |caption=Cella/7.1}} represents a ground-plan of the temple of ''Fortuna Virilis'', now remaining at Rome, on which the part within the dark lines is the cella. <gallery> File:Cella 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 141.jpg|Cella/1.1 File:Cella 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 141.jpg|Cella/2.1 File:Cella 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|Cella/4.1 File:Cella 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|Cella/5.1 File:Cella 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 142.jpg|Cella/7.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] [[Category:Classed Index/The Baths]] [[Category:Classed Index/Manufacture of Oil and Wine]] [[Category:Classed Index/Places of Worship]] drt50j51bbk13kpq6kux70n2i4qfat8 Illustrated Companion to the Latin Dictionary/Cellio 0 311787 2683541 2671411 2024-11-11T15:39:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683541 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELL'IO'''. Same as [[Illustrated Companion to the Latin Dictionary/Cellarius|CELLARIUS]]. Inscript. ''ap.'' Grut. 582. 10. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ndrrysb7per9paa02n73cyt51ohbct7 Illustrated Companion to the Latin Dictionary/Cellularius 0 311788 2683542 2671412 2024-11-11T15:39:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683542 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELLULA'RIUS'''. A ''monk'' or ''friar'', so called from the small conventual cells in which the religious orders dwelt. Sidon. ''Epist.'' ix. 9. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 78534ypscfqxx95s3oi8cuhxfho3zv6 Illustrated Companion to the Latin Dictionary/Cellula 0 311789 2683544 2671413 2024-11-11T15:39:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683544 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELL'ULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cella|CELLA]]. Any small or ordinary kind of chamber, such as those described and represented in CELLA 4. Ter. ''Eun.'' ii. 3. 18. Pet. ''Sat.'' 11. 1. 2. The interior of a small shrine or temple, as described in [[Illustrated Companion to the Latin Dictionary/Cella|CELLA]] 7. Pet. ''Sat.'' 136. 9. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] pdo5bgyt6td76oo1kbjuy6qq1o9t7lk Illustrated Companion to the Latin Dictionary/Celox 0 311790 2683545 2671415 2024-11-11T15:39:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683545 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CELOX'''. The same as [[Illustrated Companion to the Latin Dictionary/Celes|CELES]], 2. Ennius, ''ap.'' Isidor. ''Orig.'' xxx. 1. 22. Liv. xxxvii. 27. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] 9en52n0hqad7rswjt4kxjhasa72nu20 Illustrated Companion to the Latin Dictionary/Cenotaphium 0 311791 2683546 2671416 2024-11-11T15:40:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683546 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENOTAPH'IUM''' ({{lang|grc|κενοτάφιον}}). A cenotaph, or honorary tomb erected in memory of a person whose body could not be found, or whose ashes had been deposited elsewhere (Lamprid. ''Alex. Sev.'' 63.); hence also called ''[[Illustrated Companion to the Latin Dictionary/Tumulus|tumulus]] honorarius'' (Suet. ''Claud.'' 1.), and ''inanis'' (Virg. ''Aen.'' iii. 303.), because it was erected merely out of compliment to the deceased, and did not contain any of his remains. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sepulchres]] 6qsuhywn709v5pter5jot9ylnrfhnry Illustrated Companion to the Latin Dictionary/Censor 0 311792 2683547 2671417 2024-11-11T15:40:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683547 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENSOR''' ({{lang|grc|τιμητής}}). A Roman [[Illustrated Companion to the Latin Dictionary/Magistratus|magistrate]] of high rank, whose duty it was to rate the property of the citizens by taking the ''census''; to superintend their conduct and morals; and to punish those who had misconducted themselves, by degradation and removal from their rank, offices, or position in society. Thus he could deprive the senator of his seat in the house; the [[Illustrated Companion to the Latin Dictionary/Eques|knight]], of the horse allowed him at the public expense, which was equivalent to breaking him; or he could remove any citizen from his tribe into one of less influence or rank. (Liv. xxvii. 11. Suet. ''Aug.'' 37. Polyb. vi. 13. 3.) He wore no distinctive badge, nor particular costume, beyond the usual ones of his consular rank; and, consequently, when a censor is represented on coins or medals, he is merely draped in the [[Illustrated Companion to the Latin Dictionary/Toga|toga]], and sitting on a [[Illustrated Companion to the Latin Dictionary/Sella|curule chair]], as in the coin of Claudius in Spanheim, vol. ii. p. 101. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 00ehfx84yz9btn5604mlb3thdcglkhs Illustrated Companion to the Latin Dictionary/Centaurus 0 311793 2683548 2671418 2024-11-11T15:40:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683548 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENTAU'RUS''' ({{lang|grc|κένταυρος}}). A ''centaur''; a savage race of men who dwelt between the mountains Pelion and Ossa in Thessaly, and were destroyed in a war with their neighbours, the Lapithae. But the poets and artists converted them into a fabulous race of monsters, half man and half horse, whence termed ''bimembres'' (Virg. ''Aen.'' viii. 293. Ovid, ''Met.'' xv. 283.); in which form they are represented waging war with the Lapithae in the [[Illustrated Companion to the Latin Dictionary/Metopa|metopes]] of the Parthenon, on the [[Illustrated Companion to the Latin Dictionary/Templum|temples]] of Theseus at Athens, and of Apollo Epicurius near Phigaleia in Arcadia. In the works of Greek art they are represented of both sexes, frequently playing upon some musical instrument, and the figure is always remarkable for the consummate grace and skill with which the artists of that nation contrived to unite the otherwise incongruous parts of two such dissimilar forms. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=figure |imagelink=Media:Centaurus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 143.jpg|figure |caption=Centaurus/1.1}} of a female centaur, as being less common, is selected for the illustration, from a very beautiful relief in bronze, of Greek workmanship, discovered at Pompeii. <gallery> File:Centaurus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 143.jpg|Centaurus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] qgp51a4pd9hpa8dw5mitou55yp8z9nn Illustrated Companion to the Latin Dictionary/Centonarii 0 311795 2683549 2671420 2024-11-11T15:40:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683549 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENTONA'RII'''. ''Piece-brokers'', and persons who made and sold pieces of patchwork, made up from old cast-off garments; the dealing in which formed a regular trade at Rome, where such economical articles were extensively used for blankets to extinguish conflagrations (Ulp. ''Dig.'' 33. 7. 12.); to protect [[Illustrated Companion to the Latin Dictionary/Tentorium|tents]] and military machines against an enemy's missiles (Caes. ''B. C.'' ii. 9.), and other purposes enumerated in [[Illustrated Companion to the Latin Dictionary/Cento|CENTO]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Cloth-workers and Clothiers]] fv2pfd1ah84ub5v0si43bzn7v41pd5h Illustrated Companion to the Latin Dictionary/Cento 0 311796 2683550 2671421 2024-11-11T15:40:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683550 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENTO''' ({{lang|grc|κέντρων}}. Generally, any covering or garment composed of different scraps of cloth sewed together, like patch-work, which the ancients employed as clothing for their slaves (Cato, ''R. R.'' 59. Columell. i. 8. 9.), as counterpanes for beds (Macrob. ''Sat.'' i. 6.), or other common purposes; whence the same name was also given to a poem made up of verses or scraps collected from different authors, like the ''Cento Nuptialis'' of Ausonius. 2. Specially, a cloth of the same common description; used as a saddle-cloth under the saddle of a beast of burden, to prevent it from galling the back, as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cento 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|annexed example |caption=Cento/2.1}} from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Herculaneum. Veget. ''Vet.'' ii. 59. 2. <gallery> File:Cento 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|Cento/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] [[Category:Classed Index/Saddles and Trappings]] ddxof1qomslc2l39ajdmateu4l6txfj Illustrated Companion to the Latin Dictionary/Centunculus 0 311797 2683551 2671422 2024-11-11T15:40:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683551 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENTUN'CULUS'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cento|CENTO]]; and applied in the same senses as there mentioned (Apul. ''Met.'' i. p. 5. Liv. vii. 4. Edict. Dioclet. p. 21.); and from a passage of Apuleius (''Apol.'' p. 422. ''mimi centunculo''), the same word is also believed to indicate a dress of chequered pattern, like what is now called ''harlequin's'', which is undoubtedly of great antiquity; for in the Museum at Naples, there is preserved a fictile vase on which Bacchus is represented in a burlesque character, and draped precisely like our modern harlequin. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Outward Apparel]] hz9228itg8nui94dammh4hob5z7lnwq Illustrated Companion to the Latin Dictionary/Centurio 0 311798 2683552 2671423 2024-11-11T15:41:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683552 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CENTU'RIO''' ({{lang|grc|ἑκατοντάρχης}}). A ''centurion''; an officer in the Roman army, of lower rank than the [[Illustrated Companion to the Latin Dictionary/Tribunus|tribunes]], by whom he was appointed. His post on the field of battle was immediately in front of the [[Illustrated Companion to the Latin Dictionary/Aquila|eagle]] (Veget. ''Mil.'' ii. 8.); and the distinguishing badge of his rank was a rod (''[[Illustrated Companion to the Latin Dictionary/Vitis|vitis]]''), with which he used to correct his men when refractory or negligent of their duties. (Plin. ''H. N.'' xiv. 3.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustrations |imagelink=Media:Centurio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|illustrations |caption=Centurio/1.1}} present the figures of two centurions, the one on the left-hand of the reader, from a sepulchral bas-relief, with the inscription {{Illustrated Companion to the Latin Dictionary/Inscription|text=QUINTUS PUBLIUS FESTUS. CENTUR. LEG. XI.}}; he has his rod in the right hand, is likewise decorated with ''[[Illustrated Companion to the Latin Dictionary/Phalerae|phalerae]]'', and wears greaves (''[[Illustrated Companion to the Latin Dictionary/Ocrea|ocreae]]''), as the Roman soldiers did in early times; the other shows a centurion of the age of Trajan, from a bas-relief formerly belonging to the [[Illustrated Companion to the Latin Dictionary/Arcus|triumphal arch]] of that emperor, but now inserted in the arch of Constantine; he has his [[Illustrated Companion to the Latin Dictionary/Galea|helmet]] on, the rod in his right hand, and in the original composition the bearer of the eagle (''[[Illustrated Companion to the Latin Dictionary/Aquilifer|aquilifer]]'') stands by his side. <gallery> File:Centurio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|Centurio/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Officers of the Army]] tnzb50laxggl4e4x5z9726c3yakp1mq Illustrated Companion to the Latin Dictionary/Cepotaphium 0 311799 2683553 2671424 2024-11-11T15:41:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683553 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CEPOTAPH'IUM''' ({{lang|grc|κηποτάφιον}}). A tomb in a garden; or a garden to which a degree of religious veneration became attached, in consequence of its having a [[Illustrated Companion to the Latin Dictionary/Sepulcrum|sepulchre]] erected within it. Inscript. ''ap.'' Fabretti, p. 80. n. 9. Id. p. 115. n. 293. Compare D. Joann. Evang. xix. 41. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sepulchres]] cjprczlmikjide3vy8yzlqievkev14p Illustrated Companion to the Latin Dictionary/Cera 0 311800 2683554 2671425 2024-11-11T15:41:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683554 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CE'RA'''. Wax; and thence used to designate things made of wax; as the waxen masks or likenesses of a man's ancestors, which the Roman families of distinction preserved in cases placed round the [[Illustrated Companion to the Latin Dictionary/Atrium|atrium]] (Ovid. ''Fast.'' i. 591. Juv. viii. 19.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cera 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|example |caption=Cera/1.1}}, from a sepulchral bas-relief, which represents a wife bewailing the death of her husband, whose likeness is placed in a small case against the wall of the apartment where the scene is laid. 2. A set of [[Illustrated Companion to the Latin Dictionary/Tabella|tablets]] for writing on with the style (''[[Illustrated Companion to the Latin Dictionary/Stylus|stylus]]''), made of thin slabs or leaves of wood, coated with wax, and having a raised margin all round to preserve the contents from friction. They were made of different sizes, and varied in the number of their leaves, whence the word in this sense is applied in the plural (Quint. x. 3. 31. and 32. Juv. i. 63.), and the tablets themselves are distinguished by the number of leaves they contained; as ''cerae duplices'', a tablet with two slabs only, like the bottom figure on the left-hand of the engraving; ''cerae triplices'' (Mart. ''Ep.'' xiv. 6.), a tablet containing three leaves, one between the two outsides, like the top figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Cera 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 145.jpg|engraving |caption=Cera/2.1}}; ''cerae quintuplices'' (Mart. ''Ep.'' xiv. 4.), one with five leaves, or three centre ones and two outsides, like the right-hand figure at the bottom of the wood-cut, all of which examples are copied from [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]] at Pompeii. When the singular number is used, as ''prima, secunda, extrema cera'' (Hor. ''Sat.'' ii. 5. 53. Cic. ''Verr.'' ii. 1. 36. Suet. ''Jul.'' 83.), it indicates the first, second, or last page of the tablets. <gallery> File:Cera 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 144.jpg|Cera/1.1 File:Cera 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 145.jpg|Cera/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Tablets]] 9sfvthk8bkvgdlepy3l6tr2pgph3qzd Illustrated Companion to the Latin Dictionary/Ceraula 0 311801 2683555 2671426 2024-11-11T15:41:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683555 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERAU'LA''' ({{lang|grc|κεραύλης}}). Properly a Greek word Latinized, and corresponding with the Roman [[Illustrated Companion to the Latin Dictionary/Cornicen|CORNICEN]]. Apul. ''Met.'' p. 171. ''Ceraula doctissimus, qui cornu canens adambulabat.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 8sx8r2t7drti7qte0kp5sv84ynj631r Illustrated Companion to the Latin Dictionary/Cerberus 0 311802 2683556 2671427 2024-11-11T15:41:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683556 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CER'BERUS''' ({{lang|grc|Κέρβερος}}). The dog which kept watch at the entrance to the nether world; a monster fabled to have sprung from Typhaon and Echidna, and to have been dragged upon earth by Hercules as the last and most difficult of his twelve labours. In reality Cerberus was a dog belonging to the king of the Molossians, whose country produced the finest breed of dogs known to the ancients, and which are believed to be represented by the marble statues now preserved in the Vatican, exhibiting two dogs of very powerful frames, with long hair upon the neck and shoulders like the mane of a lion. The poets metamorphosed these hairs into snakes (Hor. ''Od.'' ii. 85.), and, to increase the horror, some gave the animal a hundred heads (Hor. ''Od.'' ii. 34.), others fifty (Hesiod. ''Theogn.'' 312., though in verse 771. he has but one), and others limited the number to three (Soph. ''Trachin.'' 1109.), the centre one being that of a lion, with the head of a wolf on one side, and of an ordinary dog on the other (Macrob. ''Sat.'' i. 20.). This is the usual type under which he is mostly portrayed by the [[Illustrated Companion to the Latin Dictionary/Pictor|painters]] and [[Illustrated Companion to the Latin Dictionary/Scalptor|sculptors]] of antiquity (Mus. Pio-Clem. tom. ii. tav. 1. Bartoli, ''Lucerne'', part 2. tav. 7. Cod. Vat. &c.); though examples are not wanting in which the ''fabulous'' is made subordinate to the ''real'' character of the monster, as in a group of Hercules and Cerberus in the Vatican (Mus. Pio-Clem. ii. 8.), where the leonine head and mane of the Molossian dog is strongly marked, and made to predominate entirely over the other two, which are executed upon a much smaller scale, and, as it were, rather indicated than developed. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] suotr73a9rpn9dj3j30oqa2aaldczkq Illustrated Companion to the Latin Dictionary/Cercurus 0 311804 2683557 2671430 2024-11-11T15:42:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683557 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERCU'RUS''' ({{lang|grc|κέρκουρος}} or {{lang|grc|κερκοῦρος}}). An open vessel, invented by the Cyprians, propelled by [[Illustrated Companion to the Latin Dictionary/Remus|oars]], fast in its movement and used for the transport of merchandize, as well as in warfare. (Liv. xxxiii. 19. Lucil. ''Sat.'' viii. 3 ed. Gerlach. Plaut. ''Merc.'' i. 1. 86. Plin. ''H. N.'' vii. 57. Herod. vii. 97.) Its characteristic properties are nowhere described; but Scheffer (''Mil. Nav.'' ii. 2. p. 75.) is of opinion that the [[Illustrated Companion to the Latin Dictionary/Remigium|oarage]], instead of running the whole length of the vessel, only ranged from the [[Illustrated Companion to the Latin Dictionary/Prora|prow]] to about midship, so that the after part would serve as a hold for the freight in the manner represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Cercurus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|annexed illustration |caption=Cercurus/1.1}}, copied by Panvinus (''de Lud. Circen.'' ii. 11.) from a bronze medal, which, if that notion be correct, will afford a model of the vessel in question. <gallery> File:Cercurus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|Cercurus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ships and Boats]] 21cldnsdy2eobwrzbb2zki4yukpxn2n Illustrated Companion to the Latin Dictionary/Cerdo 0 311805 2683558 2671431 2024-11-11T15:42:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683558 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERDO'''. A workman of inferior description, or who belonged to the lowest class of operatives (Juv. iv. 153. Pers. iv. 51.): the particular trade which he practised is likewise designated by the addition of another substantive as ''sutor cerdo'' (Mart. ''Ep.'' iii. 59.), a ''cobbler''; ''cerdo faber'' (Inscript. ''ap.'' Spon. ''Miscell. Erudit. Antiq.'' p. 221.), a journeyman [[Illustrated Companion to the Latin Dictionary/Ferrarius|smith]]; and so on for other trades. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Trades and Industrial Occupations]] qh58jkpnjc13xmf1xj2th52gf5qbiwv Illustrated Companion to the Latin Dictionary/Cereus 0 311806 2683559 2671433 2024-11-11T15:42:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683559 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CE'REUS'''. A wax candle, made with the pith of a rush coated with wax; also a [[Illustrated Companion to the Latin Dictionary/Fax|torch]] made of the fibres of papyrus twisted together, and covered with wax. Cic. ''Off.'' iii. 20. Plaut. ''Curc.'' i. 1. 9. Val. Max. iii. 6. 4. and [[Illustrated Companion to the Latin Dictionary/Candela|CANDELA]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Lights and Lighting]] iqv72z7jxzb01j162dhf5u29u91jmsh Illustrated Companion to the Latin Dictionary/Ceriolare 0 311807 2683560 2671434 2024-11-11T15:42:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683560 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERIOLA'RE'''. A stand or holder for [[Illustrated Companion to the Latin Dictionary/Cereus|wax-candles]] and [[Illustrated Companion to the Latin Dictionary/Fax|torches]], similar to the example engraved at p. 107 (''s.'' [[Illustrated Companion to the Latin Dictionary/Candelabrum|CANDELABRUM]], 1.); but utensils of this description were also made in a variety of fanciful forms and patterns according to the taste of the artist who designed them, for one is mentioned in an inscription (''ap.'' Grut. 175. 4.) of bronze, with the figure of Cupid holding a ''[[Illustrated Companion to the Latin Dictionary/Calathus|calathus]]''. Compare Inscript. ''ap.'' Maffei, ''Mus. Veron.'' p. 83. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 3atpwgyyco9ff81s6y22zfqfp1jn8sl Illustrated Companion to the Latin Dictionary/Cernuus 0 311808 2683561 2671435 2024-11-11T15:42:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683561 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CER'NUUS''' ({{lang|grc|κυβιστητήρ}}). Literally, with the face turned down towards the ground; hence a ''tumbler'', or one who entertains the public by feasts of jumping, throwing summersets in the air, falling head over heels, walking with his face downwards, and other similar exhibitions, such as we still see practised in our [[Illustrated Companion to the Latin Dictionary/Via|streets]] and fairs. (Lucil. ''Sat.'' iii. 20. Serv. ''ad'' Virg. ''Aen.'' x. 894.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cernuus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|illustration |caption=Cernuus/1.1}} represents one of these tumblers, from the collection in the Collegio Romano. (Caylus, iii. 74.) 2. Amongst the Greeks feats of this nature were frequently exhibited by females, who were introduced with the dancing and singing girls, to amuse the guests at an entertainment, and whose skill and suppleness of body were really extraordinary. One of their favourite exhibitions consisted in making a summerset backwards, between a number of swords or knives stuck in the ground, at small intervals from one another, with their points upwards, as represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=following illustration |imagelink=Media:Cernuus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|following illustration |caption=Cernuus/2.1}}, from a Greek fictile vase; to perform this feast was termed {{lang|grc|ξίφη}} or {{lang|grc|εἰς μαχαίρας κυβιστᾶν}}. Plat. ''Symp.'' p. 190. A. Xen. ''Symp.'' ii. 11. <gallery> File:Cernuus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|Cernuus/1.1 File:Cernuus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 146.jpg|Cernuus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feats of Strength or Dexterity]] m1ctetx7fy7wsqw3d19coqlnavtxzq6 Illustrated Companion to the Latin Dictionary/Ceroma 0 311809 2683562 2671436 2024-11-11T15:43:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683562 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERO'MA''' ({{lang|grc|κήρωμα}}). Properly, an unguent, made of oil and wax compounded together, with which the bodies of wrestlers were anointed previously to being rubbed over with fine sand (Mart. ''Ep.'' vii. 32.); whence the same term is also used to designate the chamber in which this operation was performed. Plin. ''H. N.'' xxxv. 2. Senec. ''Brev. Vit.'' 12. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Gymnasium and Palaestra]] phhunqyk4fp6h6qu00k9gh2jstahrg6 Illustrated Companion to the Latin Dictionary/Ceruchi 0 311810 2683563 2671437 2024-11-11T15:43:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683563 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERU'CHI''' ({{lang|grc|κεροῦχοι}}). The ropes which run from each arm of the [[Illustrated Companion to the Latin Dictionary/Antenna|sail-yard]] to the top of the [[Illustrated Companion to the Latin Dictionary/Malus|mast]], corresponding with what are now called in nautical language "''the lifts.''" (Lucan. viii. 177. Id. x. 494.) Their object was to keep the yard in a level and horizontal position upon the mast, which it could not preserve without a support of this nature; and the largest class of vessels, which had a yard of great length and weight, were furnished with a double pair of lifts, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Ceruchi 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|example |caption=Ceruchi/1.1}}, from the Vatican Virgil; while the smaller and ordinary sized had only one. <gallery> File:Ceruchi 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|Ceruchi/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Rigging]] hjvy0xouz1qdwshiuqr1xngm24cyni7 Illustrated Companion to the Latin Dictionary/Cervical 0 311811 2683564 2671439 2024-11-11T15:43:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683564 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERVI'CAL''' ({{lang|grc|προσκεφάλαιον, ὑπαυχένιον}}). A bolster, cushion, or squab for supporting the back of the head and neck on a bed or dining couch. (Suet. ''Nero'', 6. Mart. xiv. 146.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cervical 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|illustration |caption=Cervical/1.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii. <gallery> File:Cervical 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|Cervical/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Beds and Couches]] 74oxkzv5jmxvftuwsl4vaebrmkf06hu Illustrated Companion to the Latin Dictionary/Cervisia 0 311812 2683565 2671440 2024-11-11T15:43:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683565 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERVI'SIA''' or '''CEREVE'SIA'''. A beverage extracted from barley, like our ''beer'' or ''ale''; which was the ordinary drink of the Gauls. (Plin. ''H. N.'' xxii. 82.) The same name, according to Servius (''ad'' Virg. ''Georg.'' iii. 379.), was also given to a beverage extracted from the fruit of the service tree, which would correspond more closely with our ''cider''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 7to1osjglgob4hmdisj9toxvvg2bvz2 Illustrated Companion to the Latin Dictionary/Cervi 0 311813 2683566 2671441 2024-11-11T15:43:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683566 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERVI'''. In military language, large branches of trees, having the smaller ones left on, and shortened at a certain distance from the stock, so as to present the appearance of a stag's horn. (Varro, ''L. L.'' v. 117.) They were stuck in the ground, to impede the advance of an enemy's column, a charge of cavalry over a plain, which afforded no natural obstructions (Sil. Ital. x. 412. Liv. xliv. 11.), and as a palisade or protection to any vulnerable or important position. Caes. ''B. G.'' vii. 72. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Fortification]] 0kcl9ve5pn1x04dux7es6wm9gqx2jct Illustrated Companion to the Latin Dictionary/Ceryceum 0 311814 2683567 2671442 2024-11-11T15:43:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683567 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERYCE'UM''' ({{lang|grc|κηρύκειον}}). A Greek word Latinised; same as [[Illustrated Companion to the Latin Dictionary/Caduceus|CADUCEUS]]. Martian. Capell. 4. p. 95. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] t23g1u7c6gq8px1rfedx28j3016szcw Illustrated Companion to the Latin Dictionary/Ceryx 0 311815 2683568 2671444 2024-11-11T15:44:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683568 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CERYX''' ({{lang|grc|κήρυξ}}). A Greek word, used in a Latin form by Seneca (''Tranquill.'' 3.); ''a Greek herald, marshal'', or ''pursuivant'', who occupied a similar position amongst that people, and performed the same sort of duties as the ''[[Illustrated Companion to the Latin Dictionary/Fetiales|Fetiales]]'' and ''[[Illustrated Companion to the Latin Dictionary/Legatus|Legati]]'' of the Romans. His distinctive badge was a wand ({{lang|grc|κηρύκειον}}, ''[[Illustrated Companion to the Latin Dictionary/Caduceus|caduceus]]''); his person was held sacred and inviolable; and his most honourable employment consisted in carrying flags of truce between conflicting armies, and messages between hostile states, a duty which the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Ceryx 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|illustration |caption=Ceryx/1.1}}, from a fictile vase, is represented as in the act of commencing. He is armed with sword and [[Illustrated Companion to the Latin Dictionary/Hasta|spear]]; has the herald's wand in his right hand; and stands before a burning [[Illustrated Companion to the Latin Dictionary/Ara|altar]], upon which he has just sacrificed, preparatory to starting on his journey; the sentiment of departure being indicated, according to the customary practice of the Greek artists, by certain conventional signs, such as the travelling boots, the [[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]] thrown loosely over the arm, and the hat slung behind his back. Besides this, in his character of marshal and pursuivant, the ''Ceryx'' possessed the power of interposing between and separating combatants, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Ceryx 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 148.jpg|annexed example |caption=Ceryx/1.2}}, also from a fictile vase; was authorized to summon the assemblies of the people, and keep order in them, and to superintend the arrangements at a sacrifice, as well as at public and private festivals. 2. A ''public crier''; more closely allied to the Roman ''[[Illustrated Companion to the Latin Dictionary/Praeco|praeco]]''; whose business it was to make proclamations in the public assemblies (Aristoph. ''Ach.'' 42. seq.), and to enjoin silence by sound of trumpet at the national games, whilst the solemn eulogium ({{lang|grc|κήρυγμα}}) was pronounced upon the victor (Fabri. ''Agon.'' ii. 3. Mosebach ''de Praecon. Vet.'' § 32{{mdash}}34.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=following figure |imagelink=Media:Ceryx 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 148.jpg|following figure |caption=Ceryx/2.1}}, from a Greek marble in the Vatican; he is represented as just beginning to sound his trumpet by the side of the conqueror, who is in the act of placing on his head the [[Illustrated Companion to the Latin Dictionary/Corona|crown]] which he has just received from the president ({{lang|grc|ἀγωνοθέτης}}), whilst on the other side of the composition a pair of [[Illustrated Companion to the Latin Dictionary/Pancratium|Pancratiastae]] are contending. <gallery> File:Ceryx 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 147.jpg|Ceryx/1.1 File:Ceryx 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 148.jpg|Ceryx/1.2 File:Ceryx 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 148.jpg|Ceryx/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] ak7px3ywmoa6ff9qyjpx90zz5rh713u Illustrated Companion to the Latin Dictionary/Cesticillus 0 311816 2683569 2671445 2024-11-11T15:44:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683569 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CESTICIL'LUS'''. A porter's knot, for carrying burdens on the head. Festus, ''s. v.'' Compare [[Illustrated Companion to the Latin Dictionary/Arculum|ARCULUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 83tazb82h4iwod13icw3cfi872gb1g7 Illustrated Companion to the Latin Dictionary/Cestrosphendone 0 311817 2683570 2671446 2024-11-11T15:44:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683570 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CESTROSPHEN'DONE''' ({{lang|grc|κεστροσφενδόνη}}). A weapon of warfare, first employed by the soldiers of Perseus in the Macedonian war, consisting in a short dart, the head of which was two spans broad, affixed to a wooden stock of the thickness of a man's finger, and half a cubit in length, and furnished with three short wooden wings, similar to the feathers of an [[Illustrated Companion to the Latin Dictionary/Sagitta|arrow]]. It was discharged from a [[Illustrated Companion to the Latin Dictionary/Funda|sling]]. Liv. xlii. 65. Polyb. xxvii. 9. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Bows, Slings, etc.]] 9qtei92n2bzvu38fm7ag2h55jsox1aw Illustrated Companion to the Latin Dictionary/Cestrum 0 311818 2683571 2671447 2024-11-11T15:44:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683571 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CESTRUM''' ({{lang|grc|κέστρον}}). A sort of graver or etching needle employed in the process of [[Illustrated Companion to the Latin Dictionary/Encaustica|encaustic painting]] on ivory. It is supposed that the instrument was heated by fire, and that the traits to be delineated were burnt into the tablet with its point, and then filled in with liquid wax; but the whole subject of encaustic painting, and the manner in which the operation were conducted, is very obscure and uncertain. Plin. ''H. N.'' xxxxv. 41. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sculpture, etc.]] n0ejajegpby22ogqz7huzf5kv1obgcy Illustrated Companion to the Latin Dictionary/Cestus 0 311819 2683572 2671448 2024-11-11T15:44:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683572 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CESTUS''' ({{lang|grc|κεστός}}, sc. {{lang|grc|ἱμάς}}). In a general sense, any band or tie (Varro, ''R. R.'' i. 8. 6.); but the word is properly a Greek adjective, meaning ''embroidered'', whence it is more frequently used in a special sense to designate the ''girdle of Venus'', upon which a representation of the passions, desires, joys, and pains of love was embroidered (Hom. ''Il.'' xiv. 214. Mart. ''Ep.'' vi. 13. Id. xiv. 206. and 207.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cestus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 149.jpg|illustration |caption=Cestus/1.1}} introduced is from a bas-relief of the Museo Chiaramonti, representing a figure of Venus draped in the archaic style; consequently from some very early type, which makes it trustworthy. It will be perceived, that the ''cestus'' on this figure is worn lower down than the ordinary female's girdle (''[[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]]'', 1.), and higher up than the young women's zone (''[[Illustrated Companion to the Latin Dictionary/Zona|zona]]'', or ''[[Illustrated Companion to the Latin Dictionary/Cingulum|cingulum]]'', 2.), which may account for the uncertainty prevailing amongst scholars respecting the proper place which the ''cestus'' occupied on the person, and for the apparent indecision of the passages, which have led some to place it over the loins (as Winkelmann), and others immediately under the bosom (as Heyne and Visconti); whereas in the example, it is really placed in an intermediate position between the two. 2. The glove worn by boxers, more commonly written [[Illustrated Companion to the Latin Dictionary/Caestus|CAESTUS]], which see. <gallery> File:Cestus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 149.jpg|Cestus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Cinctures]] 1wl4mp4jeg0q377osyhmqyb9ge303rm Illustrated Companion to the Latin Dictionary/Cetariae 0 311820 2683573 2671449 2024-11-11T15:45:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683573 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CETA'RIAE''' or '''CETA'RIA'''. Shallow places or fishing grounds upon a coast, frequented by large fish at certain periods of the year, when they are taken by the fishermen; such as the places in the Mediterranean, where the tunny fish is now caught. Hor. ''Sat.'' ii. 5. 44. Plin. ''H. N.'' ix. 19. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 56ervmtu7ey7pk6qu6g227z537vui3j Illustrated Companion to the Latin Dictionary/Cetarii 0 311821 2683574 2671451 2024-11-11T15:45:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683574 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CETA'RII'''. A class of fishermen, who took the larger kinds of fish, such as ''tunnies'', upon the ''[[Illustrated Companion to the Latin Dictionary/Cetariae|cetariae]]'' (Varro, ''ap.'' Non. ''s. v.'' p. 49.), salted them down, and sold them in shops belonging to themselves. Columell. viii. 17. 12. Terent. ''Eun.'' ii. 2. 26. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 4v00lc4tcmk2dxd9tmpp0vw9rng0msv Illustrated Companion to the Latin Dictionary/Cetratus 0 311822 2683575 2671452 2024-11-11T15:45:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683575 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CETRA'TUS'''. One who bears the small round target, called ''[[Illustrated Companion to the Latin Dictionary/Cetra|cetra]]'', which was characteristic of some barbarous nations, but not of the Romans. Caes. ''B. C.'' i. 70. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 2vbatncldw2topwkqiwzu2ev7kqafx3 Illustrated Companion to the Latin Dictionary/Cetra 0 311823 2683576 2671453 2024-11-11T15:45:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683576 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CETRA'''. A small round shield (Varro, ''ap.'' Non. ''s. v.'' p. 555. and p. 82.), covered with hide (Serv. ''ad'' Virg. ''Aen.'' vii. 732.); chiefly employed by the natives of Africa, Spain, and ancient Britain (Tac. ''Agr.'' 36.), the form and character of which is believed to be preserved in the ''target'' of the Scottish highlanders. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Shields]] qfxwxv40aggvsa4xinssopzdowsbs6k Illustrated Companion to the Latin Dictionary/Chalatorius 0 311824 2683577 2671454 2024-11-11T15:45:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683577 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHALATO'RIUS''', sc. ''funis'' ({{lang|grc|ἐπίτονος}}, sc. {{lang|grc|ἰμάς}}). The rope by which a [[Illustrated Companion to the Latin Dictionary/Antenna|sail-yard]] is raised and lowered on the [[Illustrated Companion to the Latin Dictionary/Malus|mast]], corresponding with the ''halyard'' of modern nautical language. It was fastened on the middle of the yard, and run up through a block affixed to the mast, from which the end descended to the deck, where it was worked by the sailors. (Veget. ''Mil.'' iv. 15.) It is probably derived from {{lang|grc|χαλάω}}, to slacken, loosen, or let down; and allied to the {{lang|grc|χαλινός}}, or bridle of the Greek sailors. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Rigging]] dghv9gwird2wtmwl6xqac61przvl3ar Illustrated Companion to the Latin Dictionary/Chalcidicum 0 311825 2683578 2671455 2024-11-11T15:45:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683578 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHALCID'ICUM''' ({{lang|grc|Χαλκιδικόν}}). A large, low, and deep porch, covered with its own roof, supported on [[Illustrated Companion to the Latin Dictionary/Parastas|pilasters]], and appended to the entrance front of a building, where it protects the principal doorway, and forms a grand entrance to the whole edifice (Becchi, ''del Calcidico e della Cripta di Eumachia'', § 21{{mdash}}43.), in the manner represented by the following {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Chalcidicum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 150.jpg|engraving |caption=Chalcidicum/1.1}}, which represents a stucture of similar character, now remaining in front of the very ancient church of S. Giorgio in Velabro at Rome, believed to occupy the site of the original [[Illustrated Companion to the Latin Dictionary/Basilica|Basilica]] Semproniana in the [[Illustrated Companion to the Latin Dictionary/Forum|Forum]] Boarium. Structures of this kind received their name from the city of Chalcis (Festus, ''s. v.''), where, it may be presumed, they were first introduced, or of the most frequent occurrence; and they were added on to private as well as public edifices, not merely as an ornament to the façade, but for the purpose of affording shelter to persons whilst waiting on the outside for their turn to be admitted, or who transacted their business under them; to the palaces of kings and great personages (Hygin. ''Fab.'' 184. Auson. ''Perioch. Odyss.'' 23. Procop. ''de Aedific. Justin.'' i. 10.); to the basilicae, courts of justice, and merchants' changes (Vitruv. v. 1.), where they could serve to contain the articles of merchandize, the sale of which was negotiated in the interior; to the [[Illustrated Companion to the Latin Dictionary/Curia|curia]], the town-hall, and senate-house (Dion Cass. li. 22. August. ''Mon. Ancyran.'' ''ap.'' Grut. p 232. 4.), perhaps for the reception of the slaves awaiting their masters, and of the people naturally congregating about such places for curiosity or business. The external character and appearance of these appendages is sufficiently indicated by the preceding wood-cut; and their general plan, with reference to the rest of the edifice, by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=next one |imagelink=Media:Chalcidicum 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 150.jpg|next one |caption=Chalcidicum/1.2}}, which represents the ground-plan of an extensive building at Pompeii, constructed by the priestess Eumachia, consisting of an enclosed gallery (''[[Illustrated Companion to the Latin Dictionary/Crypta|crypta]]'', {{Illustrated Companion to the Latin Dictionary/Inscription|text=A}}), an open one (''[[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]'', {{Illustrated Companion to the Latin Dictionary/Inscription|text=B}}) adjoining, which encloses a courtyard or area ({{Illustrated Companion to the Latin Dictionary/Inscription|text=C}}) in the centre; the whole being covered by a grand entrance, fronting the [[Illustrated Companion to the Latin Dictionary/Forum|forum]], with the name {{Illustrated Companion to the Latin Dictionary/Inscription|text=CHALCIDICUM}} inscribed upon a slab of marble affixed to the wall. <gallery> File:Chalcidicum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 150.jpg|Chalcidicum/1.1 File:Chalcidicum 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 150.jpg|Chalcidicum/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] dgd8378qf09w23ms2397y70etvfb7rq Illustrated Companion to the Latin Dictionary/Chamulchus 0 311826 2683579 2671456 2024-11-11T15:46:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683579 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHAMUL'CHUS''' ({{lang|grc|χαμουλκός}}). A sort of dray employed in the transport of very weighty substances, such as large blocks of marble, [[Illustrated Companion to the Latin Dictionary/Columna|columns]], [[Illustrated Companion to the Latin Dictionary/Obeliscus|obelisks]], &c., which lay low upon the ground (whence the name, from {{lang|grc|χαμαὶ}} the ground, and {{lang|grc|ἕλκω}}, to draw), and probably resembled those now used for similar purposes. Ammian. xvii. 4. 14. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Carts]] 4uhy1xd7651vqsci5cna4i8k2l3fwjc Illustrated Companion to the Latin Dictionary/Character 0 311827 2683580 2671457 2024-11-11T15:46:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683580 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHARAC'TER''' ({{lang|grc|χαρακτήρ}}). In general, any sign, note, or mark, stamped, engraved, or otherwise impressed upon any substance, like the device upon coins, seals, &c.; and in a more special sense, the brand or mark burnt into the flanks of oxen, sheep, or horses, in order to distinguish the breed, certify the ownership, or for other purposes of a similar nature, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Character 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 151.jpg|example |caption=Character/1.1}}, which shows the brand upon a race-horse, from a small antique bronze. Columell. xi. 2. 14. 2. The iron instrument with which such marks were made. Isidor. ''Orig.'' xx. 7. <gallery> File:Character 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 151.jpg|Character/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/The Horse]] 3ccq8gi0j6elnv9arufvwgzogxvy5e4 Illustrated Companion to the Latin Dictionary/Charistia 0 311828 2683581 2671458 2024-11-11T15:46:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683581 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHARIS'TIA''' ({{lang|grc|Χαρίστια}} or {{lang|grc|Χαριτήσια}}). The feast of the Charities; a family banquet, to which none but relatives or members of the same family were invited, and the object of which was to reconcile any differences which might have arisen amongst them, and to preserve the kindred united and friendly with one another. (Val. Max. ii. 1. 8. Ov. ''Fast.'' ii. 617.) It was celebrated on the 19th of February (viii. Cal. Mart.), which was thence termed the "kinsmen's day"{{mdash}}''lux propinquorum''. Mart. ''Ep.'' ix. 56. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 340ydsopdgl2tkwqp6d0digbfyk6gym Illustrated Companion to the Latin Dictionary/Charistion 0 311829 2683582 2671459 2024-11-11T15:46:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683582 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHARIS'TION''' ({{lang|grc|χαριστίων}}). An instrument for weighing; but of what precise character, or in what it differed from the balance (''[[Illustrated Companion to the Latin Dictionary/Libra|libra]]'') and steelyard (''[[Illustrated Companion to the Latin Dictionary/Statera|statera]]'') is not ascertained. Inscript. ''ap.'' Don. cl. 2. n. 67. Not. Tires. p. 164. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 3nj9yr4bz6nsr96wi649rwmo8w5xxsg Illustrated Companion to the Latin Dictionary/Charta 0 311830 2683583 2671460 2024-11-11T15:46:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683583 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHARTA''' ({{lang|grc|χάρτης}}). Writing-paper, made from layers of the papyrus, of which eight different qualities are enumerated by Pliny (''H. N.'' xiii. 23.):{{mdash}}1. ''Augustana'', subsequently called ''Claudiana'', the best quality; 2. ''Liviana'', the next best; 3. ''Hieratica'', originally the best, and the same as ''charta regia'' of Catullus (xix. 16.); 4, 5, 6. ''Amphitheatrica, Saitica, Leneotica'', inferior kinds, named after the places where they were respectively manufactured. 7. ''Fanniana'', made at Rome, and named from its maker Fannius; 8. ''Emporetica'', coarse paper, not used for writing, but only for packing ''merchandize'', whence its name. To these may be added, 9. ''charta dentata'', the surface of which was smoothed and polished by rubbing over with the tooth of some animal, to procure a glossy face for the [[Illustrated Companion to the Latin Dictionary/Arundo|pen]] to glide over, like our "hot-pressed" paper (Cic. ''Q. Fr.'' ii. 15. Plin. ''H. N.'' xiii. 25.); and 10. ''charta bibula'', a transparent, and spongy sort of paper, which let the ink run, and showed the letters through. Plin. ''Ep.'' viii. 15. 2. Compare Plin. ''H. N.'' xiii. 24. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Paper and Writing Materials]] qnlvnuqfxs21r5840ygxlyaarx90556 Illustrated Companion to the Latin Dictionary/Chele 0 311831 2683584 2671461 2024-11-11T15:47:03Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683584 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHE'LE''' ({{lang|grc|χηλή}}). Properly, a Greek word, which signifies a cloven foot; a pair of crooked and serrated claws, like those of a crab; the talons of a bird; or the claw of a wild beast; whence in that language, it is employed to designate several different instruments, possessing in their forms or manner of usage a resemblance to any one of these natural objects: as a netting needle; a breakwater to protect the mouth of a harbour, when made in the form of a claw set open (see the plan of the port at Ostia, s. [[Illustrated Companion to the Latin Dictionary/Portus|PORTUS]], letter {{Illustrated Companion to the Latin Dictionary/Inscription|text=K}}); a pair of pincers or pliers, with bent arms like claws, &c. By the Romans, for a similar reason, the same name is given to a particular part of some military engines, such as the ''[[Illustrated Companion to the Latin Dictionary/Ballista|ballista]]'' and ''[[Illustrated Companion to the Latin Dictionary/Scorpio|scorpio]]'', which was a sort of claw, or nipper, made to open and seize upon the trigger or chord of the machine whilst it was being drawn back to produce the rebound which discharged the missile. Vitruv. x. 11. 7. Id. x. 10. 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Machines and Engines of War]] cwamkpl8ui17nephnhjdvge83x20a7t Illustrated Companion to the Latin Dictionary/Chelonium 0 311832 2683585 2671462 2024-11-11T15:47:14Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683585 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHELO'NIUM''' ({{lang|grc|χελώνιον}}). A bracket or collar affixed to the uprights of a certain machine for moving heavy weights (''[[Illustrated Companion to the Latin Dictionary/Machina|machina tractoria]]'') at their lowest extremities, into which the pivot (''[[Illustrated Companion to the Latin Dictionary/Cardo|cardo]]'') of a revolving axle and wheel (''[[Illustrated Companion to the Latin Dictionary/Sucula|sucula]]'') was inserted; like that in which the axle of a ''[[Illustrated Companion to the Latin Dictionary/Plaustrum|plaustrum]]'' turned. Vitruv. x. 2. 2. 2. A collar of similar description, fastened to the top of an upright beam in another kind of contrivance for raising weights (''[[Illustrated Companion to the Latin Dictionary/Polyspaston|polyspaston]]''), to which the block and pullies (''[[Illustrated Companion to the Latin Dictionary/Trochlea|trochleae]]'') were affixed. Vitruv. x. 2. 8. 3. A particular member in a ''[[Illustrated Companion to the Latin Dictionary/Catapulta|catapulta]]''; called also ''[[Illustrated Companion to the Latin Dictionary/Pulvinus|pulvinus]]''. Vitruv. x. 10. 5. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] gy8holjc4wd1764e47ojctxr5gpv6ps Illustrated Companion to the Latin Dictionary/Chelys 0 311833 2683586 2671463 2024-11-11T15:47:25Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683586 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHELYS''' ({{lang|grc|χέλυς, χελώνη}}). Properly, a Greek word, adopted into the Roman language by poets; but the genuine word is [[Illustrated Companion to the Latin Dictionary/Testudo|TESTUDO]], under which its meanings are illustrated and explained. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Stringed Instruments]] 4h4af6lerjavdyt289g9dw2s1cicmd9 Illustrated Companion to the Latin Dictionary/Cheniscus 0 311834 2683587 2671464 2024-11-11T15:47:36Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683587 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHENIS'CUS''' ({{lang|grc|χηνίσκος}}). An ornament resembling the head and neck of a goose ({{lang|grc|χήν}}), sometimes placed on the stern of a vessel (Apul. ''Met.'' xi. p. 250.), but more frequently in ancient monuments, at the head. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cheniscus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 152.jpg|illustration |caption=Cheniscus/1.1}} represents three of these figures; the centre one in detail, from an ancient bas-relief, of which there is a cast in the British Museum; the one on the left hand, over the stern, from Trajan's [[Illustrated Companion to the Latin Dictionary/Columna|Column]]; and that on the right, over the [[Illustrated Companion to the Latin Dictionary/Prora|prow]], from the Vatican Virgil. <gallery> File:Cheniscus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 152.jpg|Cheniscus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Parts and Ornaments of Vessels]] b5lv8wp1y9l7jq5xx252yokdawgrdal Illustrated Companion to the Latin Dictionary/Chenoboscion 0 311835 2683588 2671465 2024-11-11T15:47:47Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683588 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHENOBOSCI'ON''' ({{lang|grc|χηνοβοσκεῖον}}). An enclosure, with its appurtenances, attached to a country-house or farm, appropriated to the breeding and keeping of geese, large flocks of which were maintained on some estate. (Varro, ''R. R.'' xii. 10. 1.) It consisted of a spacious yard on the outside of the farm-house and buildings (Columell. viii. 1. 4.), surrounded by a wall nine feet high, which formed the back of an open gallery or colonnade (''[[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]''), under which the pens (''[[Illustrated Companion to the Latin Dictionary/Hara|harae]]'') for the birds were situated. These were built of [[Illustrated Companion to the Latin Dictionary/Structura|masonry]] or [[Illustrated Companion to the Latin Dictionary/Latericius|brickwork]], each being three feet square, and closed in front by a door. The site selected, where possible, was contiguous to a stream or pool of water; if not, an artificial tank was made for the purpose; and near to, or adjoining, a field of meadow grass, or one sown with artificial grasses, where the soil required it. Columell. viii. 14. 1{{mdash}}2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] c04j8b27s7bms9yc1k532r6p1f7lb73 Illustrated Companion to the Latin Dictionary/Chiliarchus 0 311836 2683589 2671466 2024-11-11T15:47:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683589 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHILIAR'CHUS''' or '''CHILIAR'CHOS''' ({{lang|grc|χιλιάρχης}} or {{lang|grc|χιλίαρχος}}). The commander of a thousand men; a word more especially employed by the Greeks to designate the Persian ''vizîr'' (Xen. ''Cyrop.'' ii. 1. 23. Nepos, ''Con.'' 3.); and applied by the Romans to an officer who commanded the [[Illustrated Companion to the Latin Dictionary/Classiarii|marines]], or soldiers who manned a fleet. Tac. ''Ann.'' xv. 51. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] tm1ck320sz93qq2wibvjx9bt9r9yhku Illustrated Companion to the Latin Dictionary/Chimaera 0 311837 2683590 2671467 2024-11-11T15:48:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683590 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIMAE'RA''' ({{lang|grc|Χίμαιρα}}). Literally, a she-goat, which the poets and artists of Greece converted into a monster, spouting fire, composed of three different animals{{mdash}}the head of a lion, the body of a wild goat, ending in a dragon's tail; fabled to have been killed by Bellerophon. Hor. Ovid. Tibull. Hom. &c. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dekty1zr5ewm36i17sco3qlhsmh6l2d Illustrated Companion to the Latin Dictionary/Chiramaxium 0 311838 2683591 2671468 2024-11-11T15:48:20Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683591 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIRAMAX'IUM''' ({{lang|grc|χειραμάξιον}}). An ''invalid's-chair'' upon wheels, which could be drawn or pushed forward by the hands of a slave, in the same manner as now practised. (Pet. ''Sat.'' 28. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Chiramaxium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 152.jpg|illustration |caption=Chiramaxium/1.1}} represents a marble chair now in the British Museum, but which originally belonged to the baths of Antoninus at Rome, where it was doubtless employed as a ''[[Illustrated Companion to the Latin Dictionary/Sella|sella balnearis]]'' or ''pertusa''; but the two small wheels carved as ornaments on the sides, and in imitation of the moveable invalid's chair of wood, in which they were wheeled to and from the [[Illustrated Companion to the Latin Dictionary/Balineae|baths]], establish at once the meaning of the word, and the harmony between ancient customs and our own in this particular. <gallery> File:Chiramaxium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 152.jpg|Chiramaxium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carriages]] k52lb8t30ieavlavcwvlpblq9a6ya66 Illustrated Companion to the Latin Dictionary/Chiridota 0 311839 2683592 2671469 2024-11-11T15:48:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683592 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIRIDO'TA''' ({{lang|grc|χειριδωτός}}, sc. {{lang|grc|χιτών}}). Properly a Greek word, and an adjective, but sometimes used substantively by the Romans (Capitolin. ''Pertinax'', 8.); and applied to a [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]] with long sleeves reaching down to the hand ({{lang|grc|χείρ}}), more especially characteristic of the Asiatic and Celtic races, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Chiridota 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|annexed figure |caption=Chiridota/1.1}}, from the Niobe group, representing the tutor (''[[Illustrated Companion to the Latin Dictionary/Paedagogus|paedagogus]]'') of the younger children, a class of men usually selected for that duty from the inhabitants of Asia Minor. Amongst the male population of Greece, and of Rome in the earlier times, sleeved tunics were not worn, excepting by people who affected foreign habits, or of luxurious and effeminate characters; hence when mention is made of persons so dressed, there is always an implied sense of reproach concealed under it. (Scipio Afr. ''ap.'' Gell. vii. 12. 2. Cic. ''Cat.'' ii. 10. Suet. ''Cal.'' 52.) But in both countries they were permitted to females, as shown by numerous monuments both of Greek and Roman artists, and in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Chiridota 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|annexed example |caption=Chiridota/1.2}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii; whence the sarcasm of Virgil (''Aen.'' ix. 616.), where the Trojans are called women, and not men, because their tunics had long sleeves. <gallery> File:Chiridota 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|Chiridota/1.1 File:Chiridota 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|Chiridota/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Under-Clothing]] onmg01h446a6i94qy8ls36zdjj23103 Illustrated Companion to the Latin Dictionary/Chironomia 0 311840 2683593 2671470 2024-11-11T15:48:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683593 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIRONOM'IA''' ({{lang|grc|χειρονομία}}). The art of gesticulating or talking with the hands and by gestures, with or without the assistance of the voice. (Quint. i. 11. 17.) This art was of very great antiquity, and much practised by the Greeks and Romans, both on the stage and in the tribune, induced by their habit of addressing large assemblies in the open air, where it would have been impossible for the majority to comprehend what was said without the assistance of some conventional signs, which enabled the speaker to address himself to the eye as well as the ear of his audience. These were chiefly made by certain positions of the hands and fingers, the meaning of which was universally recognized and familiar to all classes, and the practice itself reduced to a regular system, as it remains at the present time amongst the populace of Naples, who will carry on a long conversation between themselves by mere gesticulation, and without pronouncing a word. It is difficult to illustrate such a matter in a work like this; but the act is frequentyly represented on the Greek vases, and other works of ancient art, by signs so clearly expressed, and so similar in their character to those still employed at Naples, that a common lazzaroni, when shown one of these compositions, will at once explain the purport of the action, which a scholar with all his learning cannot divine (Iorio, ''Mimica degli Antichi'', p. 369.) In the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Chironomia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|illustration |caption=Chironomia/1.1}}, for instance, which is copied from a Greek fictile vase, it is self-evident that the two females are engaged in a woman's quarrel; the one on the left, by her forward attitude and index finger pointedly directed towards the other, making some angry accusation against her; whilst the backward movement of the body exhibited by the figure on the right, the sudden cessation of her music, and the arms thrown open and upwards, present a very natural expression of surprise, either feigned or real, on her part. Thus much would be readily divined by any one. But the subject of the quarrel? That is told by the positions of the hands and fingers. It is a love quarrel, arising from jealousy; for the exact gesture employed by a modern Neapolitan to signify ''love'', viz. joining together the tips of the fore-finger and thumb of the left hand, is exhibited by the figure on the left side of the [[Illustrated Companion to the Latin Dictionary/Pictura|picture]]; whilst the other woman not only expresses surprise by her attitude, but with her right hand raised up towards the shoulder, and all its fingers wide open and erect, denies the insinuation, and declares her indignation at the accusation; for such is the gesture which a Neapolitan employes to signify a negative, more especially when what is said excites his astonishment and displeasure. Thus these few gestures represent a long dialogue. The cause of quarrel is, without doubt, the sitting Faun, who, while affecting to play away so resolutely between the angry damsels, has been detected in making signs incautiously to the nymph with the tambourine, and which were perceived by his old flame who stands behind him. <gallery> File:Chironomia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 153.jpg|Chironomia/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] c8a8k6zwh5eyasyqtflc6bc3bljvx00 Illustrated Companion to the Latin Dictionary/Chironomos 0 311841 2683594 2671471 2024-11-11T15:48:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683594 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIRON'OMOS''' and '''CHIRON'OMON''' ({{lang|grc|χειρονόμος}}). Generally, any person who employs the art of gesticulation to express his meaning without the aid of language, as explained in the [[Illustrated Companion to the Latin Dictionary/Chironomia|previous article]]; thence also, a [[Illustrated Companion to the Latin Dictionary/Mimus|pantomimic actor]] on the [[Illustrated Companion to the Latin Dictionary/Theatrum|stage]] (Juv. ''Sat.'' vi. 63.); and one who performs any duty with regular, studied, or theatrical movements; whence the same term is applied by the satirists to the slave who carved up the dishes at great entertainments with a pompous flourish of his knife. Juv. ''Sat.'' v. 121. Compare Pet. ''Sat.'' 36. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] d1xjkpph1h4m0ehs14595t8lnknzwwa Illustrated Companion to the Latin Dictionary/Chirurgus 0 311842 2683595 2671472 2024-11-11T15:49:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683595 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHIRUR'GUS''' ({{lang|grc|χειρουργός }}). A surgeon, who performs operations, as distinguished from a medical practitioner. The Roman doctor (''[[Illustrated Companion to the Latin Dictionary/Medicus|medicus]]'') of early times exercised both departments of the healing art; but, about the time of Tiberius, surgery began to be practised as a distinct profession. Cels. ''Praef.'' vii. Becker, ''Gallus'', p. 224. transl. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 37945avx951y9a8p8ppeh2dprlacvcf Illustrated Companion to the Latin Dictionary/Chlamydatus 0 311843 2683596 2671473 2024-11-11T15:49:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683596 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHLAMYDA'TUS''' ({{lang|grc|χλαμυδωτός}}). Clad in the ''[[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]]'', or Grecian mantle; which, from the nature of the garment, might be put on in a variety of ways, presenting very different characters, but all studiously arranged with a view of appearing graceful and becoming. (Ovid. ''Met.'' ii. 733.) The most simple and usual were the following:{{mdash}} 1. The narrowest part of the mantle (see the right-hand figure ''s.'' [[Illustrated Companion to the Latin Dictionary/Chlamys|CHLAMYS]] was passed round the back of the neck, and the two corners brought together in front of the throat, where they were joined by a buckle, clasp, or brooch, so that the goars might be turned back over the shoulders (''demissa ex humeris.'' Virg. ''Aen.'' 263.), and the middle or longest part would hang down behind as far as the knees, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Chlamydatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 154.jpg|annexed figure |caption=Chlamydatus/1.1}}, from the Panathenaic [[Illustrated Companion to the Latin Dictionary/Zophorus|frieze]] in the British Museum. 2. Or, a portion of the narrow part of the left-hand figure ''s.'' [[Illustrated Companion to the Latin Dictionary/Chlamys|CHLAMYS]], was folded down, in order to make a longer line, and then fastened sideways over the right shoulder by a brooch, &c.; so that the mantle completely enveloped the left arm, leaving the right one, as well as the whole side, uncovered, whilst the four corners hung down on the same side parallel to one another, two in front and two behind, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Chlamydatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|annexed figure |caption=Chlamydatus/2.1}}, from a Greek vase. 3. Or, one side of it was carried across the chest, and thrown over the left shoulder, so as closely to envelope the upper part of the person, as low as the wrists (Apul. ''Flor.'' ii. 15. 2.); an arrangement more especially adopted on horseback, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Chlamydatus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|annexed example |caption=Chlamydatus/3.1}}, from the Panathenaic [[Illustrated Companion to the Latin Dictionary/Zophorus|frieze]] in the British Museum. <gallery> File:Chlamydatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 154.jpg|Chlamydatus/1.1 File:Chlamydatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|Chlamydatus/2.1 File:Chlamydatus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|Chlamydatus/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] mdi7ud6r5vlcmux61z2k7fu7g29vrec Illustrated Companion to the Latin Dictionary/Chlamyda 0 311844 2683597 2671474 2024-11-11T15:49:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683597 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHLAM'YDA'''. Same as [[Illustrated Companion to the Latin Dictionary/Chlamys|CHLAMYS]]. Apul. ''Met.'' xi. p. 256. Id. ''Flor.'' ii. 15. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 1ilk2txwvpi8u5gtikcey2iae36m2d4 Illustrated Companion to the Latin Dictionary/Chlamys 0 311845 2683598 2671475 2024-11-11T15:49:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683598 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHLAM'YS''' ({{lang|grc|χλαμύς}}). A light and short mantle, originating with the inhabitants of Thessaly or of Macedonia, whence it was imported into other parts of Greece, and became the regular equestrian costume of the Athenian youths, from the period of their becoming {{lang|grc|ἔφηβος}} until the age of manhood. (Plutarch. ''Alex.'' 26. Pollux. x. 124. Apul. ''Met.'' x. p. 233.) It consisted of an oblong square piece of cloth, to each side of which a goar ({{lang|grc|πτέρυξ}}) was attached, sometimes in the form a right-angled, and at others of an obtuse-angled triangle, so that the whole, when spread out, would form a mantle of similar shape and dimensions to the {{Illustrated Companion to the Latin Dictionary/Image Location|text=diagrams |imagelink=Media:Chlamys 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|diagrams |caption=Chlamys/1.1}} introduced above. The different ways in which it was adjusted and worn are described and illustrated in the [[Illustrated Companion to the Latin Dictionary/Chlamydatus|preceding article]]. 2. Properly speaking, the chlamys belongs to the national costume of the Greeks, but not of the Romans, though it was occasionally adopted, even at an early period, by some of the last-mentioned people, as by L. Scipio and Sylla (Cic. ''Rabir. Post.'' 10. Val. Max. iii. 2. and 3.); but these are both mentioned as singular instances. In some cases too, it is ascribed to women{{mdash}}to Dido by Virgil (''Aen.'' iv. 137.), and to Agrippina by Tacitus (''Ann.'' xii. 56.). <gallery> File:Chlamys 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 155.jpg|Chlamys/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] 9rtg7ltidbbxmtdg8qveqcho3mqb1hk Illustrated Companion to the Latin Dictionary/Choragium 0 311846 2683599 2671476 2024-11-11T15:49:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683599 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORA'GIUM''' ({{lang|grc|χορήγιον}}). The furniture, scenery, dresses, &c. belonging to a [[Illustrated Companion to the Latin Dictionary/Theatrum|theatre]], which are necessary in presenting a play upon the stage, or, as our [[Illustrated Companion to the Latin Dictionary/Histrio|actors]] call it, "''the property.''" Festus, ''s. v.'' Plaut. ''Capt. Prol.'' 60. 2. A large apartment behind the stage, where the "property" was kept; or, perhaps, where the actors, and in a Greek theatre, the [[Illustrated Companion to the Latin Dictionary/Chorus|Chorus]], dressed or rehearsed. (Vitruv. v. 9. 1. Demosth. p. 403. 22. Reiske.) It formed one of the appurtenances constructed in the spacious [[Illustrated Companion to the Latin Dictionary/Porticus|porticoes]] at the back of a theatre (Vitruv. ''l. c.''), as may be seen on the plan of Pompey's theatre, introduced as an illustration under [[Illustrated Companion to the Latin Dictionary/Theatrum|THEATRUM]]. 3. A sort of spring in hydraulic machines. Vitruv. x. 8. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Chorus]] ni9emhb74jrc5qpc8beqdo8mm2v7r98 Illustrated Companion to the Latin Dictionary/Choragus 0 311847 2683600 2671477 2024-11-11T15:49:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683600 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORA'GUS'''. The person who provided the [[Illustrated Companion to the Latin Dictionary/Choragium|scenery]], ornaments, dresses, &c., necessary for presenting a play upon the Roman [[Illustrated Companion to the Latin Dictionary/Theatrum|stage]], which he sometimes furnished at his own expense, but more usually from monies levied on the community, and paid over to him by the aediles. Plaut. ''Pers.'' i. 3. 78. 2. ({{lang|grc|χορηγός}}). Amongst the Greeks, the ''choragus'' was the person who defrayed the costs for bringing out a ''[[Illustrated Companion to the Latin Dictionary/Chorus|Chorus]]''; and the leader of the Chorus was sometimes designated by the same name. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Chorus]] 7rpu4eq96ii4tqds3u76dxjvy6s04c1 Illustrated Companion to the Latin Dictionary/Choraules 0 311848 2683601 2671478 2024-11-11T15:50:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683601 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORAU'LES''' and '''CHORAU'LA''' ({{lang|grc|χοραύλης}}). A musician who accompanied the ''[[Illustrated Companion to the Latin Dictionary/Chorus|Chorus]]'' of the Greek [[Illustrated Companion to the Latin Dictionary/Theatrum|theatre]], or any other number of singers in a concert generally, upon the double pipes; as contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Auloedus|auloedus]]'', who played an instrument solo without vocal music. (Suet. ''Galb.'' 12. Plin. ''H. N.'' xxxvii. 3. Mart. ''Ep.'' ix. 78.) The costume and instrument of these performers are shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=figure |imagelink=Media:Choraules 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|figure |caption=Choraules/1.1}} annexed, from a drawing by Fulvius Ursinus, in the Vatican Library, copied from a statue discovered on the Appian way, with the name {{Illustrated Companion to the Latin Dictionary/Inscription|text=CHORAULES}} inscribed upon its base. <gallery> File:Choraules 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|Choraules/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Chorus]] [[Category:Classed Index/Musicians]] 4ydz2qtkue0jk4x7ziphvneu940by7n Illustrated Companion to the Latin Dictionary/Chorea 0 311849 2683602 2671479 2024-11-11T15:50:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683602 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORE'A''' ({{lang|grc|χορεία}}). A choral dance; i. e. in which the performers join hand in hand, so as to form a circle and dance to the sound of their own voices, precisely as represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Chorea 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|illustration |caption=Chorea/1.1}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] in the [[Illustrated Companion to the Latin Dictionary/Balineae|baths]] of Titus at Rome. Virg. ''Cul.'' 19. Ovid. ''Met.'' viii. 581. Claud. ''B. Gild.'' 448. <gallery> File:Chorea 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|Chorea/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] b0pzrskmvlmdphdze9p358mz87ddspf Illustrated Companion to the Latin Dictionary/Chorobates 0 311850 2683603 2671480 2024-11-11T15:50:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683603 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHOROB'ATES'''. An instrument used for taking the level of water, and of the country through which it is to be conducted. Vitruv. viii. 5. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] iejt8nlcv3vd52qk4zxrdfpgkmmjevz Illustrated Companion to the Latin Dictionary/Chorocitharista 0 311851 2683604 2671481 2024-11-11T15:50:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683604 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHO'ROCITHARIS'TA'''. A musician who accompanies a [[Illustrated Companion to the Latin Dictionary/Chorus|chorus]] of singers on the ''[[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]''. Suet. ''Dom.'' 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] cfvqv43kk1vhq5h29ewvm7hi6vls1ux Illustrated Companion to the Latin Dictionary/Chors 0 311852 2683605 2671482 2024-11-11T15:50:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683605 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORS''', '''CORS''', or '''COHORS''' ({{lang|grc|χόρτος}}). A farm, or straw-yard, which constituted one of the principal appendages belonging to a country villa, where the whole live stock, cattle, pigs, poultry, &c., were kept, stalled, and foddered. It consisted of a large court, covered with litter, for the purpose of making dressing for the land, provided with a tank, where the cattle were watered when brought up for the night; and enclosed all round by numerous outbuildings, including sheds for the carts, [[Illustrated Companion to the Latin Dictionary/Aratrum|ploughs]], and agricultural implements, as well as stabling, stalls, sties, and houses for the cattle, and other domestic animals (''turba cortis'', Mart. ''Ep.'' iii. 58.), forming the live stock of the farm. (Varro, ''L. L.'' v. 88. Id. ''R. R.'' 1. 13. 2. and 3. Vitruv. vi. 6. 1.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Chors 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|illustration |caption=Chors/1.1}} annexed, which represents the yard in which the followers of Ulysses were kept when changed into swine, from a miniature of the Vatican Virgil, will serve to convey a notion of the general plan and character of an ancient farm-yard and its dependencies. 2. A sheep pen, made with hurdles and netting, and set up on the lands where the flock pastured, to protect them at night. (Varro, ''R. R.'' ii. 2. 9.) Also a permanent enclosure surrounded by high stone walls, in which sheep were stalled. Columell. vii. 3. 8. <gallery> File:Chors 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 156.jpg|Chors/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] 8qh1rui6zkjc0idxb546esemsmtxs0a Illustrated Companion to the Latin Dictionary/Chorus 0 311853 2683606 2671483 2024-11-11T15:51:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683606 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHORUS''' ({{lang|grc|χορός}}). A band or company of persons engaged in dancing and singing, more especially when their songs and dances were performed in honour, or as part of the worship, of some divinity. Cic. ''Phil.'' v. 6. Virg. ''Aen.'' viii. 718. Suet. ''Cal.'' 37. Hor. ''Od.'' i. 1. 31. 2. The chorus of singers in a dramatic entertainment on the Greek [[Illustrated Companion to the Latin Dictionary/Theatrum|stage]]. The performers in it were entirely distinct from the [[Illustrated Companion to the Latin Dictionary/Histrio|actors]], though they sometimes performed the part of interlocutors. The Roman drama had no chorus. Hor. ''A. P.'' 193. 204. 283. Aul. Gell. xix. 10. 3. A choral or round dance. (Mart. ''Ep.'' iv. 44. Compare Tibull. ii. 8. 88.) Same as [[Illustrated Companion to the Latin Dictionary/Chorea|CHOREA]]; where see the illustration. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Chorus]] 8gihppp4h9dsn2djdvttke8lhnk1p4g Illustrated Companion to the Latin Dictionary/Chrysendeta 0 311854 2683607 2671484 2024-11-11T15:51:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683607 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHRYSEN'DETA''' ({{lang|grc|χρυσένδετα}}). The name given to a particular manufacture of plate employed by the wealthy Romans for their table services, but the precise character of which is not ascertained; excepting that the name itself and the epithets applied to it, appear to indicate that the articles were made upon a basis of silver, with ornaments of gold either inlaid, or chased in relief upon it. Mart. ''Ep.'' ii. 43. Id. vi. 94. Id. xiv. 97. and compare Cic. ''Verr.'' iv. 21{{mdash}}23. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] kdm2rnllcul8fupua53biggfe39mwr3 Illustrated Companion to the Latin Dictionary/Chytra 0 311855 2683608 2671485 2024-11-11T15:51:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683608 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHYT'RA''' ({{lang|grc|χύτρα}}). A common kind of earthenware pot in use amongst the Greeks, employed for boiling and cooking, or any ordinary purpose; and, therefore, left in its natural rough state of red clay, without any sort of decoration or [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. (Aristoph. ''Pac.'' 923. Athen. ix. 73. Cato, ''R. R.'' 157. 11., where, however, some editions read ''scutra''.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Chytra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 157.jpg|illustration |caption=Chytra/1.1}}, from an original, represents the form of these pots according to Panofka, ''Recherches sur les véritables Noms des Vases Grecs'', i. 28. <gallery> File:Chytra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 157.jpg|Chytra/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] egp3t1oeqfaupn264rvmfu03acpq6i0 Illustrated Companion to the Latin Dictionary/Chytropus 0 311856 2683609 2671486 2024-11-11T15:51:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683609 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CHYT'ROPUS''' ({{lang|grc|χυτρόπους}}). A ''[[Illustrated Companion to the Latin Dictionary/Chytra|chytra]]'' made with legs, so that it could be set over the fire without being placed upon a trivet, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Chytropus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 157.jpg|annexed figure |caption=Chytropus/1.1}}, from an original after Panofka. Hesiod. ''Op.'' 746. Vulg. ''Levit.'' xi. 35. <gallery> File:Chytropus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 157.jpg|Chytropus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] nr6aunie4h50qefnixp1mt63vf0mt9r Illustrated Companion to the Latin Dictionary/Cibilla 0 311857 2683610 2671487 2024-11-11T15:51:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683610 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIBILL'A'''. The reading of some editions in a passage of Varro (''L. L.'' v. 118.) for [[Illustrated Companion to the Latin Dictionary/Cilliba|CILLIBA]]; which see. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] jc9jvrehqhi5bm2z4a0kg6xiqfk5tc0 Illustrated Companion to the Latin Dictionary/Ciborium 0 311858 2683611 2671488 2024-11-11T15:52:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683611 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIBO'RIUM''' ({{lang|grc|κιβώριον}}). Literally, the seed-pod of the Egyptian bean (''colocasia''); and thence a drinking vessel of Greek invention, so termed from its resemblance to the form of that fruit. Hor. ''Od.'' ii. 7. 22. Schol. Vet. ''ad l.'' Athen. xi. 54. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] pk0vaoqphiyq21ah32xreoq66hmfh3m Illustrated Companion to the Latin Dictionary/Ciconia 0 311859 2683612 2671489 2024-11-11T15:52:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683612 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CICO'NIA'''. Literally, a ''stork''; but also applied to a mimic gesture expressive of ridicule or contempt, produced by bending the forefinger into the form of a stork's neck, and pointing it towards the person ridiculed with a rapid motion of the two top joints up and down. Pers. i. 58. Hieron. ''Epist.'' 125. 18. 2. A contrivance employed by farmers to test a labourer's work in spade husbandry, and prove if all his trenches were dug to a uniform and proper width and depth. It consisted of an upright, with a cross-bar affixed to it, at right angles, like the letter T inverted, so that the long branch measured the depth, the two shorter arms the width and evenness of the trench. Columell. iii. 13. 11. 3. ''Ciconia composita''. A contrivance of the same description as the preceding, but not quite so simple; invented by Columella, to remedy some inconveniences experienced in the use of that instrument, which led to frequent disputes between the farmer and his labourers, without insuring him against being deceived by them; inasmuch as it required a very sharp eye to see that the instrument was placed fairly upright in the furrow, and not in a slanting position, which would make the trench appear deeper than it really was. For this purpose he added two cross-bars to the original instrument, nailed on it in the form of the letter X, and suspended a line and plummet from the point where they intersected each other; thus, the extreme ends of the cross-bars and tail-piece proved the width of the trench at top and bottom, and showed if the sides were dug fair and even throughout; the height of the machine measured the exact depth of the trench; and the plumb line prevented disputes by indicating at once whether it was inserted in a horizontal position or not. (Columell. iii. 13. 12.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Ciconia 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|illustration |caption=Ciconia/3.1}} is not from the antique, but is a conjectural diagram by Schneider, constructed in accordance with Columella's description, and inserted here in order to convey a better idea than words alone can express. 4. A name given by the ancient Spaniards to the machine for raising water from a well, which we call a "swipe," and the Romans termed [[Illustrated Companion to the Latin Dictionary/Tolleno|TOLLENO]]. Isidor. ''Orig.'' xx. 15. 3. <gallery> File:Ciconia 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|Ciconia/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Agricultural Implements]] nzlauczzmsgks8clmxgtztmx8mah98f Illustrated Companion to the Latin Dictionary/Cicuta 0 311860 2683613 2671490 2024-11-11T15:52:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683613 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CICU'TA'''. Literally, the ''hemlock''; whence transferred to things made out of the stalks of that plant, especially the ''[[Illustrated Companion to the Latin Dictionary/Arundo|Pan's pipes]]''. Virg. ''Ecl.'' ii. 36. Lucret. v. 1382. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 5mihjtjiqviiu75d6jixk23btdgxwkx Illustrated Companion to the Latin Dictionary/Cicuticen 0 311861 2683614 2671491 2024-11-11T15:52:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683614 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CICU'TICEN'''. A performer on the ''[[Illustrated Companion to the Latin Dictionary/Arundo|Pan's pipes]]'', made of the [[Illustrated Companion to the Latin Dictionary/Cicuta|hemlock]] stalks. (Sidon. ''Carm.'' i. 15.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cicuticen 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|illustration |caption=Cicuticen/1.1}} is from a small ivory figure in the Florentine Museum. <gallery> File:Cicuticen 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|Cicuticen/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Musicians]] llrbfuzgl87hqvf57u8ihok3fvxsd2a Illustrated Companion to the Latin Dictionary/Cidaris 0 311862 2683615 2671492 2024-11-11T15:52:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683615 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CID'ARIS''' ({{lang|grc|κίδαρις}} and {{lang|grc|κίταρις}}). The ''royal'' bonnet worn by the kings of Persia, Armenia, and Parthia, which had a tall, stiff, and straight crown, encircled by a blue diadem ornamented with white spots (Curt. iii. 3.). All these particulars, with the exception of the colour, are distinctly visible in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cidaris 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|illustration |caption=Cidaris/1.1}}, which represents Tigranes, king of Armenia, from a Syrian model. 2. The bonnet worn by the high-priest of the Jews. Hieron. ''Epist.'' 64. 2. and 13. <gallery> File:Cidaris 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|Cidaris/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Coverings for the Head]] fy42091lujlel5v0exwxb1atgr6x4m9 Illustrated Companion to the Latin Dictionary/Cilibantum 0 311863 2683616 2671493 2024-11-11T15:52:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683616 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CILIBAN'TUM'''. A wine or drinking table of ''circular'' form, supported upon ''three'' legs; for circular tables, on a ''single'' stem, had an appropriate name of their own {{mdash}} ''[[Illustrated Companion to the Latin Dictionary/Monopodium|monopodia]]''. Tables of this kind are frequently represented in the Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]], from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Cilibantum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|annexed illustration |caption=Cilibantum/1.1}} is copied, with the drinking vessels (''[[Illustrated Companion to the Latin Dictionary/Capis|capides]]'', ''[[Illustrated Companion to the Latin Dictionary/Capula|capulae]]'') upon it, precisely as mentioned by Varro, ''L. L.'' v. 121. <gallery> File:Cilibantum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 158.jpg|Cilibantum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Meals]] [[Category:Classed Index/Tables]] b6ce02ctmp6g1qgrdevyuoddhc9no5b Illustrated Companion to the Latin Dictionary/Cilicium 0 311864 2683617 2671494 2024-11-11T15:53:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683617 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CILIC'IUM''' ({{lang|grc|κιλίκιον}}). A coarse kind of cloth made of goats' hair, used for various purposes, in the army and navy more especially, and probably resembling the material now used for coal-sacks and horses' nose-bags. Cic. ''Verr.'' ii. 1. 38. Liv. xxxviii. 7. Veget. ''Mil.'' iv. 6. Serv. ''ad'' Virg. ''Georg.'' iii. 313. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Different Fabrics]] gu6bancsg75g03hraw4jalmka8hlrjq Illustrated Companion to the Latin Dictionary/Cilliba 0 311865 2683618 2671495 2024-11-11T15:53:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683618 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIL'LIBA''' ({{lang|grc|κιλλίβας}}). A Greek word, signifying literally the ''trestle'', which forms a stand for anything; whence it was adopted by the Romans to designate a ''dining-table'' of ''square'' form, supported by trestles underneath, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cilliba 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|illustration |caption=Cilliba/1.1}}, from the Vatican Virgil, which represents the table at which the companions of Ulysses fed, when changed into beasts. Square dining tables were usually employed by the early Romans; but had fallen into disuse before the age of Varro, when circular ones were mostly adopted; except in camps for the military mess, where the old form was retained as more convenient. Varro, ''L. L.'' v. 118. <gallery> File:Cilliba 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|Cilliba/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/The Meals]] [[Category:Classed Index/Tables]] cihp89oew0gnupvjj5cxr90hgxj3myz Illustrated Companion to the Latin Dictionary/Cinaedus 0 311866 2683619 2671496 2024-11-11T15:53:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683619 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINAEDUS''' ({{lang|grc|κίναιδος}}). A ''dancing-master'', who taught the art of dancing in a school (Scipio Afr. ''ap.'' Macrob. ''Sat.'' ii. 10. Non. ''s. v.'' p. 5. Plaut. ''Mil.'' iii. 73.); for in early times, while this kind of exercise was confined to religious and warlike dances, it was not esteemed unbecoming; but with the corruption of manners, when mimetic and lascivious dances were introduced upon the stage, the name was likewise given to the performers in these exhibitions, and thence, in a more indefinite meaning, it became a term of reproach for any one who indulged in the indelicate propensities for which the stage dancers were notorious. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] tficfobnnl07h5lo5bxocjyah2o8lkc Illustrated Companion to the Latin Dictionary/Cincinnatus 0 311867 2683620 2671497 2024-11-11T15:53:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683620 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCINNA'TUS'''. Having the hair of the head twisted into long corkscrew curls or ringlets (''[[Illustrated Companion to the Latin Dictionary/Cincinnus|cincinni]]''). Cic. ''in Senat.'' 5. Id. ''pro Sext.'' 11. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] igdkk2w8b7lnztxyna03q905xu55i9l Illustrated Companion to the Latin Dictionary/Cincinnus 0 311868 2683621 2671498 2024-11-11T15:53:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683621 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCIN'NUS''' ({{lang|grc|ἕλιξ}}). A ''ringlet'', or long corkscrew curl of hair, like the twist of a fringe (Cic. ''Pis.'' 11.), or the tendril of a vine (Varro, ''R. R.'' i. 31. 4.), as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cincinnus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|example |caption=Cincinnus/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. Though ringlets of this kind are natural to some few individuals, the term mostly implies that they were artificially produced with the curling-irons. <gallery> File:Cincinnus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|Cincinnus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Hair and Beard]] nvln8hp10k7d32by5p3o5hf2c04nqf1 Illustrated Companion to the Latin Dictionary/Cincticulus 0 311869 2683622 2682949 2024-11-11T15:54:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683622 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCTIC'ULUS'''. Diminutive of CINCTUS, ''-us''; a short petticoat or kilt worn by boys wound the loins in the same way as the ''[[Illustrated Companion to the Latin Dictionary/Cinctus (noun)|cinctus]]'' by grown-up persons. Plaut. ''Bacch.'' iii. 3. 28. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] e1sn50g4zz49dupvlpu0l1dz1kt4jhw Illustrated Companion to the Latin Dictionary/Cinctorium 0 311870 2683623 2671500 2024-11-11T15:54:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683623 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCTO'RIUM'''. A belt worn round the waist, for the purpose of attaching the sword (Mela, ii. 1.), as contradistinguished from the baldrick (''[[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]''), which was slung over the shoulder. The [[Illustrated Companion to the Latin Dictionary/Consul|consuls]], [[Illustrated Companion to the Latin Dictionary/Tribunus|tribunes]], and superior officers of the Roman army are always represented on the [[Illustrated Companion to the Latin Dictionary/Columna|columns]] and [[Illustrated Companion to the Latin Dictionary/Arcus|arches]] with their swords attached by a ''cinctorium'', as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cinctorium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|example |caption=Cinctorium/1.1}}, from a bas-relief in the [[Illustrated Companion to the Latin Dictionary/Capitolium|Capitol]] at Rome; but the orderlies, or common men, carry theirs suspended from a ''balteus''. <gallery> File:Cinctorium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|Cinctorium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Swords]] 6t35mbbcjio54pe8dmeeweafh0pgcax Illustrated Companion to the Latin Dictionary/Cinctus (noun) 0 311871 2683624 2671501 2024-11-11T15:54:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683624 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCTUS''', ''-us'' ({{lang|grc|διάζωμα, περίζωμα}}). A sort of petticoat, like the Scotch kilt, reaching from the waist to the knees, or thereabouts, which was worn in early times, instead of the [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]], by persons of the male sex, engaged in active or laborious employments. Isidor. ''Orig.'' xix. 33. 1. Varro, ''L. L.'' v. 114., as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cinctus_1 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|illustration |caption=Cinctus_1/1.1}}, from a terra-cotta lamp. 2. A waist-band worn over the tunic (Plin. ''H. N.'' xxviii. 9. Suet. ''Nero'', 51.); same as [[Illustrated Companion to the Latin Dictionary/Cingula|CINGULA]] and [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]], 3. 3. ''Cinctus Gabinus.'' A particular manner of adjusting the ''[[Illustrated Companion to the Latin Dictionary/Toga|toga]]'' (Liv. v. 46. Id. viii. 9.), in which one end of it was thrown over the head, and the other passed round the waist behind (Serv. ''ad'' Virg. ''Aen.'' vii. 612.), so as to present the appearance of a girdle, precisely as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Cinctus_1 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 160.jpg|annexed figure |caption=Cinctus_1/3.1}}, from the Vatican Virgil. <gallery> File:Cinctus_1 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 159.jpg|Cinctus 1/1.1 File:Cinctus_1 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 160.jpg|Cinctus 1/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] [[Category:Classed Index/Cinctures]] jhmjbpsdxi0t3w11ohcsh01zbm0m3t5 Illustrated Companion to the Latin Dictionary/Cinctus (adjective) 0 311872 2683625 2671502 2024-11-11T15:54:34Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683625 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCTUS''', ''-a, -um''. Generally, wearing a girdle, belt, or sash of any kind, and applied to both sexes; to females, who wore a girdle under the breast (Ovid. ''Met.'' vi. 59. and [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]], 1.), or, like a zone, round the loins (Curt. iii. 3. and [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]], 2.); to men, who wore a girdle over the [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]] (Plaut. ''Curc.'' ii. 1. 5. and [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]], 3.); or their swords attached to a waist-band (''gladio cinctus'', Liv. xxxviii. 21. and [[Illustrated Companion to the Latin Dictionary/Cinctorium|CINCTORIUM]]); and to [[Illustrated Companion to the Latin Dictionary/Venator|huntsmen]] who carried their [[Illustrated Companion to the Latin Dictionary/Culter|knives]] in a waist-band (''cultro venatorio cinctus'', Suet. ''Aug.'' 35. and 19.). 2. ''Cinctus alte.'' See [[Illustrated Companion to the Latin Dictionary/Alticinctus|ALTICINCTUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Cinctures]] nc23iqzcouoe05nnjpsjr4a8my1itet Illustrated Companion to the Latin Dictionary/Cinctutus 0 311873 2683626 2682955 2024-11-11T15:54:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683626 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINCTU'TUS'''. Clothed after the fashion of the early ages; i. e. with nothing but a short kilt (''cinctus'', {{lang|grc|περίζωμα}}) round the loins, as represented in the [[Illustrated Companion to the Latin Dictionary/Cinctus (noun)|last illustration but one]]. Hor. ''A. P.'' 50. Ovid. ''Fast.'' v. 101. Compare Plutarch, ''Rom.'' 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Cinctures]] 8co2o7c3x415xwswumu4ukm4cb06byf Illustrated Companion to the Latin Dictionary/Cinerarium 0 311874 2683627 2671504 2024-11-11T15:54:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683627 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINERA'RIUM'''. A niche in a tomb, adapted for the reception of a large cinerary urn, or a [[Illustrated Companion to the Latin Dictionary/Sarcophagus|sarcophagus]], as contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Columbarium|columbarium]]'', which was of smaller dimensions, and only formed to receive a pair of jars (''[[Illustrated Companion to the Latin Dictionary/Olla|ollae]]''). (Inscript. ''ap.'' Grut. 850. 10. ''Ap.'' Fabrett. 16. 71. {{Illustrated Companion to the Latin Dictionary/Inscription|text=CALPURNIA EMIT COLUMBARIA N. IV. OLLAS. N. VIII. ET CINERARIUM MEDIANUM.}}) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cinerarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 160.jpg|illustration |caption=Cinerarium/1.1}}, which represents one side of a sepulchral chamber, as it appeared when first excavated, presents an arrangement similar to that set forth by the preceding inscription, with two ''columbaria'' at bottom, over which are the same number of cinerary niches for urns, and a larger one in the centre (''cinerarium medianum''), with its sarcophagus. <gallery> File:Cinerarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 160.jpg|Cinerarium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Sepulchres]] rpqg1x0snahzr2almx3tzajkmfpc2it Illustrated Companion to the Latin Dictionary/Cinerarius 0 311875 2683628 2671505 2024-11-11T15:55:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683628 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINERA'RIUS'''. A slave who waited upon the ''[[Illustrated Companion to the Latin Dictionary/Ornatrix|ornatrix]]'' while engaged in dressing her mistress's hair. His chief duty consisted in heating the curling irons in the ashes (''cineres''), whence the name (Varro, ''L. L.'' v. 129.); but in some cases, he also performed the part of a [[Illustrated Companion to the Latin Dictionary/Tonsor|barber]]. Catull. 61. 138. Seneca, ''Constant. Sap.'' 14. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] i1q5u5v3umrmwj1pmkvgxv1zcvg2ajj Illustrated Companion to the Latin Dictionary/Cingillum 0 311876 2683629 2671506 2024-11-11T15:55:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683629 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CINGIL'LUM'''. A diminutive of [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]]; but in a passage of Petronius (''Sat.'' 67. 4.), the only one in which the word occurs, it is clearly used to designate an article of female attire worn on the upper part of the person, and reaching from the shoulders to a little below the waist; for, when Fortunata appears at the banquet of Trimalchio, she wears a yellow ''cingillum'' over a cherry-coloured [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]], which is seen below it; the tunic also being sufficiently short to leave the bangles round her ankles, and her Greek shoes exposed to view {{mdash}} ''galbino succincta cingillo ita, ut infra cerasina appareret tunica, et periscelides tortae, phaecasiaeque inauratae''. It must, therefore, have resembled what we now term a ''jacket'' or ''spenser'', such as is frequently represented in the Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]], from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cingillum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|illustration |caption=Cingillum/1.1}} is copied; and if the tunic were only drawn up a little higher through its girdle, so as to leave the feet and ankles exposed, it would strictly accord with the entire costume described. <gallery> File:Cingillum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|Cingillum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Under-Clothing]] eaczqj912xwy7v7z2sa135ng08mw9e7 Illustrated Companion to the Latin Dictionary/Cingula 0 311877 2683630 2671507 2024-11-11T15:55:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683630 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIN'GULA'''. A ''girth'' or ''surcingle'' by which the saddle pad is fastened, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cingula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|example |caption=Cingula/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Antoninus. Ovid. ''Rem. Am.'' 236. Calpurn. ''Ecl.'' vi. 41. 2. A man's girdle round the waist. Ovid, ''A. Amat.'' iii. 444. and [[Illustrated Companion to the Latin Dictionary/Cingulum|CINGULUM]] 3. <gallery> File:Cingula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|Cingula/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Saddles and Trappings]] bik0ld438lfu7kz45e7a1ntg0yr7xjl Illustrated Companion to the Latin Dictionary/Cingulum 0 311878 2683631 2682961 2024-11-11T15:55:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683631 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIN'GULUM''' ({{lang|grc|ταινία}}). A band, sash, or girdle worn by females over the [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]], and close under the bosom, in order to make the dress sit close, and becomingly on the person, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=figure annexed |imagelink=Media:Cingulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|figure annexed |caption=Cingulum/1.1}}, from a Greek statue. Isidor. ''Orig.'' xix. 33. 1. Virg. ''Aen.'' i. 492. 2. ({{lang|grc|ζώνη}}). A girdle or sash also worn by females, and especially young unmarried women, but fastened lower down the body, just above the hips, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Cingulum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|annexed illustration |caption=Cingulum/2.1}}, representing Electra, from a marble found at Herculaneum, with the sash drawn by its side, from a Greek vase. In this sense the term is also applied to the Cestus of Venus. Festus. ''s. v.'' Val. Flacc. vi. 470. and [[Illustrated Companion to the Latin Dictionary/Cestus|CESTUS]]. 3. ({{lang|grc|ζωστήρ}}). A man's girdle, worn round the waist, and outside the tunic, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cingulum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|example |caption=Cingulum/3.1}}, from a statue at Naples. It served for carrying any small article suspended from it, and especially to shorten the tunic, when the wearer was engaged in active exercise, by drawing up the lower part to any desirable height. Pet. ''Sat.'' 21. 2. and [[Illustrated Companion to the Latin Dictionary/Alticinctus|ALTICINCTUS]]. 4. ({{lang|grc|μίτρα, ζωστήρ, ζώνη}}). A ''soldier's belt'', made of metal, or of leather plated with metal, worn round the loins to secure the bottom of the cuirass (see the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Clipeatus|CLIPEATUS]] 1.), and protect the belly. It was fastened by hooks, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cingulum 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|example |caption=Cingulum/4.1}}, from an original of bronze found in a warrior's tomb at Paestum; and over this the sword belt (''[[Illustrated Companion to the Latin Dictionary/Cinctorium|cinctorium]]'') was also strapped, whence Virgil, in describing the armour of Pallas (''Aen.'' xii. 942.), includes both of these by the plural ''cingula'', for the shoulder band (''[[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]''), which supported the shield, is separately mentioned. 5. ({{lang|grc|διάζωμα, περίζωμα}}). An ''article in female attire'' similar to the ''[[Illustrated Companion to the Latin Dictionary/Cinctus (noun)|Cinctus]]'' of males (Varro, ''L. L.'' v. 114.), viz. a short petticoat reaching from the waist to the knees, which was worn in early times instead of a tunic, especially by women who led an active or laborious life; whence it is very commonly assigned to the Amazonian women on the fictile vases, from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cingulum 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|illustration |caption=Cingulum/5.1}} is copied. <gallery> File:Cingulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|Cingulum/1.1 File:Cingulum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|Cingulum/2.1 File:Cingulum 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 161.jpg|Cingulum/3.1 File:Cingulum 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|Cingulum/4.1 File:Cingulum 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|Cingulum/5.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Cinctures]] [[Category:Classed Index/Defensive Armour]] 9qd79wqlpdlok7k5agkkevar9lpcv1n Illustrated Companion to the Latin Dictionary/Ciniflo 0 311879 2683633 2671509 2024-11-11T15:55:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683633 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIN'IFLO'''. A slave attached to the female part of the household, whose business it was either to heat the irons for the ''[[Illustrated Companion to the Latin Dictionary/Ornatrix|ornatrix]]'' (Schol. Acron. ''ad'' Hor. ''Sat.'' i. 2. 98.) when she was dressing her mistress's hair; or, according to Servius (''ad'' Virg. ''Aen.'' xii. 611.), to procure and administer the powder (''cinis'') which women employed for tinting their hair of a light auburn colour. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dzbh2jxy2tw4yyljz0clv903otiq5i8 Illustrated Companion to the Latin Dictionary/Cippus 0 311880 2683634 2671510 2024-11-11T15:56:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683634 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIPPUS''' ({{lang|grc|στήλη}}). A short round post or pillar of stone set up to mark the boundaries between adjacent lands or neighbouring states. (Simplic. ''ap.'' Goes. p. 88.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cippus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|illustration |caption=Cippus/1.1}} represents one of these stones, now preserved in the Museum of Verona. From the inscription (one of the oldest authentic Roman inscriptions extant) we learn that it was set up by Atilius Saranus, who was dispatched by the senate, as proconsul, to reconcile a dispute between the people of Ateste (''Este'') and Vincentia (''Vicenza'') respecting their boundaries. 2. A low pillar, sometimes round, but more frequently rectangular, erected as a tomb-stone over the spot where a person was buried, or employed as a tomb for containing the ashes after they had been collected from the [[Illustrated Companion to the Latin Dictionary/Rogus|funeral pyre]], by persons who could not afford the expense of a more imposing fabric. (Pers. i. 37.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cippus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|illustration |caption=Cippus/2.1}} represents an elevation and section of a cippus, which formerly stood on the Via Appia; the section, on the left hand, shows the movable lid, and the cavity for receiving the ashes. 3. A strong post, formed out of the trunk of a tree, with the weaker branches cut off, sharpened to a point, and driven into the ground to serve as a palisade in military fortifications. Caes. ''B. G.'' vii. 73. <gallery> File:Cippus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|Cippus/1.1 File:Cippus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 162.jpg|Cippus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Sepulchres]] 9qq53f1n8txkylegluap0byy1n99jsg Illustrated Companion to the Latin Dictionary/Circinus 0 311881 2683635 2671511 2024-11-11T15:56:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683635 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIR'CINUS''' ({{lang|grc|διαβήτης}}). A ''pair of compasses'', employed by carpenters, architects, [[Illustrated Companion to the Latin Dictionary/Lapidarius|masons]], and [[Illustrated Companion to the Latin Dictionary/Scalptor|sculptors]], for describing circles, measuring distances, or taking the thickness of solids. (Caes. ''B. G.'' i. 38. Vitruv. iix. 8. 2.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Circinus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|illustration |caption=Circinus/1.1}} represents three sorts of compasses, similar to those still in use; on the right a pair of proportional compasses, on the left a pair of callipers, and a small common compass in the centre, all copied from originals found at Pompeii. <gallery> File:Circinus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|Circinus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carpentry and Tools for Working in Wood]] [[Category:Classed Index/Stone-masons and Builders]] 3yaqa450ordan697c9gdjgq2vxz1h7b Illustrated Companion to the Latin Dictionary/Circitores 0 311882 2683636 2671512 2024-11-11T15:56:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683636 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCITO'RES'''. Surveyors of the Roman [[Illustrated Companion to the Latin Dictionary/Aquaeductus|aqueducts]], whose duty it was to visit the different lines for the purpose of seeing if any parts wanted repairs, and that no frauds had been committed by the insertion of improper pipes, in order to divert the water without permission, or draw off a larger quantity of it than the law allotted. Frontin. ''Aq.'' 117. 2. In the Roman armies, a detachment of men appointed to go the rounds at certain intervals, and see that all the watches were regularly kept, and all the sentries at their posts. Veget. ''Mil.'' iii. 8. Inscript. ''ap.'' Murat. 540. 2. 3. Commercial travellers, employed by certain manufacturers and tradesmen, to carry round and dispose of the goods they made. Ulp. ''Dig.'' 14. 3. 15. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Aqueducts]] [[Category:Classed Index/Troops]] bt3xb44xri1vz64ul42320q0ttloxfx Illustrated Companion to the Latin Dictionary/Circuitor 0 311883 2683637 2671513 2024-11-11T15:56:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683637 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCU'ITOR'''. A watchman or looker out, employed upon a farm or country villa, to go the rounds and protect the gardens and fields from depredations. Pet. ''Priap.'' 16. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0fstlnuxqugz58tuewiejwsmtnqbs29 Illustrated Companion to the Latin Dictionary/Circulator 0 311884 2683638 2671514 2024-11-11T15:56:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683638 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCULA'TOR'''. A strolling [[Illustrated Companion to the Latin Dictionary/Pilarius|juggler]], or mountebank, who goes about getting money by showing off tricks and sleights of hand (Celsus, v. 27. 3. Apul. ''Met.'' i. p. 3.); or with trained animals (Paul. ''Dig.'' 47. 11. 11.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Circulator 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|annexed illustration |caption=Circulator/1.1}}, from a terra-cotta lamp. <gallery> File:Circulator 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|Circulator/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feats of Strength or Dexterity]] 3hm7qi4fp9w6etejcx8aozbvi9ju4ko Illustrated Companion to the Latin Dictionary/Circulus 0 311885 2683639 2671515 2024-11-11T15:56:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683639 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIR'CULUS''' ({{lang|grc|κύκλος}}). A circle; thence, applied to various things which have a circular figure: as{{mdash}} 1. The hoop of a cask (''[[Illustrated Companion to the Latin Dictionary/Cupa|cupa]]''), by which the staves are bound together, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Circulus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|example |caption=Circulus/1.1}} from Trajan's [[Illustrated Companion to the Latin Dictionary/Columna|Column]]. Pet. ''Sat.'' 60. 3. Plin. ''H. N.'' xiv. 27. Id. xvi. 30. 2. A particular kind of cake or biscuit, made in the form of a ring. Varro, ''L. L.'' v. 106. Vopisc. ''Tac.'' 6. 3. A circular dish, upon which food was brought up and placed upon the table (Mart. ''Ep.'' xiv. 138.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Circulus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|illustration |caption=Circulus/3.1}}, from the Vatican Virgil; whereas many dishes were only handed round to the guests, without being deposited on the dining table. 4. The broad belt in the sphere, which contains the twelve signs of the zodiac, and represents the sun's track through them, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Circulus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 164.jpg|annexed example |caption=Circulus/4.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. Aul. Gell. xiii. 9. 3. 5. An imaginary circle in the heavens, or which astronomers describe on the celestial globe, for the purpose of marking out certain regions of the sky, and explaining the course of the planets, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Circulus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 164.jpg|illustration |caption=Circulus/5.1}}, from a statue of Atlas bearing the heavens on his shoulders. Varro, ''L. L.'' vi. 8. Cic. ''Somn.'' Scip. 3. Ovid. ''Met.'' ii. 516. <gallery> File:Circulus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|Circulus/1.1 File:Circulus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 163.jpg|Circulus/3.1 File:Circulus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 164.jpg|Circulus/4.1 File:Circulus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 164.jpg|Circulus/5.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Plates and Dishes]] 1npppk79z3i5k5u2n3a90cu562yhvhx Illustrated Companion to the Latin Dictionary/Circumcidaneus 0 311886 2683640 2671516 2024-11-11T15:57:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683640 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCUMCIDA'NEUS'''. Literally, ''cut round''; but the word is employed in a special sense to designate an inferior quality of newly-made wine, or must, produced by repeated squeezings under the press beam. To understand distinctly the meaning of the word and the quality of the article intended by it, we have only to reflect, that when the fresh grapes had been crushed in a vat by the naked feet, the residue of stalks and skins (''[[Illustrated Companion to the Latin Dictionary/Pes|pes]]'') was carried in a mass to the pressing machine (''[[Illustrated Companion to the Latin Dictionary/Torcular|torcular]]''), and there subjected to the action of a powerful beam (''[[Illustrated Companion to the Latin Dictionary/Prelum|prelum]]'') screwed down upon it, which extracted all the juice remaining in them. This operation would naturally cause a portion of the mass to bulge out beyond the edge of the surfaces between which it was squeezed, without being thoroughly pressed. It was therefore, ''cut off all round'' with a [[Illustrated Companion to the Latin Dictionary/Culter|knife]], and again placed under the beam, and the juice it yielded was the ''circumcidaneum''. When the mass of skins was enclosed in a basket (''[[Illustrated Companion to the Latin Dictionary/Fiscina|fiscina]]''), or between laths of wood (''[[Illustrated Companion to the Latin Dictionary/Regula|regulae]]''), it was purposely to prevent it from bulging out, and, consequently, when so treated, there was no ''circumcidaneum'' produced. Cato, ''R. R.'' 23. 4. Varro. ''R. R.'' i. 24. Columell. xii. 36. Plin. ''H. N.'' xiv. 23. and 25. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Manufacture of Oil and Wine]] g8su44jl7o6iprp5ebgp1zghxaxwwa1 Illustrated Companion to the Latin Dictionary/Circumcisorium 0 311887 2683641 2671517 2024-11-11T15:57:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683641 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCUMCISO'RIUM'''. An instrument employed by veterinaries for bleeding cattle in the feet. Veget. ''Vet.'' i. 26. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 3zwezva1tfrnhnfisvnxk7726ut7dw9 Illustrated Companion to the Latin Dictionary/Circumsitium 0 311888 2683642 2671518 2024-11-11T15:57:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683642 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCUMSIT'IUM'''. (Varro, ''R. R.'' i. 54.) Same as [[Illustrated Companion to the Latin Dictionary/Circumcidaneus|CIRCUMCIDANEUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] qxooencz46ez31840cgcpu4z5fqyskd Illustrated Companion to the Latin Dictionary/Circus 0 311889 2683643 2671519 2024-11-11T15:57:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683643 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRCUS''' ({{lang|grc|Κίρκος.}}) Polyb. xxx. 13. 2.) A Roman circus, or ''race-course'', which, in the earliest times, was nothing more than a flat open space, round which temporary wooden platforms or scaffoldings were raised for the spectators to stand upon; but even before the destruction of the monarchy, a permanent building was constructed for the purpose, and laid out upon a regular plan, ever afterwards retained until the final dissolution of the empire; and then the entire edifice, with its race-course and appendages, were included under the general name of circus. Liv. i. 35. Varro, ''L. L.'' v. 135. Dionys. iii. 68. The ground-plan was laid out in an oblong form, terminating in a semicircle at one extremity, and enclosed at the opposite end by a pile of buildings called "the town" (''[[Illustrated Companion to the Latin Dictionary/Oppidum|oppidum]]''), under which the stalls (''[[Illustrated Companion to the Latin Dictionary/Carcer|carceres]]'') for the horses and chariots were distributed, marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=A. A.}} in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Circus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 165.jpg|engraving |caption=Circus/1.1}}, which represents the ground-plan of a circus still remaining in considerable preservation on the Appian Way, near Rome, commonly known as the Circus of Caracalla. A long low wall (''[[Illustrated Companion to the Latin Dictionary/Spina|spina]]'', {{Illustrated Companion to the Latin Dictionary/Inscription|text=B}} on the plan) was built lengthways down the course, so as to divide it, like a barrier, into two distinct parts; and at each of its ends was placed a goal (''[[Illustrated Companion to the Latin Dictionary/Meta|meta]]''), round which the chariots turned; the one nearest to the stables ({{Illustrated Companion to the Latin Dictionary/Inscription|text=C}}) being termed ''meta prima'', the farthest one ({{Illustrated Companion to the Latin Dictionary/Inscription|text=D}}) ''meta secunda''. It will be perceived that the two sides of the circus in the example are not quite parallel to each other, and that the ''spina'' is not exactly equidistant from both sides. Perhaps this is an exceptional case, only adopted in structures of a limited extent, like the present one, with the object of affording most room for the chariots at the commencement of the race, when they all started abreast; but when the goal at the bottom ({{Illustrated Companion to the Latin Dictionary/Inscription|text=D}}) had been turned, their position would be more in column than in line; and consequently less width would be required across that side of the course. For a similar reason, the right horn of the circus is longer than the left; and the stalls ({{Illustrated Companion to the Latin Dictionary/Inscription|text=A A}}) are arranged in the segment of a circle, of which the centre falls exactly in the middle point ({{Illustrated Companion to the Latin Dictionary/Inscription|text=E}}), between the first ''meta'' and the side of the building, at which the race commenced. The object of this was that all the chariots, as they came out from their stalls, might have the same distance to pass over before they reached the spot where the start took place, which was at the opening of the course, where a chalked rope (''[[Illustrated Companion to the Latin Dictionary/Linea|alba linea]]'', {{Illustrated Companion to the Latin Dictionary/Inscription|text=E}}) was fastened across from two small marble pillars (''[[Illustrated Companion to the Latin Dictionary/Hermulae|hermulae]]''), and loosened away from one side, as soon as all the horses had brought up fairly abreast of it, and the signal for the start had been displayed. The outbuilding ({{Illustrated Companion to the Latin Dictionary/Inscription|text=F}}) is the emperor's box (''pulvinar''); and the one on the opposite side ({{Illustrated Companion to the Latin Dictionary/Inscription|text=G}}) supposed to have been intended for the [[Illustrated Companion to the Latin Dictionary/Magistratus|magistrate]] (''editor spectaculorum''), at whose charge the games were exhibited. In the centre of the end occupied by the stalls was a grand entrance ({{Illustrated Companion to the Latin Dictionary/Inscription|text=H}}), called ''porta pompae'', through which the Circensian procession entered the ground before the races commenced; another one was constructed at the circular extremity ({{Illustrated Companion to the Latin Dictionary/Inscription|text=I}}), called ''porta triumphalis'', through which the victors left the ground in a sort of [[Illustrated Companion to the Latin Dictionary/Triumphus|triumph]]; a third is situated on the right side ({{Illustrated Companion to the Latin Dictionary/Inscription|text=K}}), called ''porta libitinensis'', through which the killed or wounded drivers were conveyed away, and two others ({{Illustrated Companion to the Latin Dictionary/Inscription|text=L L}}) were left close by the ''carceres'', through which the chariots were driven into the ground. As regards the external and internal elevation of the edifice, a circus was constructed upon a similar design to that adopted for [[Illustrated Companion to the Latin Dictionary/Theatrum|theatres]] and amphitheatres; consisting on the outside of one or more stories of arcades, according to the size and grandeur of the building, through which the spectators entered upon the [[Illustrated Companion to the Latin Dictionary/Scalae|staircases]], leading into the interior of the fabric. The interior was arranged in rows of [[Illustrated Companion to the Latin Dictionary/Sedes|seats]], divided into tiers, and separated by stairs and landing-places, in the same manner as described and illustrated under the word [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|AMPHITHEATRUM]]; of which a fair idea may be conceived from the {{Illustrated Companion to the Latin Dictionary/Image Location|text=next engraving |imagelink=Media:Circus 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|next engraving |caption=Circus/1.2}}, representing the ancient race-course at Constantinople, as it appears on an old map, executed before that city was taken by the Turks. Though a ruin, it shows distinctly the arcades and outer shell of the building; some fragments of the rows of seats for the spectators; the ''spina'', with its [[Illustrated Companion to the Latin Dictionary/Obeliscus|obelisks]] and [[Illustrated Companion to the Latin Dictionary/Columna|columns]] nearly perfect; the ''meta prima'' on the right hand of it; the ''oppidum'' and ''carceres'', arranged on a curved line, like the first example; and one of the gates, through which the chariots entered the ground, like those marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=L L}} on the ground-plan; it is besides remarkable as affording the only known instance in which the superstructure of a circus is exhibited. <gallery> File:Circus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 165.jpg|Circus/1.1 File:Circus 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|Circus/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Racecourse and Races]] [[Category:Classed Index/Public Places and Buildings]] 1zyx2f0wer7dl853oeej0icescg94j8 Illustrated Companion to the Latin Dictionary/Cirratus 0 311890 2683644 2671521 2024-11-11T15:57:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683644 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRRA'TUS'''. Of men or women (Mart. ix. 30. Ammian. xiv. 6. 20.); see [[Illustrated Companion to the Latin Dictionary/Cirrus|CIRRUS]] 1. Of cloth fabrics (Capitol. ''Pertinax.'' 8.); see [[Illustrated Companion to the Latin Dictionary/Cirrus|CIRRUS]] 8. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] c1b1g5e13c4zwh8c3jswinsyvbmn5td Illustrated Companion to the Latin Dictionary/Cirrus 0 311891 2683645 2671522 2024-11-11T15:58:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683645 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIRRUS'''. Properly, a lock of curly hair, growing in a full and natural curl, as contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Cincinnus|Cincinnus]]'', a ringlet or twisted curl, mostly made with the irons; such, for instance, as was natural to the youth of Greece, before they attained the age of manhood, when their locks were cut off, and dedicated to some deity (Varro, ''ap.'' Non. ''s. v.'' p. 94.); or to the Germans (Juv. ''Sat.'' xiii. 164.) and Gauls, who were distinguished amongst the ancients for the abundance and beauty of their hair, and, consequently, in all works of art, are universally characterized by this property. See the illustration, ''s.'' [[Illustrated Companion to the Latin Dictionary/Comatus|COMATUS]]. 2. ''Cirrus in vertice'' ({{lang|grc|μαλλòς ἀθλητοῦ}}, Gloss. Vet.) A tuft of hair drawn up all round the head, and tied into a bunch on the occiput, as was the practice of athletes, wrestlers, boxers, &c., in order to avoid being seized by the hair in the heat of contest, as exhibited in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cirrus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|illustration |caption=Cirrus/2.1}}, from a bas-relief in the Vatican, representing a pair of ''[[Illustrated Companion to the Latin Dictionary/Pancratias|Pancratiastae]]''. The example likewise explains a passage of Suetonius (''Nero'', 45.), in which it is related, that during the insurrection of Vindex, and while the city of Rome was suffering severely from famine, a vessel arrived from Alexandria, which, instead of being laden with grain, only brought a cargo of fine sand for the use of the athletes maintained by the emperor. The population, enraged at this, fastened a tuft of hair (''cirrus in vertice'') on the top of all his statues, with a pasquinade below in Greek characters, alluding to the insurrection of Vindex, and thus implying that the emperor, as an athlete, was about to commence a contest in which he would be worsted. 3. The ''forelock'' of a horse, when tied up into a tuft at the top of his head, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cirrus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|example |caption=Cirrus/3.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]], instead of being left to fall over his forehead, when it was called ''[[Illustrated Companion to the Latin Dictionary/Capronae|capronae]].'' Veget. ''Vet.'' iv. 2. 4. The ''fetlock tuft'' of a horse. Veget. ''Vet.'' ii. 28. Id. iv. 1. 5. The ''topknot'', or tuft upon the heads of certain birds. Plin. ''H. N.'' xi. 4. 6. A tuft of flowers, which grow in close bunches or tufts. Plin. ''H. N.'' xxvi. 20. 7. The arms of the polypus, which are divided into numerous feelers, like a bunch of hair. Plin. ''H. N.'' xxvi. 37. 8. The ''fringe'' on a piece of cloth (Phaedr. ii. 5. 13.), which was produced by leaving the ends of the warp threads upon the cloth after it was taken from the loom, instead of cutting them off. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cirrus 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|example |caption=Cirrus/8.1}} is from a Pompeian painting; and compare the article and illustration ''s. [[Illustrated Companion to the Latin Dictionary/Tela|Tela recta]].'' <gallery> File:Cirrus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|Cirrus/2.1 File:Cirrus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 166.jpg|Cirrus/3.1 File:Cirrus 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|Cirrus/8.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Hair and Beard]] [[Category:Classed Index/The Horse]] [[Category:Classed Index/The Gymnasium and Palaestra]] 1r2bl6v9y12824vsz6t3xz0g9b56in9 Illustrated Companion to the Latin Dictionary/Cisiarium 0 311892 2683647 2671523 2024-11-11T15:58:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683647 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISIA'RIUM'''. A manufactory where gigs (''[[Illustrated Companion to the Latin Dictionary/Cisium|cisia]]'') were built. Inscript. ''ap.'' Fabrett. p. 91. 179. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] i83sky9furcgmhnodph5b4fssl9spzg Illustrated Companion to the Latin Dictionary/Cisiarius 0 311893 2683648 2671524 2024-11-11T15:58:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683648 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISIA'RIUS'''. One who builds gigs (''[[Illustrated Companion to the Latin Dictionary/Cisium|cisia]]''). Inscript. ''ap.'' Mur. p. 979. 6. p. 108. 4. 2. The driver of a hired gig (''cisium''), like our cab driver. Ulp. ''Dig.'' 19. 2. 13.) See the ''[[Illustrated Companion to the Latin Dictionary/Cisium|next wood-cut]]'', and observe that the driver sits on the ''near side'', which is still the practice in Italy. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 04bh8hqwsegypsngbe5z8e7aj4u1ivh Illustrated Companion to the Latin Dictionary/Cisium 0 311894 2683649 2671525 2024-11-11T15:58:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683649 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIS'IUM'''. A light two-wheeled ''chaise'' or ''gig'' (Non. ''s. v.'' p. 86.), employed by the Romans as a public and private conveyance, when rapidity of transit was required. (Cic. ''Phil.'' ii. 31. Id. ''Rosc. Am.'' 7. Virg. ''Catal.'' viii. 3.) It carried two persons, the driver and another, was open in front, and furnished with shafts, to which one, or sometimes two, outriggers (Auson. ''Ep.'' viii. 6. '' cisio trijugi''), were occasionally added, as is still the practice in the Neapolitan calessin. Most of these particulars are shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cisium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|example |caption=Cisium/1.1}}, copied from a bas-relief on the monument at Igel; but which is incorrectly given in the English edition of Wyttenbach's Treves, where the outrigger is omitted. <gallery> File:Cisium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|Cisium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Carriages]] nagb682y2axfurzbtxzldngtn61hofa Illustrated Companion to the Latin Dictionary/Cisorium 0 311895 2683650 2671526 2024-11-11T15:58:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683650 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISO'RIUM'''. A sharp cutting instrument employed by veterinaries. Veget. ''Vet.'' ii. 22. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 229iq5hfajvf7fxnpgcm78701x2ywzw Illustrated Companion to the Latin Dictionary/Cissybium 0 311896 2683651 2671527 2024-11-11T15:58:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683651 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISSYB'IUM''' ({{lang|grc|κισσύβιον}}). A Grecian drinking bowl, with a handle; originally made of ivy wood, but, subsequently, distinguished by a wreath of ivy leaves and berries carved upon it. Macrob. ''Sat.'' v. 21. Theocr. ''Id.'' i. 27. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Drinking Cups]] 4cl3v9gpu07edn5cwxdv53l8gaa25sf Illustrated Companion to the Latin Dictionary/Cista 0 311897 2683652 2671528 2024-11-11T15:59:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683652 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTA''' ({{lang|grc|κίστη}}). A ''deep cylindrical basket'', covered with a lid, and made of wickerwork (Plin. ''H. N.'' xv. 18. n. 2. Id. xvi. 77.), which was employed in various ways, as its form and character rendered it applicable. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|example |caption=Cista/1.1}} here introduced is copied from a Roman bas-relief; but baskets of a similar form and character are frequently represented both in sculpture and [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. When ''square cistae'' are mentioned (Columell. xii. 54. 2.), the very addition of the epithet implies an unusual shape; and the uniform character of the following illustrations, all representing different objects which bore the common name of ''cista'', is sufficient to declare the figure which presented itself to the ancient mind in correspondence with that name. 2. A ''money-box'' (Hor. ''Ep.'' i. 17. 54. Cic. ''Verr.'' ii. 3. 85.), undoubtedly of smaller dimensions than the coffer or chest, of which an illustration is introduced ''s.'' [[Illustrated Companion to the Latin Dictionary/Arca|ARCA]] 1. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=specimen |imagelink=Media:Cista 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|specimen |caption=Cista/2.1}} here annexed is from an original of earthenware, which has a slit at the top for dropping in the money, like those now used by the licensed beggars in the Italian towns. 3. A ''book-basket'' (Juv. iii. 206.), similar to the ''capsa'' in form and character, but made of wicker-work, instead of wood, and like that also used for other similar purposes, as for keeping clothes (Poeta vet. ''ap.'' Quint. viii. 3. 19.) See the illustrations ''s.'' [[Illustrated Companion to the Latin Dictionary/Capsa|CAPSA]]. 4. A basket employed at the [[Illustrated Companion to the Latin Dictionary/Comitium|Comitia]] and in the courts of justice, into which the voters and the judges cast the tablets (''[[Illustrated Companion to the Latin Dictionary/Tabella|tabellae]]'') by which their votes or sentences were declared. (Auctor. ''ad'' Herenn. 1. 12. Plin. ''H. N.'' xxxiii. 2. § 7. Manutius ''de Comit. Rom.'' xv. p. 572. Wunder. ''Codex Erfutens.'' p. 158. seqq.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cista 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|illustration |caption=Cista/4.1}} is from a coin of the Cassian family, and represents a voter dropping his tablet of acquittal (marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=A}} for ''absolvo'') into the ''cista''. 5. The ''mystic cist'', a covered basket, box, or case, in which the sacred utensils and other articles appertaining to the rites of Ceres and Bacchus were enclosed, in order to conceal them from the eyes of profane beholders, whilst carried in solemn procession upon the festivals appointed for those deities; for all the ceremonies connected with their worship were conducted in profound secrecy. (Catull. 64. 260. Tibull. i. 7. 48. Compare Ov. ''A. Am.'' ii. 609.) There is no doubt that the ''cista'' employed for this purpose was, in the first instance a mere ''wicker basket'', similar to the one delineated in the first wood-cut which illustrates this article; for it is so represented on numerous coins and bas-reliefs, where the wicker-work is expressed in detail; but, subsequently, or amongst wealthy congregations, it was made of more costly materials, and elegant workmanship, as proved by two originals in bronze now preserved at Rome; one of which was found near the ancient Labicum, the other at Praeneste. The latter is represented in the annexed {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Cista 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|engraving |caption=Cista/5.1}}. It stands upon three feet; the handles by which it was carried are observable at the sides; the lid is surmounted by two figures, a bacchante and a faun; and the outside is covered with a design in outline, representing the reception of the Argonauts in the arsenal at Cyzicus. In it were found the following objects; another small case, a model of a kid, and of a panther, a ''[[Illustrated Companion to the Latin Dictionary/Patera|patera]]'', a ''[[Illustrated Companion to the Latin Dictionary/Ligula|ligula]]'', a sharp pointed instrument like the ''[[Illustrated Companion to the Latin Dictionary/Stylus|stylus]]'', and a piece of metal of triangular form, the ''pyramid'' ({{lang|grc|πυραμίς}}), mentioned by Clemens of Alexandria as one of the articles usually contained in these cases. The other one, found at Labicum, is similar in form, material, and style of execution; excepting that it has three figures on the lid; Bacchus in the centre draped with a robe covered with stars, to indicate that he was the nocturnal Bacchus (''Nyctelius Pater'', Ov. ''A. Am.'' i. 567.), at which time the orgies were celebrated (Serv. ''ad Aen.'' iv. 303. Compare Liv. xxxix. 8. seqq.); and a Faun in the ''[[Illustrated Companion to the Latin Dictionary/Nebris|nebris]]'' on each side of him. The inside contained a ''[[Illustrated Companion to the Latin Dictionary/Patera|patera]]'', on which the contest between Pollux and Amicus king of Bebrycia, with Diana between them, was represented in contorniate figures, the names of each being inscribed over them in a very ancient Latin form, {{Illustrated Companion to the Latin Dictionary/Inscription|text=POLUCES}}, {{Illustrated Companion to the Latin Dictionary/Inscription|text=AMUCES}}, and {{Illustrated Companion to the Latin Dictionary/Inscription|text=LOSNA}}, the old name for Diana. Under the feet of the figures on the lid, there is an inscription, resembling in its spelling and Latinity the style of that on the Duilian Column; and testifying that the vessel was presented by a female, and made by a Roman artist of the name of Novius Plautius:{{mdash}} {{Illustrated Companion to the Latin Dictionary/Inscription|text=DINDIA . MACOLNIA . FILEA . DEDIT . NOVIOS . PLAVTIOS . MED. ROMAI. FECID.}} <gallery> File:Cista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 167.jpg|Cista/1.1 File:Cista 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|Cista/2.1 File:Cista 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|Cista/4.1 File:Cista 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 168.jpg|Cista/5.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Baskets]] [[Category:Classed Index/Implements of Worship and Sacrifice]] tepb3v9tr8iwn1vz5ttkuvkz3twarkw Illustrated Companion to the Latin Dictionary/Cistellatrix 0 311898 2683653 2683353 2024-11-11T15:59:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683653 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTELLA'TRIX'''.<ref group="Note" name="Rich1849_Cestellatrix"/> A female slave, who had charge of her mistress's clothes, trinkets, &c. kept in a ''[[Illustrated Companion to the Latin Dictionary/Cista|cista]]''. Plaut. ''Trin.'' ii. 1. 30. == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="Rich1849_Cestellatrix">In the 1849-edition of Anthony Rich's "Illustrated Companion to the Latin Dictionary, and Greek Lexicon", this article is listed as "CESTELLA'TRIX", which is an obvious misspelling.</ref> }} == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] 1g5oahlw4hjzw3aiith783w9jidtuni Illustrated Companion to the Latin Dictionary/Cistella 0 311899 2683654 2671530 2024-11-11T15:59:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683654 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTELLA''' ({{lang|grc|κιστίς}}). A small [[Illustrated Companion to the Latin Dictionary/Cista|CISTA]]. Plaut. ''Cist.'' iv. 1. 3. Ter. ''Eun.'' iv. 6. 15. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0wq1j32nfq10itk0egjnboa6gffcors Illustrated Companion to the Latin Dictionary/Cistellula 0 311900 2683655 2671531 2024-11-11T15:59:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683655 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTELL'ULA'''. A very small ''[[Illustrated Companion to the Latin Dictionary/Cista|cista]]''; diminutive of [[Illustrated Companion to the Latin Dictionary/Cistella|CISTELLA]]. Plaut. ''Rud.'' ii. 3. 60. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] trkd964g3uh0dosp1ykm8iv2q5h7j7u Illustrated Companion to the Latin Dictionary/Cisterna 0 311901 2683656 2671532 2024-11-11T15:59:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683656 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTER'NA'''. An artificial tank or reservoir, sunk in the ground, and frequently covered in with a roof (Varro, ''R. R.'' i. 11.), for the purpose of collecting and preserving good water for the use of a household. (Columell. i. 5. Pallad. i. 17.) It differs from our "cisterns," which are above ground; and from a "well" (''puteus''), which is supplied by springs. 2. ''Cisterna frigidaria''. Perhaps an ice house. Pet. ''Sat.'' 73. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 90i6xoycoggdava48pcp3wxxnis5vdg Illustrated Companion to the Latin Dictionary/Cistifer 0 311902 2683657 2671533 2024-11-11T16:00:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683657 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIS'TIFER'''. One who carries a ''[[Illustrated Companion to the Latin Dictionary/Cista|cista]]'', box, or burden; a ''porter''. Mart. ''Ep.'' v. 17. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] g2ardbhovtwhj9wln0h9o8is239754o Illustrated Companion to the Latin Dictionary/Cistophorus 0 311903 2683658 2671535 2024-11-11T16:00:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683658 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CISTOPH'ORUS''' ({{lang|grc|κιστοφόρος}}). One who carried the mystic case ([[Illustrated Companion to the Latin Dictionary/Cista|CISTA]], 5.) in certain religious processions. In the rites of Ceres and Bacchus, or of the Egyptian deities, Isis and Osiris, this service was performed by ''women'', as represented in the annexed {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cistophorus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 169.jpg|illustration |caption=Cistophorus/1.1}} from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. The wreath of ivy leaves and berries (''[[Illustrated Companion to the Latin Dictionary/Corymbus|corymbus]]'') round the head, show her to have been a follower of Bacchus; and the bird's eye observable on the head of the jug indicates a priestess of Osiris, whose symbol amongst the Egyptians was an eye (Winkelm. ''Cab. Stosch.'' p. 2.); and as Bacchus and Osiris were the same deity, under different names, it is clear that she is a ''cistophora'', and not a ''[[Illustrated Companion to the Latin Dictionary/Canephora|canephora]]'', as the editors of the Museo Borbonico have erroneously termed her, from want of attention to the above particulars. In the ceremonies of Bellona, on the contrary, the ''[[Illustrated Companion to the Latin Dictionary/Cista|cista]]'' was carried by men, as proved by an ancient marble discovered on the Monte Mario near Rome, which bears the following inscription:{{mdash}}{{Illustrated Companion to the Latin Dictionary/Inscription|text=L. LARTIO . ANTHO . CISTOPHORO . AEDIS . BELLONAE}}, &c., and a figure of the ''cistophorus'' carved upon it. He is draped in a manner closely resembling the preceding figure, with a [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]] reaching to the feet, but slightly raised, so as to expose an under one beneath it; a ''[[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]'' over the shoulder; a chaplet round the head; and an ''[[Illustrated Companion to the Latin Dictionary/Infula|infula]]'' hanging down in front of the breast; in the right hand a lustral branch, and in the left two double axes (''[[Illustrated Companion to the Latin Dictionary/Bipennis|bipennes]]''), characteristic of the priests of Bellona. Inscript. ''ap.'' Don. 62. and 135. Compare Demosth. p. 313. 28. ed. Reiske. Giovanni Lami, ''Dissertaz. sopra le Ciste Mistiche''. 2. A silver coin, worth about four [[Illustrated Companion to the Latin Dictionary/Drachma|drachmae]], which passed current in Asia, whence the expression ''in cistophoro'' (Cic. ''Att.'' xi. 1.) is equivalent to saying "in Asiatic money." It received the name either from having an impression of the sacred ''[[Illustrated Companion to the Latin Dictionary/Cista|cista]]'' upon it, or, as is more probable, of the shrub ''cistus'' ({{lang|grc|κίστος}}). <gallery> File:Cistophorus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 169.jpg|Cistophorus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Foreign Coins]] [[Category:Classed Index/Ministers and Attendants]] tikffpicke52j9vexobx52rjxvsk3q3 Illustrated Companion to the Latin Dictionary/Cistula 0 311904 2683659 2671536 2024-11-11T16:00:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683659 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CIS'TULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cista|CISTA]]. Plaut. Amph. i. 1. 264. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 8vvjofnek5uhewr2wl0vfva24x5a5f0 Illustrated Companion to the Latin Dictionary/Cithara 0 311905 2683661 2683355 2024-11-11T16:00:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683661 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CITH'ARA''' ({{lang|grc|κιθάρα, κίθαρις}}). A stringed instrument of very great antiquity, resembling in form the ''human chest and neck'' (Isidor. ''Orig.'' ii. 3. 22.), and so corresponding with our ''guitar'', a term which comes to us through the Italian ''chitarra''; the Roman ''c'' and Italian ''ch'' having the same sound as the greek {{lang|grc|κ}}. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cithara 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|illustration |caption=Cithara/1.1}} here introduced, from an ancient bas-relief preserved in the hospital of St. John in Lateran at Rome, agrees so closely with the description which Isidorus gives of the instrument, as to leave little doubt that it preserves the real form of the ''cithara'', in the strict and original sense of that word; although it may have been sometimes applied by the Greek poets in a less special or determinate meaning. See also the two following words and illustrations ([[Illustrated Companion to the Latin Dictionary/Citharista|CITHARISTA]], [[Illustrated Companion to the Latin Dictionary/Citharistria|CITHARISTRIA]]). <gallery> File:Cithara 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|Cithara/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Stringed Instruments]] kktkrm1jgvn0cm6pxyazp4nvdl5cndj Illustrated Companion to the Latin Dictionary/Citharista 0 311906 2683662 2671538 2024-11-11T16:00:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683662 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CITHARIS'TA''' ({{lang|grc|κιθαριστής}}). One who plays upon the ''[[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]'', or ''guitar''. (Cic. ''Phil.'' v. 6.) Homer describes the manner in which the player held this instrument by saying that it was placed ''upon the arm'' ({{lang|grc|ἐπωλένιον κιθαρίζων}}. ''Hymn. Merc.'' 432.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Citharista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|annexed wood-cut |caption=Citharista/1.1}}, representing an Egyptian ''citharista'', from the tombs at Thebes. It affords also a further confirmation that the character ascribed to the ''cithara'' in the [[Illustrated Companion to the Latin Dictionary/Cithara|last article]] is the correct one, and will likewise serve as an authority for correcting the false reading {{lang|grc|ὑπολένιον}} in the same hymn (v. 507.). It was sometimes suspended across the shoulders by a ''[[Illustrated Companion to the Latin Dictionary/Balteus|balteus]]'' (Apul. ''Flor.'' ii. 15. 2. and [[Illustrated Companion to the Latin Dictionary/Citharistria|next wood-cut]]), and, like the [[Illustrated Companion to the Latin Dictionary/Lyra|lyre]], was occassionally struck with the ''[[Illustrated Companion to the Latin Dictionary/Plectrum|plectrum]]'', instead of the fingers. Hom. ''l. c.'' 498. <gallery> File:Citharista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|Citharista/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Musicians]] cl7s4drjp02fe84t9h50f4m7ch2t9yp Illustrated Companion to the Latin Dictionary/Citharistria 0 311907 2683664 2671539 2024-11-11T16:00:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683664 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CITHARIS'TRIA''' ({{lang|grc|κιθαριστρία, κιθαριστρίς}}). A female player upon the ''[[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]'' or ''guitar''. (Terent. ''Ph.'' i. 2. 32. and compare [[Illustrated Companion to the Latin Dictionary/Citharista|CITHARISTA]].) These women were frequently introduced, together with dancing and singing girls, to amuse the guests at an entertainment; and the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Citharistria 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|engraving |caption=Citharistria/1.1}}, from a tomb at Thebes in Egypt, is evidently intended to represent a character of that description, as is apparent from the attention bestowed upon the decoration of her person, the hair, earrings, necklace, bracelets on the arms and wrists, the shoes, and transparent drapery. <gallery> File:Citharistria 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 170.jpg|Citharistria/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Musicians]] ftxewnwokikhx10sdmv57exezve06vp Illustrated Companion to the Latin Dictionary/Citharoeda 0 311908 2683665 2671540 2024-11-11T16:01:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683665 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CITHAROE'DA'''. A female who plays the ''[[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]'', and at the same time accompanies it with her voice. Inscript. ''ap.'' Grut. 654. 2. ''ap.'' Mur. 941. 1. and compare [[Illustrated Companion to the Latin Dictionary/Citharistria|CITHARISTRIA]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Musicians]] ih62a0uuxj5mcg0qd4sh1h03gf0xg1p Illustrated Companion to the Latin Dictionary/Citharoedus 0 311909 2683666 2671541 2024-11-11T16:01:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683666 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CITHAROED'US''' ({{lang|grc|κιθαρῳδός}}). One who plays upon the ''[[Illustrated Companion to the Latin Dictionary/Cithara|cithara]]'', and sings at the same time. Quint. i. 12. 3. Id. iv. 1. 2. Cic. ''Mur.'' 13. and compare [[Illustrated Companion to the Latin Dictionary/Citharista|CITHARISTA]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] anjnudjbdo9l2jkk4fkz0o8r02bg1n9 Illustrated Companion to the Latin Dictionary/Clabulare 0 311910 2683667 2671542 2024-11-11T16:01:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683667 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLABULA'RE''', or '''CLAVULA'RE''', sc. ''vehiculum''. A large cart, with ''open sides made of rails'' (''clavulae'' or ''clavolae''), and intended for the conveyance of goods, as well as passengers. Under the Empire, it was commonly employed for the transport of soldiers, which was thence termed ''cursus clabularis''. (Impp. Constant. et Julian. ''Cod. Theodos.'' 6. 29. 2. Ammian. xx. 4. 11.) The cart in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Clabulare 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|illustration |caption=Clabulare/1.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, and was employed for the transport of wine. The open rail-work with which it is constructed, helps to authorize the interpretation given, which otherwise is to be regarded as more conjectural than positive. <gallery> File:Clabulare 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|Clabulare/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Carts]] pk8s9iwxadhzy82q0f2vrp9ah9c78b3 Illustrated Companion to the Latin Dictionary/Classiarii 0 311911 2683668 2671543 2024-11-11T16:01:41Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683668 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLASSIA'RII''' ({{lang|grc|ἐπιβάται}}). A class of soldiers trained for fighting on board ship (Hirt. ''B. Alex.'' 20.), thus corresponding in many respects with our ''marines''. But this branch of the military service was regarded by the Romans as less honourable than the other; for both the sailors (''nautae'') and the rowers (''[[Illustrated Companion to the Latin Dictionary/Remex|remiges]]'') are sometimes included under the general name of ''classiarii'' (Hirt. ''B. Alex.'' 2. Tac. ''Ann.'' xiv. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Classiarii 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|illustration |caption=Classiarii/1.1}} is from an ancient bas-relief published by Scheffer, ''Mil. Nav. Addend.'' <gallery> File:Classiarii 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|Classiarii/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Officers and Crew of the Marine]] mc9b24263dy29s4qe43h8py1a5p7n08 Illustrated Companion to the Latin Dictionary/Classici 0 311912 2683669 2671544 2024-11-11T16:01:52Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683669 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAS'SICI'''. Citizens who belonged to ''the first of the six classes'' into which the population of Rome was divided by Servius Tullius (Aul. Gell. vii. 13.); whence the expression ''scriptores classici'', classical authors, means those of the very first order. Aul. Gell. xix. 8. 6. 2. The horn-blowers who summoned the ''classes'' to the ''[[Illustrated Companion to the Latin Dictionary/Comitium|comitia]]'' by sound of the ''[[Illustrated Companion to the Latin Dictionary/Lituus|lituus]]'' or the ''[[Illustrated Companion to the Latin Dictionary/Cornu|cornu]]''. Varro, ''L. L.'' v. 91. [[Illustrated Companion to the Latin Dictionary/Cornicen|CORNICEN]], [[Illustrated Companion to the Latin Dictionary/Liticen|LITICEN]]. 3. Same as [[Illustrated Companion to the Latin Dictionary/Classiarii|CLASSIARII]]; including the fighting men as well as the ship's company. Curt. iv. 3. Tac. ''Hist.'' i. 31. ''ib.'' ii. 17. 4. ''Classica corona'' (Vellej. ii. 81. 3.); same as [[Illustrated Companion to the Latin Dictionary/Corona|CORONA NAVALIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Musicians]] gwpre5z3bmnbuc29hvlevs0x5icuj93 Illustrated Companion to the Latin Dictionary/Classicum 0 311913 2683670 2671545 2024-11-11T16:02:03Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683670 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAS'SICUM'''. Properly, a signal given by sound of trumpet; whence transferred to the instrument itself by which the signal was given. Serv. ''ad'' Virg. ''Aen.'' vii. 637. Virg. ''Georg.'' ii. 539. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] cxuf5uho6n11fq22b7ip6a48u0y7zv7 Illustrated Companion to the Latin Dictionary/Clathratus 0 311914 2683671 2671546 2024-11-11T16:02:14Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683671 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLATHRA'TUS'''. Closed or protected by cross-bars of trellis (''clathri''), as explained in the [[Illustrated Companion to the Latin Dictionary/Clathri|next paragraph]]. Plaut. ''Mil.'' ii. 4. 25. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] j03dye3f0ys50w6ewu9l9sbvv6d4gma Illustrated Companion to the Latin Dictionary/Clathri 0 311915 2683672 2671547 2024-11-11T16:02:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683672 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLA'THRI'''. A ''trellis'' or grating of wood or metal employed to cover over and protect an aperture, such as a door or [[Illustrated Companion to the Latin Dictionary/Fenestra|window]], or to enclose any thing generally. (Hor. ''A. P.'' 473. Plin. ''H. N.'' viii. 7. Cato, ''R. R.'' iv. 1. Columell. viii. 17. 10.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clathri 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|example |caption=Clathri/1.1}} represents the trellis which covered in the lunettes over the stalls (''[[Illustrated Companion to the Latin Dictionary/Carcer|carceres]]'') in the [[Illustrated Companion to the Latin Dictionary/Circus|circus]] of Caracalla. <gallery> File:Clathri 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 171.jpg|Clathri/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Windows]] 8zq2hbo3y9w5gzzcdm411im3unoko2r Illustrated Companion to the Latin Dictionary/Claustrum 0 311916 2683673 2671548 2024-11-11T16:02:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683673 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAUS'TRUM'''. One of the words employed by the Romans with reference to the closing of doors; and used at times in a sense as general and indefinite as our term "fastening," which may be equally applied to a lock, a [[Illustrated Companion to the Latin Dictionary/Pessulus|bolt]], a bar, or other contrivance, when there are no governing words to indicate the nature of the fastening intended. (Cic. ''Agr.'' i. 7. Claud. ''in Eutrop.'' 1. 195.) But many other passages as distinctly imply that the word had also a special meaning, expressive of some particular object which went under that name, and which would naturally possess some analogy with the other objects designated by the same term. Of these the one which best agrees with all these requirements is a ''staple'', ''hasp'', or ''box'' fixed on to a door-post, into which the bolt of a lock, whether turned by a [[Illustrated Companion to the Latin Dictionary/Clavis|key]] or shot by the hand, was inserted in order to fasten the door, as may be seen on the Egyptian door represented in the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Cardo|CARDO]]. This interpretation will coincide with most, if not all, of the expressions made use of in describing a forcible entry; which are such as these{{mdash}}to break through, pull out, or force back, the ''claustrum;'' and as the ancient doors were commonly made in two flaps, or had fastening at top and bottom, the plural ''claustra'' is mostly used (''ad claustra pessuli recurrunt'', for shutting (Apul. ''Met.'' i. p. 10. Varior.); ''claustra perfringere'', to break open (Id. p. 8.); ''evellere'' (Id. p. 70.); ''revelli'' (Liv. v. 21. Cic. ''Verr.'' ii. 4. 23.); ''claustris, quae accuratissime affixa fuerunt, violenter evulsis'' (Apul. ''Met.'' iii. p. 46.). Compare [[Illustrated Companion to the Latin Dictionary/Clausula|CLAUSULA]]. 2. Poetically, for the door itself (Mart. x. 28.); or the [[Illustrated Companion to the Latin Dictionary/Porta|gates]] of a city. Ovid. Met. iv. 86. 3. A cage or den in which wild beasts are enclosed. Hor. ''Od.'' iii. 11. 44. Stat. ''Sylv.'' ii. 5. 4. 4. In plural, the stalls for the horses in the [[Illustrated Companion to the Latin Dictionary/Circus|Circus]]. (Hor. ''Epist.'' i. 14. 9. Stat. ''Theb.'' vi. 399.) Same as [[Illustrated Companion to the Latin Dictionary/Carcer|CARCERES]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Locks and Fastenings]] 1v6br1qz0ahqx52pyqonwekohj0kn7p Illustrated Companion to the Latin Dictionary/Clausula 0 311917 2683674 2671549 2024-11-11T16:02:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683674 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAU'SULA'''. The ''handle'' of a [[Illustrated Companion to the Latin Dictionary/Strigilis|strigil]] (Apul. ''Flor.'' ii. 9. 2.), or other instrument, when made in such a manner that the hand was inserted into it, so that it formed a ring or guard all round it, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Clausula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|annexed example |caption=Clausula/1.1}}, from an original bronze strigil found in the baths at Pompeii. The ''clausula'' is thus contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Capulus|capulus]]'', a ''straight'' handle or haft, and from ''[[Illustrated Companion to the Latin Dictionary/Ansa|ansa]]'', a handle ''affixed to another'' object. The word is also allied to ''[[Illustrated Companion to the Latin Dictionary/Claustrum|claustrum]]'', the staple into which a bolt shoots, to which it has a considerable resemblance. <gallery> File:Clausula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|Clausula/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] 79oss8jgfn1eh86aah98i9do8z5tvgy Illustrated Companion to the Latin Dictionary/Clavarium 0 311918 2683675 2671550 2024-11-11T16:02:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683675 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVA'RIUM'''. An allowance of money made to the Roman soldiery, for the purpose of providing nails (''clavi caligares'') for their boots. Tac. ''Hist.'' iii. 50. and [[Illustrated Companion to the Latin Dictionary/Clavus|CLAVUS]], 5. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] llzqjgap3h6dqgsnww3x66gfgrloiyu Illustrated Companion to the Latin Dictionary/Clavator 0 311919 2683676 2671551 2024-11-11T16:03:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683676 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVA'TOR'''. Either a suttler, or soldier's servant, who carried his baggage (Plaut. ''Rud.'' iii. 5. 25.), in which sense it would be synonymous with [[Illustrated Companion to the Latin Dictionary/Calones|CALO]]; or, a recruit, who practised his exercises with a wooden stave ([[Illustrated Companion to the Latin Dictionary/Clava|CLAVA]], 2.) before being entrusted with a sword. Festus, ''s. Calones''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Servants and Camp-followers]] jocxr7ij23tzgn4iqtwilzy4fivdocx Illustrated Companion to the Latin Dictionary/Clavatus 0 311920 2683677 2671553 2024-11-11T16:03:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683677 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVA'TUS'''. ''Striped with gold, purple'', or other colours. It was customary amongst the Romans to weave stripes of this nature into their cloth fabrics, both such as were intended to be made up into garments (Vopisc. ''Bonos.'' 15.), as those which were manufactured for mere household purposes, such as table linen, napkins, &c. Lamprid. ''Alex. Sev.'' 37. [[Illustrated Companion to the Latin Dictionary/Clavus|CLAVUS]], 8, 9. 2. ''Studded with nails'', in reference to boots and shoes (Festus, ''s. v. Clavata''), implying either that the sole is set thick with hob-nails, like the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|example |caption=Clavatus/2.1}}, representing the sole or underneath part of a terra-cotta lamp made in the form of a shoe; or that it is armed with sharp projecting points, like the soldier's boot (''[[Illustrated Companion to the Latin Dictionary/Caliga|caliga]]''), which is represented by the illustration to [[Illustrated Companion to the Latin Dictionary/Clavus|CLAVUS]], 5. 3. Covered with prickles, spikes, or projections, like a mace or [[Illustrated Companion to the Latin Dictionary/Clava|club]]. <gallery> File:Clavatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|Clavatus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feet]] rld0cbj0m6f2flbu3iwdlkv4ya5py7a Illustrated Companion to the Latin Dictionary/Clava 0 311921 2683678 2671554 2024-11-11T16:03:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683678 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVA''' ({{lang|grc|ῥόπαλον}}). A stout, rough stick, thickening towards the butt-end, such as we might term a ''cudgel;'' sometimes used in an offensive manner (Cic. ''Verr.'' ii. 4. 43.), and frequently carried out of affectation by the ancient philosophers, instead of a walking stick (Sidon. ''Epist.'' iv. 11. ix. 9. Id. ''Carm.'' xv. 197.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Clava 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|annexed figure |caption=Clava/1.1}} of Democritus, from an engraved gem. 2. A heavy stick or stave, with which recruits were made to go through their exercises in lieu of a sword, and which they used against the dummy or manikin (''[[Illustrated Companion to the Latin Dictionary/Palus|palus]]''), a wooden figure set up for the purpose. Cic. ''Senect.'' 16. Veget. ''Mil.'' ii. 11. 3. ({{lang|grc|ῥόπαλον.}} Soph. ''Tr.'' 512.) A ''club'' or ''bludgeon'', such as was used by Hercules and Theseus. (Prop. iv. 9. 39. Suet. ''Nero'', 53.) It is always represented by the ancient [[Illustrated Companion to the Latin Dictionary/Scalptor|sculptors]] and [[Illustrated Companion to the Latin Dictionary/Pictor|painters]] as a formidable weapon, made thick and heavy at one extremity, and gradually tapering towards the other, by which it was held in the hand; and frequently with the knots left rough upon it (''irrasa'', Sil. Ital. viii. 584.); as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clava 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|example |caption=Clava/3.1}}, representing the club of Hercules, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. Compare [[Illustrated Companion to the Latin Dictionary/Claviger|CLAVIGER]], 1. 4. ({{lang|grc|κορύνη, ῥόπαλον σιδήρῳ τετυλωμένον}}). A ''mace'', or war club, having an iron head, thickly studded with knobs or sharp spikes, affixed to the wooden handle. In this form it is mentioned by Homer (''Il.'' vii. 141.), and by Herodotus (vii. 63.), when describing the accoutrements of the Assyrians who followed the army of Xerxes, and is represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Clava 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|engraving |caption=Clava/4.1}}, from an ancient Roman fresco painting of the Villa Albani, where it appears as the weapon of Mars; thus proving that the Romans were also acquainted with the implement, though they do not appear to have designated it by any characteristic name. <gallery> File:Clava 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|Clava/1.1 File:Clava 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 172.jpg|Clava/3.1 File:Clava 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|Clava/4.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Other Weapons]] dmi6w2k7r8ninmkkeeteqm1y0nh6es6 Illustrated Companion to the Latin Dictionary/Clavicula 0 311922 2683679 2671555 2024-11-11T16:03:41Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683679 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVIC'ULA''' ({{lang|grc|κλειδίον}}). Diminutive of [[Illustrated Companion to the Latin Dictionary/Clavis|CLAVIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dl46mmvhtpjg7q32511fdn53h2j0nqh Illustrated Companion to the Latin Dictionary/Claviger 0 311923 2683680 2671556 2024-11-11T16:03:52Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683680 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLA'VIGER''' ({{lang|grc|κορυνήτης}}). Armed with a ''[[Illustrated Companion to the Latin Dictionary/Clava|club]]''; or with a ''mace''. The club is well known as one of the weapons used by Hercules, whence he is distinguished by the epithet ''claviger'' (Ov. ''Met.'' xv. 22.); but in early times, and amongst many of the nations of antiquity, it was employed in warfare, as by the Dacians, on the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan, and by the rustic inhabitants of Latium in their contests with the Trojans, in the miniatures of the Vatican Virgil, from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Claviger 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|annexed figure |caption=Claviger/1.1}} is copied. The example under [[Illustrated Companion to the Latin Dictionary/Clava|CLAVA]], 4. shows the club in its improved form of a ''mace''; and illustrates the word ''claviger'', in the sense of a ''mace-bearer''. 2. ({{lang|grc|κλειδοῦχος}}). Bearing a [[Illustrated Companion to the Latin Dictionary/Clavis|key]]; an epithet given by the Romans to Janus, because he was supposed to be the guardian and overseer of all men's doors (Ovid, ''Fast.'' i. 228. Macrob. ''Sat.'' i. 9.); and by the Greeks to Cupid (Wink. ''Mon. Ined.'' 32.), which implied that he had the power of opening and shutting the abodes of Love; but more especially to Hecate triformis, as the goddess who kept the keys of Hades, and who is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Claviger 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|annexed engraving |caption=Claviger/2.1}}, from a small bronze statue. <gallery> File:Claviger 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 173.jpg|Claviger/1.1 File:Claviger 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|Claviger/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Other Weapons]] 5jfiiaa4p2nwjt9wvzvl526o02du3z7 Illustrated Companion to the Latin Dictionary/Clavis 0 311924 2683681 2671557 2024-11-11T16:04:03Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683681 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVIS''' ({{lang|grc|κλείς}}). A ''key'' adapted for opening a regular lock with wards, for raising a latch, or moving a mere bolt; and including all the varieties in form, size, or use, of which the following illustrations afford examples:{{mdash}} 1. A ''door-key''; made with regular wards, very like those now in use; as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|example |caption=Clavis/1.1}} annexed, from an original found at Pompeii. These were of the largest description, and employed for fastening the [[Illustrated Companion to the Latin Dictionary/Porta|gates]] of a city, the external doors of a house or other building, the [[Illustrated Companion to the Latin Dictionary/Cella|cellars]], store-houses, &c., and were carried by the officers or slaves who had charge of such respective localities, suspended from the girdle round their waists;{{mdash}}a purpose indicated by the tongue and eye in the preceding example. 2. A small key, such as was kept by the mistress of the house (''materfamilias''), or used for locking up closets, armoires, trinket-cases, book or money-boxes (see [[Illustrated Companion to the Latin Dictionary/Capsa|CAPSA]], where the lock and hasp is shown), &c., like the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavis 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|example |caption=Clavis/2.1}}, from the ''Dactyliotheca'' of Gorlaeus. Hor. ''Epist.'' i. 20. 3. Id. ''Sat.'' ii. 3. 146. 3. ''Clavis Laconica.'' A particular kind of key, probably invented in Egypt, though the Greeks ascribe its origin to the Laconians; supposed to be made with three teeth, like the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavis 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|example |caption=Clavis/3.1}} from an Egyptian original preserved in the British Museum. It was applied to the ''inside'' of the door by a person standing ''without'', who put his arm through a hole in the door made expressly for the purpose (''clavi immittendae foramen'', Apul. ''Met.'' iv. p. 70.), and then raised the latch, which fastened it, by means of the projecting teeth. This interpretation, however, mainly relies for its authority upon a passage in Plautus (''Most.'' ii. 1. 57.); in which Thranio, who is standing outside the house, and wishing to make it appear that the premises were no longer inhabited, locks the door on the outside with the door key which he held in his hand, and then orders the ''clavis Laconica'' to be given out to him, so that no one could gain ingress or egress without his assistance. But the whole subject is still very obscure and doubtful. 4. ''Clavis clausa.'' A small key, made without any neck or lever, such as the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavis 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|example |caption=Clavis/4.1}}, from an original in the ''Dactyliotheca'' of Gorlaeus, and which, consequently, would only be used for raising latches, or in small locks which required but slight force to turn them; and when introduced into the lock or door would be almost concealed by it. (Virg. ''Moret.'' 15.) But the interpretation, and indeed the reading of the passage itself, is extremely doubtful. Some think the ''clavis clausa'' and ''Laconica'' to be identical; and Aristophanes (''Thesm.'' 422.) certainly applies the epithet {{lang|grc|κρυπτὰ}} to the Laconian key with three teeth. 5. ''Clavis adultera.'' A ''false'' or ''skeleton'' key. Sall. Jugurth. 12. Compare Ovid. ''Art. Amat.'' iii. 643. 6. ''Clavis trochi'' ({{lang|grc|ἐλατήρ}}). The stick used by Greek and Roman boys for trundling their hoops (Propert. iii. 14. 6.); made of iron, with a hook at the end, or a round knob and bend in the neck, like the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavis 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|example |caption=Clavis/6.1}}, from a bas-relief of the Villa Albani. The epithet ''adunca'', applied to it by Propertius (''l. c.''), will suit either form. The manner of using the clavis, and the hook, is seen in the illustration to [[Illustrated Companion to the Latin Dictionary/Trochus|TROCHUS]]. <gallery> File:Clavis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|Clavis/1.1 File:Clavis 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|Clavis/2.1 File:Clavis 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 174.jpg|Clavis/3.1 File:Clavis 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|Clavis/4.1 File:Clavis 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|Clavis/6.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Locks and Fastenings]] 41vvgamzh89ihr8xuz14ug7eomj32ve Illustrated Companion to the Latin Dictionary/Clavulus 0 311925 2683682 2671558 2024-11-11T16:04:14Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683682 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLA'VULUS'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Clavus|CLAVUS]]; probably, also, a nail without a head (Cato, ''R. R.'' xxi. 3.); as ''clavulus capitatus'' (Varro, ''R. R.'' ii. 9. 15.), a small-headed nail. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 4ygb5q5r5lkfrtbpe7w0jw7d76t9avy Illustrated Companion to the Latin Dictionary/Clavus 0 311926 2683683 2671559 2024-11-11T16:04:25Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683683 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLAVUS''' ({{lang|grc|ἦλος}}). A nail for fixing or fastening one thing to another. Many specimens of ancient nails, of various forms and sizes, of bronze as well as iron, are preserved in the Cabinets of Antiquities, resembling in most respects those now in use. The Latin expression for driving a nail is ''clavum figere'' or ''pangere'' (Liv. vii. 3.), and the act is shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=figure annexed |imagelink=Media:Clavus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|figure annexed |caption=Clavus/1.1}}, which represents one of Trajan's soldiers making a stockade, the strength of which may be inferred from the immense size of the nail employed. 2. ''Clavus trabalis'', or ''tabularis''. A nail of the largest description, such as was employed in building, for fastening the main beams (''[[Illustrated Companion to the Latin Dictionary/Trabs|trabes]]''). Cic. ''Verr.'' vi. 21. Hor. ''Od.'' i. 35. 18. Petr. ''Sat.'' 75. 3. ''Clavus annalis''. The nail which was driven on the Ides of September in every year into the side wall of the [[Illustrated Companion to the Latin Dictionary/Templum|temple]] of [[Illustrated Companion to the Latin Dictionary/Capitolium|Jupiter Capitolinus]] (Liv. vii. 3.); a custom which is referred back to a very early period, and supposed to have been adopted as an expedient for reckoning the lapse of time before the use of letters was generally understood (Festus, ''s. v.''), and subsequently retained out of religious deference to old customs. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=fragment |imagelink=Media:Clavus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|fragment |caption=Clavus/3.1}} here introduced represents the four sides of part of a large bronze nail, now in the possession of the Italian historian Bianchini (''Storia Univers.'' tom. i. p. 156. tav. 9. {{Illustrated Companion to the Latin Dictionary/Inscription|text=A.}}), which, from the letters upon it, is believed to have been actually employed for the purpose described. 4. ''Clavus muscarius''. A nail with a large broad mushroom-shaped head (Vitruv. vii. 3. 11.), like the one represented under [[Illustrated Companion to the Latin Dictionary/Bulla|BULLA]]; but larger and of coarser workmanship. 5. ''Clavus caligaris''. A sharp nail or spike, with which the soles of soldiers' boots (''[[Illustrated Companion to the Latin Dictionary/Caliga|caligae]]'') were furnished (Plin. ''H. N.'' ix. 33. Juv. iii. 247. Id. xvi. 24. Isidor. ''Orig.'' xix. 34. 13.); the sharp ends projecting from the sole, as in our cricket shoes, in order to afford the wearer a firmer footing on the ground. (Joseph. ''Bell. Jud.'' vi. 1. 7.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clavus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 176.jpg|example |caption=Clavus/5.1}} introduced is given by Ferrarius, as copied from the [[Illustrated Companion to the Latin Dictionary/Arcus|arch]] of Constantine at Rome. He states that the spikes were clearly distinguishable in his time, but the artist has certainly committed an error in leaving the toes exposed, for the ''caliga'' was a close boot; see [[Illustrated Companion to the Latin Dictionary/Caliga|that word]], and [[Illustrated Companion to the Latin Dictionary/Caligarius|CALIGARIUS]]. 6. ''Clavus gubernaculi''. The ''helm'' or ''tiller'' of an ancient rudder; which was a cross-bar (''fustis'', Serv. ''ad'' Virg. ''Aen.'' v. 176.), fixed to the upper part of the handle (''[[Illustrated Companion to the Latin Dictionary/Ansa|ansa]]'') at right angles to it, so that it fell within the ship, and enabled the steersman to move his helm in the direction required. (Isidor. ''Orig.'' xix. 2. 12.) When the vessel was furnished with a rudder on each quarter, and sufficiently small to be managed by a single [[Illustrated Companion to the Latin Dictionary/Gubernator|helmsman]], he held a ''clavus'' in each hand; but in heavy weather, or in larger vessels, each rudder had its own helmsman. The steerage was effected in both cases by raising or depressing the ''clavus'', at the same time turning it slightly in or out, in order to give the blade of the rudder a less or greater resistance against the water; an effect well known to those who are accustomed to rowing, or steering with an [[Illustrated Companion to the Latin Dictionary/Remus|oar]]; and our own nautical phrases "helm ''up''" and "helm ''down''," which still remain in use, though expressive of a very different operation, undoubtedly originated in this practice of the ancients; for in the Latin and Anglo-Saxon Glossary of Aelfricus, the word ''clavus'' is translated ''helma'', our helm. All these particulars are clearly illustrated by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Clavus 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 176.jpg|engraving |caption=Clavus/6.1}}, which represents the after part of an ancient ship, on a bas-relief discovered at Pozzuoli. 7. A ''stripe'' of purple colour woven into the texture of a piece of cloth, as an ornament, for wearing apparel, or for the linen employed in household purposes, such as napkins, tablecloths, coverlets for couches, &c. Mart. ''Ep.'' iv. 46. 17. Pet. ''Sat.'' 32. 2. Ammian. xvi. 8. 8. 8. ''Clavus Latus''. The ''broad stripe''; an ornamental band of purple colour, running down the front of a [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]], in a perpendicular direction immediately over the front of the chest, the right of wearing which formed one of the exclusive privileges of a Roman senator, though at a later period it appears to have been sometimes granted as a favour to individuals of the [[Illustrated Companion to the Latin Dictionary/Eques|equestrian order]]. (Hor. ''Sat.'' i. 6. 28. Acro ''ad'' Hor. ''Sat.'' i. 5. 36. Quint. viii. 5. 28. Festus, ''s. v.'' Clavatus. Ovid. ''Trist.'' iv. 10. 29. Plin. ''Ep.'' ii. 9.) As the ''clavus'' was a mere shade of colour woven up with the fabric, and, consequently, possessed no ''substance'' of its own, it is not indicated upon any of the statues which represents persons of senatorial rank; for the [[Illustrated Companion to the Latin Dictionary/Scalptor|sculptor]] deals only with substantial forms, and the Roman [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]] which remain to us are mostly imitations of Greek works, representing mythological or heroical subjects, or otherwise scenes of common life. Consequently, we have no known example of the broad senatorial ''clavus'' upon any existing monument; but a fair notion of its real character may be obtained from the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Clavus 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|annexed wood-cut |caption=Clavus/8.1}}, representing the Persian ''[[Illustrated Companion to the Latin Dictionary/Sarapis|sarapis]]'', as worn by Darius, in the Pompeian [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] of the battle of Issus; and which was decorated with a similar ornament, with the exception, that the stripe of the Persian kings was white upon a purple ground, that of the Roman senators purple on a white one. 9. ''Clavus angustus''. The ''narrow stripe''; a distinctive badge of the [[Illustrated Companion to the Latin Dictionary/Eques|equestrian order]]. (Paterc. ii. 88. 2.) It was of purple colour, like the former, and also a decoration to the tunic; but differed in character, inasmuch as it consisted of two narrow stripes running parallel to each other down the front of the tunic, one on the right, and the other on the left side of the person; whence the plural ''purpurae'' (Quint. xi. 3. 138.) is sometimes used, instead of the singular, to distinguish it. In paintings of a late period, this ornament is frequently met with, similar to that on the {{Illustrated Companion to the Latin Dictionary/Image Location|text=figure annexed |imagelink=Media:Clavus 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|figure annexed |caption=Clavus/9.1}}, representing a ''[[Illustrated Companion to the Latin Dictionary/Camillus|Camillus]]'' in the Vatican Virgil. But at the period when such works were executed, it had ceased to be worn as a distinctive badge of rank; for it repeatedly occurs on figures acting in a menial capacity, such as cup-bearers and attendants at the table, who were usually attired in fine clothes, in the same way as the ancient costume of this country has now descended to a "livery." <gallery> File:Clavus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|Clavus/1.1 File:Clavus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 175.jpg|Clavus/3.1 File:Clavus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 176.jpg|Clavus/5.1 File:Clavus 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 176.jpg|Clavus/6.1 File:Clavus 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|Clavus/8.1 File:Clavus 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|Clavus/9.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Decorative Parts of the Attire]] [[Category:Classed Index/Feet]] [[Category:Classed Index/Carpentry and Tools for Working in Wood]] [[Category:Classed Index/Ship's Gear]] 13vnq7sl9fjcwo350kbbc99eh6ju6i4 Illustrated Companion to the Latin Dictionary/Clepsydra 0 311927 2683684 2671560 2024-11-11T16:04:36Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683684 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLEPSYD'RA''' ({{lang|grc|κλεψύδρα}}). An ''hour-glass'', originally employed by the Greeks, and subsequently adopted at Rome, for the purpose of measuring the time allowed to each speaker in a court of law. (Plin. ''Ep.'' ii. 11.) These glasses were made of different sizes, according to the length of time for which they were required to run; and did not differ materially from the modern ones, with the exception of being filled with water instead of sand, as may be collected from the description of Apuleius (''Met.'' iii. p. 44.), and still more from the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example annexed |imagelink=Media:Clepsydra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|example annexed |caption=Clepsydra/1.1}}, which is copied from a bas-relief of the Mattei palace at Rome. The one described by Aristotle (''Probl.'' xvi. 8.) was similar in principle, but had a sort of spout at the top for pouring in the water, which trickled out at the bottom, through several small holes. 2. Probably, also a ''water-clock'' of sufficient size to run for a number of hours, and answer the purpose of a day and night clock; the lapse of time being indicated by lines or spaces (''spatia''. Sidon. Apoll. ''Ep.'' ii. 9.) described upon the globe from which the water escaped, or upon the reservoir into which it flowed. Pliny (''H. N.'' vii. 60.) gives the name ''horologium'' to a device of this nature. <gallery> File:Clepsydra 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 177.jpg|Clepsydra/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Dials and Time Pieces]] tw5xobo68dzxv2lthuzj6qd5uh2vcbv Illustrated Companion to the Latin Dictionary/Clibanarii 0 311928 2683685 2671561 2024-11-11T16:04:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683685 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIBANA'RII'''. The name used to designate those of the Persian cavalry, whose horses, as well as the troopers, were covered with an entire suit of defensive armour (Ammian. xvi. 10. 8. ''ib.'' 12. 22. Lamprid. ''Alex. Sev.'' 56.); compare [[Illustrated Companion to the Latin Dictionary/Cataphractus|CATAPHRACTUS]], 1. and illustration. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] oeldxa6e8qu35wmqeo63d0nu1m0em26 Illustrated Companion to the Latin Dictionary/Clibanicius 0 311929 2683686 2671562 2024-11-11T16:04:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683686 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIBANIC'IUS''', sc. ''panis'' ({{lang|grc|κλιβανίτις}}). Bread baked in a ''[[Illustrated Companion to the Latin Dictionary/Clibanus|clibanus]]''. Isidor. ''Orig.'' xx. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Bakers and Bread-making]] oisp46c6jjlpou2ow72t4c7or8km3jp Illustrated Companion to the Latin Dictionary/Clibanus 0 311930 2683687 2671563 2024-11-11T16:05:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683687 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLI'BANUS''' ({{lang|grc|κλίβανος}} or {{lang|grc|κρίβανος}}). A covered vessel, made wider at bottom than top (Columell. v. 10. 4.), and pierced all round with small holes (Dioscor. ii. 81. and 96.); employed for various purposes, but more especially for baking bread. (Plin. ''H. N.'' xix. 3.) When in use, it was enveloped in hot ashes, the warmth of which penetrated through the perforations in a more regular and even temperature than could be produced by the ordinary oven. The usual material was earthenware; but when Trimalchio has his bread baked in a silver ''clibanus'' (Pet. ''Sat.'' 35. 6.), it is intended as an instance of ridiculous ostentation. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] [[Category:Classed Index/Bakers and Bread-making]] 9a1ittkabqdvrz5j07bkr4r10uqimn1 Illustrated Companion to the Latin Dictionary/Clinicus 0 311931 2683688 2671564 2024-11-11T16:05:20Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683688 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIN'ICUS''' ({{lang|grc|κλινικός}}). A ''visiting physician'', who attends his patients at the bed-side. Mart. ''Ep.'' ix. 97. 2. A sick person confined to his bed. Hieron. ''Epist.'' 105. n. 5. 3. Same as [[Illustrated Companion to the Latin Dictionary/Vespillones|VESPILLO]]; who carried out the dead upon a [[Illustrated Companion to the Latin Dictionary/Capulus|bier]] or couch. Mart. ''Ep.'' iii. 93. Id. i. 31. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Medicine and Surgery]] 3hutu2js9aju7tqx8fzzqgt3purd1y3 Illustrated Companion to the Latin Dictionary/Clinopus 0 311932 2683689 2671565 2024-11-11T16:05:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683689 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLI'NOPUS''' ({{lang|grc|κλινόπους}}). The ''foot of a bedstead''. (Lucil. ''ap.'' Macrob. ''Sat.'' vi. 4.) The ancient [[Illustrated Companion to the Latin Dictionary/Lectus|bedsteads]] were commonly supported upon four legs, like our own, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Clinopus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|illustration |caption=Clinopus/1.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. <gallery> File:Clinopus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|Clinopus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Beds and Couches]] p8dygm9gjkkhy90r6gw4ugf2htve2kx Illustrated Companion to the Latin Dictionary/Clipeatus 0 311933 2683690 2671566 2024-11-11T16:05:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683690 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIPEA'TUS''' ({{lang|grc|ἀσπιδηφόρος}}). Armed or furnished with the large round Grecian shield (''[[Illustrated Companion to the Latin Dictionary/Clipeus|clipeus]]''), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Clipeatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|example |caption=Clipeatus/1.1}} from a Greek fictile vase. Virg. ''Aen.'' vii. 793. Ovid. ''Met.'' iii. 110. Curt. vii. 9. 2. ''Clipeatus chlamyde''. Having the left arm covered with the ''[[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]]'' instead of a shield (Pacuv. ''ap.'' Non. ''s. v.'' Clypeat. p. 87.), as represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Clipeatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|annexed figure |caption=Clipeatus/2.1}}, from a fictile vase; in which manner Alcibiades is stated by Plutarch to have tried to protect himself in the combat when he lost his life. 3. ''Clipeata imago''. A portrait engraved or painted upon a ''clipeus''. (Cic. ''ap.'' Macrob. ''Sat.'' ii. 3.) See [[Illustrated Companion to the Latin Dictionary/Clipeus|CLIPEUS]], 3. <gallery> File:Clipeatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|Clipeatus/1.1 File:Clipeatus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 178.jpg|Clipeatus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Shields]] 0459ewg4g8f9bkvz37rim4kpxqg93qa Illustrated Companion to the Latin Dictionary/Clipeolum 0 311934 2683691 2671567 2024-11-11T16:05:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683691 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIPE'OLUM''' ({{lang|grc|ἀσπίδιον}}). Diminutive of [[Illustrated Companion to the Latin Dictionary/Clipeus|CLIPEUS]]. Hygin. ''Fab.'' 139. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 8br32ktewio6ybqd98wwchxeifbm1ko Illustrated Companion to the Latin Dictionary/Clipeus 0 311935 2683692 2671568 2024-11-11T16:06:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683692 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLIP'EUS''' and '''CLIP'EUM''' ({{lang|grc|ἀσπίς}}). The large round shield or buckler, more especially peculiar to the heavy-armed infantry of the Greeks (Liv. ix. 19.); but also borne by the first-class men at arms amongst the Romans, from the time of Servius (Liv. i. 43. Dion. Hal. iv. 16., which passages also prove the identity between the Latin ''clipeus'' and Greek {{lang|grc|ἀσπις}}), until the period when the citizens commenced receiving pay for their military service, when the ''[[Illustrated Companion to the Latin Dictionary/Scutum|Scutum]]'' was substituted in its stead. (Liv. viii. 8.) In form it was completely circular, but concave on the inside (''cavus''. Varro, ''L. L.'' v. 19. Compare Virg. ''Aen.'' iii. 637.), with a circumference large enough to reach from the neck to the calf of the leg (see the figure in [[Illustrated Companion to the Latin Dictionary/Clipeatus|CLIPEATUS]], 1.). It was sometimes made entirely of bronze (Liv. xlv. 33.); but more commonly of several folds of ox-hide (Virg. ''Aen.'' xii. 925. ''septemplicis''. Ovid. ''Met.'' xii. 97. ''decem''), covered with plates of metal; and occasionally upon a foundation of wicker-work (whence ''clipei'' textum. Virg. ''Aen.'' viii. 625. and {{lang|grc|ἱτέα}}. Eurip. ''Suppl.'' 697.), over which the folds of untanned leather and metal were spread. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Clipeus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|illustration |caption=Clipeus/1.1}} affords a front and side view of a Greek ''clipeus'', from two fictile vases. 2. ''Sub clipeo latere. Clipei sub orbe tegi.'' (Ovid. ''Met.'' xiii. 79. Virg. ''Aen.'' ii. 227.) A position often represented in works of art, in which the soldier kneels down, and places his shield upright before him; by which his whole person is concealed, and covered from the attacks of his assailant; in the same manner as shown by the figure which illustrates [[Illustrated Companion to the Latin Dictionary/Venabulum|VENABULUM]]. 3. A shield or plate of metal, or other material, upon which the bust of a deity, or portrait of distinguished persons was carved in relief, or painted in profile, as an honorary memento (Suet. ''Cal.'' 16. Tac. ''Ann.'' ii. 83.); a custom of very great antiquity, which owes its origin to the Trojans. (Plin. ''H. N.'' xxxv. 3. Compare Hor. ''Od.'' i. 28. 11.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Clipeus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|illustration |caption=Clipeus/3.1}} represents an original bronze ''clipeus'' of this description, with a bust of the Emperore Hadrian upon its face. 4. A shield or plate of similar character, made of marble or metal, but ornamented with other devices as well as portraits, which was used as a decoration, to be suspended in public buildings or private houses, between the pillars of a [[Illustrated Companion to the Latin Dictionary/Porticus|colonnade]], in the manner represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Clipeus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|annexed engraving |caption=Clipeus/4.1}}, from a bas-relief in terra-cotta. Liv. xxxv. 10. 5. An apparatus employed to regulate the temperature of the ''[[Illustrated Companion to the Latin Dictionary/Laconicum|Laconicum]]'', or vapour bath; which consisted in a hollow circular plate of metal, suspended by chains under an opening in the dome of the ceiling at the circular end of the thermal chamber (''[[Illustrated Companion to the Latin Dictionary/Caldarium|caldarium]]''), and immediately over the ''[[Illustrated Companion to the Latin Dictionary/Labrum|labrum]]'', by the raising or depressing of which, the temperature of the room was increased or lowered, as more or less of the cold air was permitted to enter, or of the hot air to escape. (Vitruv. v. 10.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=wood-cut |imagelink=Media:Clipeus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|wood-cut |caption=Clipeus/5.1}} represents a section of the ''Laconicum'' at Pompeii, a view of which in its present state is introduced under [[Illustrated Companion to the Latin Dictionary/Laconicum|that word]]; the squares at the bottom show the flues of the ''[[Illustrated Companion to the Latin Dictionary/Hypocaustum|hypocaustum]]''; the basin in the centre over the largest flue is the ''labrum''; and the ''clipeus'', with the chain by which it was lowered or raised up, so as to close the aperture in the ceiling above it, is an imaginary restoration, in order to elucidate the manner in which the apparatus acted; but the bronze stays for fastening the chains by which the ''clipeus'' was worked, were found affixed to the sides of the wall. It must not, however, be concealed that the positive nature of the ''clipeus'' is a point involved in much uncertainty, and that many scholars, relying upon a [[Illustrated Companion to the Latin Dictionary/Pictura|picture]] in the [[Illustrated Companion to the Latin Dictionary/Thermae|Thermae]] of Titus (represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Clipeus 5.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|annexed engraving |caption=Clipeus/5.2}}) maintain that the ''Laconicum'' was the small cupola here seen rising from the floor of the chamber, which permitted a volume of flame and hot air to raise itself above the general level of the apartment; and that the ''clipeus'', which regulated the temperature by admitting or shutting off the heat, was placed, as in the cut, under this cupola, and just over the hypocaust. But it is difficult to conceive how the apparatus could have been worked in such a situation, as both the ''clipeus'' and the chains for raising it would have become intensely hot from their proximity to the fire; besides nothing bearing even a remote resemblance to such a construction has been discovered in any of the ancient baths, and the account of Vitruvius (''l. c.'') describes almost minutely a similar disposition to that observable in the circular extremity of the thermal chamber in the Pompeian baths. As both the plans are introduced the reader has the means of judging for himself. A long array of names favours each side of the argument. <gallery> File:Clipeus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|Clipeus/1.1 File:Clipeus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|Clipeus/3.1 File:Clipeus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|Clipeus/4.1 File:Clipeus 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 179.jpg|Clipeus/5.1 File:Clipeus 5.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|Clipeus/5.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Baths]] [[Category:Classed Index/Shields]] [[Category:Classed Index/Mouldings, Ornaments, and Basement]] bq0rrl51wtnbhpk1z3dp2tfd9tspaph Illustrated Companion to the Latin Dictionary/Clitellae 0 311936 2683693 2671569 2024-11-11T16:06:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683693 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLITEL'LAE''' ({{lang|grc|κανθήλια}}). The pack-saddle upon which paniers were carried; and thence also a ''pair of panniers''; whence only used in the plural number. (Hor. ''Sat.'' i. 5. 47. Phaedr. i. 15.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Clitellae 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|illustration |caption=Clitellae/1.1}} is from an engraved chrystal in the Florentine Gallery. <gallery> File:Clitellae 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|Clitellae/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Saddles and Trappings]] dekudceiv4ztfau06z0kuxbuhae5rc3 Illustrated Companion to the Latin Dictionary/Clitellarius 0 311937 2683694 2671570 2024-11-11T16:06:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683694 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLITELL'ARIUS''' ({{lang|grc|κανθήλιος}}). A beast which carries paniers, as in the [[Illustrated Companion to the Latin Dictionary/Clitellae|preceding illustration]]. Cato, ''R. R.'' x. 1. Columell. ii. 22. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Horse]] fdecane0mdflhzvtabs9dphlw3wl61s Illustrated Companion to the Latin Dictionary/Cloacarium 0 311938 2683695 2671571 2024-11-11T16:06:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683695 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLOACA'RIUM'''. The ''sewers-rate''; a tax which was levied for the expenses of cleansing and repairing the sewers. Ulp. ''Dig.'' 7. 1. 27. Paul. ''Dig.'' 30. 39. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sewers]] 37aeg70byk1vczs21e3hokrjschxgle Illustrated Companion to the Latin Dictionary/Cloaca 0 311939 2683696 2671572 2024-11-11T16:06:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683696 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLOA'CA''' ({{lang|grc|ὑπόνομος}}). A large subterranean canal, constructed of [[Illustrated Companion to the Latin Dictionary/Structura|masonry]] or [[Illustrated Companion to the Latin Dictionary/Latericius|brickwork]], for the purpose of carrying off the rain waters from the [[Illustrated Companion to the Latin Dictionary/Via|streets]] of a town, and the impurities from private houses, which were discharged through it into some neighbouring river, thus answering to our ''sewer'' and ''drain''. (Liv. i. 38. Cic. ''Caecin.'' 13. Hor. ''Sat.'' ii. 3. 242. Strabo, v. 8. p. 197. ed. Siebenk.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cloaca 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|illustration |caption=Cloaca/1.1}} represents a street view in Pompeii, with the embouchures of two drains under the pavement, and shows the manner in which the rain waters entered them. 2. ''Cloaca Maxima''. A ''main sewer'', which received the contents of several tributary branches, and conducted them in one channel to the river. But the name is also specially given to ''the'' great sewer of Rome, which was made by the elder Tarquin for the purpose of draining off the stagnant waters of the Velabra, and low lands between the Palatine and Capitoline hills, in order to provide an area for laying out the race-course, or ''[[Illustrated Companion to the Latin Dictionary/Circus|Circus]] Maximus'', and the ''[[Illustrated Companion to the Latin Dictionary/Forum|Forum]]''. A considerable portion of this great work is still in existence, after a lapse of more than 2000 years. It consists of three concentric [[Illustrated Companion to the Latin Dictionary/Arcus|arches]] of masonry, put together without cement, and in the style called Etruscan, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed elevation |imagelink=Media:Cloaca 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 181.jpg|annexed elevation |caption=Cloaca/2.1}}, which represents the embouchure where it opens upon the Tiber, near the Sublician bridge, and part of the adjacent wall, which formed the substruction of the quay termed ''pulchrum littus''. The smallest, or innermost arch, is between 13 and 14 feet in diameter; each of the blocks composing the arch is 5 feet 10 inches wide, and rather more than 3 feet 3 inches high; the whole being composed of the dark volcanic stone (''tufa Litoide''. Brocchi, ''Suolo di Roma.''), which forms the basis of the Capitoline hill, and was the common building material during the periods ascribed to the early kings. A design showing the construction of the underground part is exhibited at p. 41. ''s.'' [[Illustrated Companion to the Latin Dictionary/Anterides|ANTERIDES]]. Plin. ''H. N.'' xxxvi. 24. 3. Dionys. iii. 67. <gallery> File:Cloaca 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 180.jpg|Cloaca/1.1 File:Cloaca 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 181.jpg|Cloaca/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Sewers]] aq3jzjse76fp9yzbip6i1jc453yp9ku Illustrated Companion to the Latin Dictionary/Cloacula 0 311940 2683697 2671574 2024-11-11T16:06:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683697 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLOA'CULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cloaca|CLOACA]]; a branch sewer communicating with the main duct. Lamprid. ''Heliog.'' 17. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sewers]] gsxcv2xeoaboon7z8yf8p0cntfjn07f Illustrated Companion to the Latin Dictionary/Clostellum 0 311941 2683698 2671575 2024-11-11T16:07:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683698 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLOSTEL'LUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Clostrum|CLOSTRUM]]. Either the key-hole of a lock; or, perhaps, the box-hasp into which the bolt of a lock shoots; and which would leave a crevice between itself and a door which did not fit close, so that a person might see through it, as mentioned by Petronius, ''Sat.'' 140. 11. Compare Senec. ''Ben.'' vii. 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Locks and Fastenings]] 4hf4kp0h4uazy00zla9iyszjinp6as7 Illustrated Companion to the Latin Dictionary/Clostrum 0 311942 2683699 2671576 2024-11-11T16:07:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683699 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLOSTRUM'''. For [[Illustrated Companion to the Latin Dictionary/Claustrum|CLAUSTRUM]]. In a general sense, any fastening like a lock (Cato, ''R. R.'' xiii. 3. Id. CXXXV. 2.); but, more definitively, the box into which a lock shoots. Senec. ''Ben.'' vii. 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] hr93w8487xh7atfjgqf8l5bx9va4u3i Illustrated Companion to the Latin Dictionary/Cluden 0 311943 2683700 2680664 2024-11-11T16:07:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683700 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLU'DEN'''. A sword used by [[Illustrated Companion to the Latin Dictionary/Histrio|actors]] upon the Roman stage, the blade of which receded into the handle immediately upon meeting with any resistance, and so produced the effect of stabbing without danger. (Apul. ''Apol.'' p. 526.)<ref name="Apol. Apol. 78"/> A device of the same kind is resorted to by modern actors; but the reading in Apuleius is not certain, and the interpretation is conjectural. == References == <references> <ref name="Apol. Apol. 78">{{Cite book|chapterurl=http://data.perseus.org/citations/urn:cts:latinLit:phi1212.phi001.perseus-lat1:78 |chapter=Apol. 78 |title=Apologia |last=Apuleius |first=Lucius |year=1912}}</ref> </references> [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Swords]] 7w6skf6khum6gnj707xqlc7gre7wjuv Illustrated Companion to the Latin Dictionary/Clunabulum 0 311944 2683701 2671579 2024-11-11T16:07:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683701 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLUNAB'ULUM''' or '''CLUNAC'ULUM'''. A small sword, or rather dagger, so called because it was worn at the back, just over the buttocks (''clunes''), as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Clunabulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 181.jpg|annexed example |caption=Clunabulum/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. Aul. Gell. x. 25. Isidor. ''Orig.'' xviii. 6. 6. 2. The same name was also given to the [[Illustrated Companion to the Latin Dictionary/Culter|knife]] of the ''[[Illustrated Companion to the Latin Dictionary/Cultrarius|cultrarius]]'', with which he ripped up the entrails of victims at the sacrifice (Festus, ''s. v.''); and which was carried in the same manner by a strap round the loins, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Clunabulum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 182.jpg|annexed figure |caption=Clunabulum/2.1}}, representing one of these servants, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. <gallery> File:Clunabulum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 181.jpg|Clunabulum/1.1 File:Clunabulum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 182.jpg|Clunabulum/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Implements of Worship and Sacrifice]] [[Category:Classed Index/Daggers]] rmmc3ycmmfffh79zooc9nom3gstkve9 Illustrated Companion to the Latin Dictionary/Clysterium 0 311945 2683703 2671580 2024-11-11T16:07:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683703 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLYSTE'RIUM''' ({{lang|grc|κλυστήριον}}). Diminutive of the [[Illustrated Companion to the Latin Dictionary/Clyster|preceding]]. Scrib. ''Compos.'' 118. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ld848z1vv8c0ol6chyk54hb6bhx93fr Illustrated Companion to the Latin Dictionary/Clyster 0 311946 2683704 2671582 2024-11-11T16:08:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683704 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CLYSTER''' ({{lang|grc|κλυστήρ}}). A ''syringe''; especially such as was used for injecting fluids into the body. Suet. ''Claud.'' 44. Plin. ''H. N.'' xxxi. 33. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Surgical Implements, etc.]] 89g1db77y5b37hrt3hxl5r85lhk8p8z Illustrated Companion to the Latin Dictionary/Cnodax 0 311947 2683705 2671583 2024-11-11T16:08:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683705 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CNODAX''' ({{lang|grc|κνώδαξ}}). A pin or pivot, affixed to the extreme ends of an axle or cylinder, and run into a socket, so as to form a support which will enable the axle to revolve. Vitruv. x. 2. 12. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 7e9g1d60bop5ocdlojsywrnau3y8ou0 Illustrated Companion to the Latin Dictionary/Coactilis 0 311948 2683706 2671584 2024-11-11T16:08:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683706 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COAC'TILIS''', sc. ''lana'' ({{lang|grc|πιλητός}} or {{lang|grc|πιλωτός}}). ''Felt'' or ''felted cloth''; that is, wool matted together by repeated manipulation and pressure until it forms a consistent texture, like a piece of cloth. Plin. ''H. N.'' viii. 73. Edict. Dioclet. p. 21. Ulp. ''Dig.'' 34. 2. 26. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Different Fabrics]] h4lozgtc3ad9ykxczwzz155lxykmaaw Illustrated Companion to the Latin Dictionary/Coactores 0 311949 2683707 2671585 2024-11-11T16:08:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683707 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COACTO'RES''' ({{lang|grc|πράκτορες}}). Receivers or collectors of taxes, duties, &c. Cic. ''Rab. Post.'' 11. Hor. ''Sat.'' i. 6. 86. 2. The rear-guard of an army, or the body of troops who brought up the rear in a line of march. Tac. ''Hist.'' ii. 68. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] 9uoyvtlb5pjxa99vin60xlx32hf2raz Illustrated Companion to the Latin Dictionary/Coactus 0 311950 2683708 2671586 2024-11-11T16:08:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683708 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COAC'TUS'''. Same as [[Illustrated Companion to the Latin Dictionary/Coactilis|COACTILIS]]. Plin. ''H. N.'' viii. 73. Caes. ''B. C.'' iii. 44. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ea5y7j26pwix85idfe77zn17vbxhrta Illustrated Companion to the Latin Dictionary/Coagulum 0 311951 2683710 2671588 2024-11-11T16:08:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683710 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COAG'ULUM''' ({{lang|grc|πυετία}}). ''Rennet''; i. e. anything used in curdling milk; for which the concreted milk found in the stomachs of suckling animals, the milky moisture contained in the stomach of a pig, as well as the stomach itself, and vinegar, was commonly employed by the Romans. (Varro, ''R. R.'' ii. 11. 4. Plin. ''H. N.'' xxiii. 63.) Hence, also, ''curdled milk'' (Plin. ''H. N.'' xxviii. 45.); and ''cheese''. Ovid. ''Fast.'' iv. 545. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] gh8b8fx1rcj0bmfg0sen2i31s1epcte Illustrated Companion to the Latin Dictionary/Coassatio 0 311952 2683711 2671589 2024-11-11T16:09:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683711 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COASSA'TIO''' ({{lang|grc|σανίδωμα}}). Any thing made of boards joined together, as the [[Illustrated Companion to the Latin Dictionary/Pavimentum|flooring]] of a house (Vitruv. vi. 6.), or the deck of a ship. Theophrast. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] rkrazzj0nkt0qot6cpjbq1tq9ocsood Illustrated Companion to the Latin Dictionary/Coa vestis 0 311953 2683712 2671590 2024-11-11T16:09:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683712 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COA VESTIS'''. The Coan robe: which was of the finest texture, and almost transparent; so that the forms of the wearers were readily apparent through the drapery, which only partially concealed them. It was, therefore, chiefly worn by females addicted to pleasure, such as singing and dancing girls, one of whom is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Coa_Vestis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 182.jpg|engraving |caption=Coa_Vestis/1.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. Plin. ''H. N.'' xi. 26. Propert. iv. 5. 55. Ov. ''A. Am.'' ii. 298. Hor. ''Sat.'' i. 2. 101. <gallery> File:Coa_Vestis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 182.jpg|Coa Vestis/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] jcsq8gfqg8jbhwbxbo9jqrm5dc1uc50 Illustrated Companion to the Latin Dictionary/Cochlearium 0 311954 2683713 2671591 2024-11-11T16:09:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683713 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COCHLEA'RIUM'''. A place where snails were bred and fattened; which were considered as a delicacy by the Roman epicures, being imported from different parts, to be reared and fed in these home nurseries. (Varro, ''R. R.'' iii. 12. 2. ''Ib.'' 14. 1. Plin. ''H. N.'' ix. 82.) The ridiculous Trimalchio has them served up to table upon silver grid-irons. Pet. ''Sat.'' 70. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 1cxdyu88l2o9x3bhk4jjltr0rnvtfp7 Illustrated Companion to the Latin Dictionary/Cochlear 0 311955 2683714 2671592 2024-11-11T16:09:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683714 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COCH'LEAR''' and '''COCHLEA'RE''' ({{lang|grc|κοχλιάριον}}). A spoon with a bowl at one end, and a sharp point at the other, for eating eggs and shell-fish (Mart. ''Ep.'' xiv. 121.); the broad end serving as an egg spoon (Pet. ''Sat.'' 33. 6.), and the point for drawing the fish out of its shell. (Plin. ''H. N.'' xxviii. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cochlear 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 183.jpg|example |caption=Cochlear/1.1}} represents an original found in Pompeii. 2. A measure of liquids; answering to our ''spoonful''. Columell. xii. 21. 3. <gallery> File:Cochlear 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 183.jpg|Cochlear/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Table Utensils]] lgw3c0xlu4da593fu39ihejxs93dazc Illustrated Companion to the Latin Dictionary/Cochlea 0 311956 2683715 2671593 2024-11-11T16:09:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683715 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COCH'LEA''' ({{lang|grc|κοχλίας}}). Literally, a snail with a spiral shell; whence applied to several other objects partaking of a spiral form; as{{mdash}} 1. A worm and screw, as a mechanical power, employed in oil, wine, and clothes [[Illustrated Companion to the Latin Dictionary/Torcular|presses]], precisely in the same manner, and formed upon similar principles to those now in daily use, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Cochlea 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 183.jpg|annexed wood-cut |caption=Cochlea/1.1}}, representing a press for cloth, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] in the fuller's establishment (''[[Illustrated Companion to the Latin Dictionary/Fullonica|fullonica]]''), at Pompeii. Vitruv. vi. 9. Plin. ''H. N.'' xviii. 74. Pallad. iv. 10. 10. Id. xi. 9. 1. 2. A contrivance for raising water, upon the principle of a screw, invented by Archimedes, and similar to the machine still to be seen in Germany, which goes by the name of the "water snail." It consisted of a long cylinder, with a hollow pipe coiled round it, like the thread of a screw; was placed in an oblique direction, with the lowest end in the water, and then made to turn round its own axis by the operation of cattle, or of a tread-wheel (''[[Illustrated Companion to the Latin Dictionary/Tympanum|tympanum]]''); as it revolved, it gradually turned the water up through the coils of the pipe from the lowest to the topmost spiral, from which it ran out, as having nothing further to support it. (Vitruv. x. 6.) It is also mentioned by Strabo (xiii. 30. p. 561. ed. Siebenk.), as being used in Egypt, where it was worked by slaves, and employed for the purpose of irrigation; indeed, a pump of this description will only raise water to a moderate height. 3. A particular kind of doorway adapted for a bull-ring, aviary, and places of such description (Varro, ''R. R.'' iii. 5. 3.), where it was requisite that all who entered or went out should be enabled to do so with rapidity and security; in order that the animals might not escape with the opening of the door, while the person inside might retreat with safety upon any sudden emergency. Schneider (Index, ''R. R.'' Script. ''s. v.'' Cavea) considers this to have been a door raised and lowered after the manner of a portcullis, synonymous, therefore, with [[Illustrated Companion to the Latin Dictionary/Cataracta|CATARACTA]]; but his proofs are far from conclusive, and the old interpretation of Gesner is more in unison with the other analogies of the word; viz. an apparatus like the one now commonly used in the foundling hospitals and convents of nuns in Italy for the purpose of introducing any thing into the interior, without opening a door, and which goes by the name of "the wheel," ''la ruota''. It is constructed upon the same principle as a dark lantern, consisting of a cylindrical box, situated in the thickness of the main wall, and made to revolve round an upright axis which runs through its centre, and fixes it in its place. An aperture is left on one part of the circumference, through which, when turned to the [[Illustrated Companion to the Latin Dictionary/Via|street]], the objects intended to be introduced are placed in the box, which is then pushed half round its axis, when the opening comes on the inside of the wall. It is obvious that such an apparatus would be particularly adapted for any of the purposes above mentioned to which the ''cochlea'' was put; and the name may have been obtained from the resemblance which such a contrivance bears to a snail within its shell, or to the spiral [[Illustrated Companion to the Latin Dictionary/Scalae|staircase]] (''[[Illustrated Companion to the Latin Dictionary/Cochlis|cochlis]]'') within its case. <gallery> File:Cochlea 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 183.jpg|Cochlea/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Doors]] [[Category:Classed Index/Pumps and Water-wheels]] 92hey8v2i51ddgwinfpuren9wqitnsu Illustrated Companion to the Latin Dictionary/Cochlis 0 311957 2683716 2671595 2024-11-11T16:10:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683716 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COCH'LIS'''. See [[Illustrated Companion to the Latin Dictionary/Columna|COLUMNA]], 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ddy80acsc2coysgukobqokn88vcs9xd Illustrated Companion to the Latin Dictionary/Coctilis 0 311958 2683717 2671596 2024-11-11T16:10:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683717 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COC'TILIS''', sc. ''[[Illustrated Companion to the Latin Dictionary/Later|later]]''. A brick hardened by burning, as contradistinguished from one dried by the sun. Varro, ''R. R.'' i. 14. Plin. ''H. N.'' vii. 57. 2. ''Murus coctilis''. A wall built of bricks hardened by the fire. Ovid. ''Met.'' iv. 58. 3. ''Coctilia'' or ''Cocta ligna'' ({{lang|grc|ξύλα κάγκανα}}). Dried or scorched wood, chopped into small pieces, and prepared by hardening over the fire sufficiently to dry up the moisture contained in it, without reducing it to charcoal (Ulp. ''Dig.'' 32. 55.), in order that it might burn readily and briskly, and not throw out a quantity of smoke. It was sold by measure (Valerian ''ap.'' Trebell. ''Claud.'' 14.), and not by weight, like other kinds of fire-wood, in particular warehouses at Rome, called ''tabernae coctiliciae''; and the preparing, as well as the selling of it, was a particular trade, to which, as we are told, the father of the Emperor Pertinax belonged. Jul. Cap. ''Pertinax'', 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Fires and Fuel]] cnbup9biwaubbkbtl01m8a11ksh2xxh Illustrated Companion to the Latin Dictionary/Coctus 0 311959 2683719 2671597 2024-11-11T16:10:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683719 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COCTUS'''. Same as [[Illustrated Companion to the Latin Dictionary/Coctilis|COCTILIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] bgeyh4v8in25l9mo8xr27qafz6nm027 Illustrated Companion to the Latin Dictionary/Coculum 0 311960 2683720 2671598 2024-11-11T16:10:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683720 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COC'ULUM'''. Apparently, a general term given to any kind of saucepan for boiling meats. Festus, ''s. v.'' Isidor. ''Orig.'' xx. 8. Cato, ''R. R.'' xi. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 99bo3zirwu943p1y3iki88b2x5s7w47 Illustrated Companion to the Latin Dictionary/Codex 0 311961 2683721 2671599 2024-11-11T16:10:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683721 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'DEX'''. A clog, or heavy log of wood, chained to the feet of slaves which they dragged about with them, and were made to sit upon. Juv. ii. 57. Prop. iv. 7. 44. 2. A ''blank book'' for writing in, made up of separate leaves bound together, like our own, as is shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Codex 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 184.jpg|annexed example |caption=Codex/2.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]]. Originally, the leaves were made of thin tablets of wood (''codices'' i. q. ''caudices''), coated with [[Illustrated Companion to the Latin Dictionary/Cera|wax]], whence the name arose and which was still retained in use, although the original material had been superseded by [[Illustrated Companion to the Latin Dictionary/Charta|paper]] or [[Illustrated Companion to the Latin Dictionary/Membrana|parchment]]. Ulp. ''Dig.'' 32. 50. Cic. ''Verr.'' i. 36. Id. ''Sull.'' 15. 3. At a later period, the word also means a ''code of laws'', as the ''Codex Justinianus'', ''Theodosianus'', &c., which it may be assumed were written in books of this description. <gallery> File:Codex 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 184.jpg|Codex/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Memorandum Books, etc.]] 60zo6g3o2chqxmfm7aifcm5moh2a5kf Illustrated Companion to the Latin Dictionary/Codicillus 0 311962 2683723 2671600 2024-11-11T16:10:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683723 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CODICIL'LUS'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Codex|CODEX]]. But in the plural, CODICILLI were a collection of small [[Illustrated Companion to the Latin Dictionary/Tabella|tablets]] employed for writing memorandums (Cic. ''Fam.'' ix. 26.), intended to be copied out fairly afterwards; to be despatched as letters to intimate friends (Cic. ''Fam.'' vi. 18.); for noting down the particulars of a will (Plin. ''Ep.'' ii. 16.); of a petition or memorial (Tac. ''Ann.'' iv. 39.), and other similar purposes. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Memorandum Books, etc.]] qo2i1w1z9r889dp6boubtbnlc3sikwl Illustrated Companion to the Latin Dictionary/Coelum 0 311963 2683724 2671601 2024-11-11T16:11:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683724 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COEL'UM''' ({{lang|grc|οὐρανός}}). A ''soffit'', or ''ceiling'', of which word it contains the elements through the French ''ciel''. (Vitruv. vii. 3. 3. Florus, iii. 5. 30. and ''coelo capitis'', the nether part of the scull, Plin. ''H. N.'' xi. 49.) The earliest buildings were only covered by an outer roof (''tectum''), the inside of which served as the ceiling; but as that was found to be an insufficient protection against the changes of weather and temperature, an inner one was afterwards contrived, which constitued the ''coelum'', and gave rise to an extra member in the entablature, denoted externally by the ''[[Illustrated Companion to the Latin Dictionary/Zophorus|zophorus]]'' or ''frieze''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ceilings]] 0g4f4qubs3o4oxnrn3yvue0m34cwftx Illustrated Companion to the Latin Dictionary/Coemeterium 0 311964 2683725 2671602 2024-11-11T16:11:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683725 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COEMETE'RIUM''' ({{lang|grc|κοιμητήριον}}). A Greek word; properly signifying a sleeping chamber (Dosiad. ''ap.'' Athen. iv. 22.); whence used by the Latin writers of a late period for a cemetery. Tertull. ''Anim.'' 51. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 1l0qnd6y0b2gdu13dwbxh4pergo7e93 Illustrated Companion to the Latin Dictionary/Coemptio 0 311965 2683727 2671603 2024-11-11T16:11:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683727 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COEMP'TIO'''. A marriage by civil contract, solemnized by a ficticious sale, at which the parties betrothed went through the ceremony of mutually selling themselves to one another, and supposed to have first come into use when intermarriages between the patrician and plebeian families became lawful, A. U. C. 308. Cic. ''Muret.'' 12. Non. Marc. ''s. v.'' Nubentes, p. 531. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Marriage]] 3afuoza0i1aq8syumlstasbgyftneda Illustrated Companion to the Latin Dictionary/Coenaculum 0 311966 2683728 2671604 2024-11-11T16:11:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683728 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COENAC'ULUM'''. An ''eating-room'', according to the original and strict meaning of the word (Varro, ''L. L.'' v. 162.); but, as the apartment appropriated for that purpose was usually situated in the upper part of the [[Illustrated Companion to the Latin Dictionary/Domus|house]], at one period of Roman history, the word came to be used much more commonly in our sense of ''a room upstairs'' (Festus, ''s. v.'' Liv. xxxix. 14.), and the plural ''coenacula'' (like the Greek {{lang|grc|ὑπερῷον}}) to designate the whole suite of rooms contained in an upper story (Cic. ''Agr.'' ii. 35.); and, as the upper stories at Rome were chiefly occupied by the poorer classes, a sense of inferiority is frequently implied by the term, so that our words ''attics'' or ''garrets'' would in such cases furnish the most appropriate translation. (Hor. ''Ep.'' i. 1. 91. Juv. x. 17.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Coenaculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 185.jpg|annexed example |caption=Coenaculum/1.1}}, from a Roman [[Illustrated Companion to the Latin Dictionary/Pictura|painting]], exhibits the external appearance of the ''coenacula''; and the two last illustrations to the article [[Illustrated Companion to the Latin Dictionary/Domus|DOMUS]], which represent the plan and elevation of a two-storied house excavated at Herculaneum, will show the manner of building and distributing the apartments of an upper story in private houses of a moderate size. 2. ''Coenaculum meritorium''. A ''hired lodging'', in an upper story. Suet. ''Vitell.'' 7. <gallery> File:Coenaculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 185.jpg|Coenaculum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] e5x1ql701ovlnxerg45xjjycdkns0zr Illustrated Companion to the Latin Dictionary/Coenatio 0 311967 2683729 2671605 2024-11-11T16:11:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683729 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COENA'TIO'''. Seems to be a general term, applied to any kind of ''eating-room''; as well to the sumptous ''banqueting-halls'' of the golden palace of Nero (Sueton. ''Nero'', 31.), as to the ordinary ''dining parlour'' of Pliny's villa. (Plin. ''Epist.'' ii. 17. 10. Ib. v. 6. 21.) Like the ''[[Illustrated Companion to the Latin Dictionary/Coenaculum|coenaculum]]'', it was situated up stairs (Juv. vii. 183. Mart. ''Ep.'' ii. 59.); and in this respect differed from ''[[Illustrated Companion to the Latin Dictionary/Triclinium|triclinium]]'', which, in the Pompeian houses, is always placed upon the ground-floor. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] lf4oe9uaj5l8r34wzxvtolx1gj34cfi Illustrated Companion to the Latin Dictionary/Coenatoria 0 311968 2683730 2671606 2024-11-11T16:12:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683730 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COENATO'RIA''', i. e. ''coenatoriae vestes''. The garments or apparel worn at the dinner table (Pet. ''Sat.'' 21. 5. Mart. x. 87. Capitol. ''Maxim. Juv.'' 4.); the precise character of which has not been ascertained; but one of them went expressly by the name of [[Illustrated Companion to the Latin Dictionary/Synthesis|SYNTHESIS]], which see. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] e1oggaowve58os9q4c58u8w4gabvqav Illustrated Companion to the Latin Dictionary/Coena 0 311969 2683731 2671607 2024-11-11T16:12:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683731 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COE'NA''' ({{lang|grc|δεῖπνον}}). The principal daily meal of the Romans; and, consequently, better translated by our word ''dinner'' than ''supper'', which is more commonly applied. It was the third meal taken in the day, i. e. after the breakfast (''[[Illustrated Companion to the Latin Dictionary/Jentaculum|jentaculum]]'') and the luncheon (''[[Illustrated Companion to the Latin Dictionary/Prandium|prandium]]'' or ''[[Illustrated Companion to the Latin Dictionary/Merenda|merenda]]''), the most usual hour being about three P.M. of our time; though the particular habits of different individuals might induce some to dine at an earlier, and others at a later hour. Plaut. Cic. Petr. Suet., &c. 2. ''Prima, altera, tertia coena''. The first, second, or third remove of dishes, or courses at a dinner. Mart. ''Ep.'' xi. 31. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Meals]] flo9h2qzwtm53z74g9uhdufwyfmuhtm Illustrated Companion to the Latin Dictionary/Coenobita 0 311970 2683732 2671608 2024-11-11T16:12:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683732 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COENOB'ITA'''. Late Latin; one who lives in a community (''[[Illustrated Companion to the Latin Dictionary/Coenobium|coenobium]]'') with others; thence a ''monk'' or ''friar''. Hieron. ''Ep.'' 22. n. 34. and 35. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] qbb9agpjyokypstsfhej6p62sjut18c Illustrated Companion to the Latin Dictionary/Coenobium 0 311971 2683733 2671609 2024-11-11T16:12:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683733 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COENOB'IUM''' ({{lang|grc|κοινόβιον}}). A monastery, or convent of monks or friars; because they live together in common. Hieron. ''Ep.'' 22. n. 36. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 785znemhmmmkqv4gwe62h1u3a4foz0b Illustrated Companion to the Latin Dictionary/Cohors 0 311972 2683734 2671610 2024-11-11T16:12:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683734 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'HORS'''. Same as [[Illustrated Companion to the Latin Dictionary/Chors|CHORS]]. Varro, ''R. R.'' iii. 3. Ovid. ''Fast.'' iv. 704. 2. A cohort, or body of infantry soldiers, constituting the tenth part of a [[Illustrated Companion to the Latin Dictionary/Legio|legion]], but which varied in numbers at different periods of the Roman history, accordingly as the legion itself was increased in numerical strength. Varro, ''L. L.'' v. 88. Cincius, ''ap.'' Gell. xvi. 4. 4. Caes. ''B. G.'' iii. 1. 3. The term is sometimes used to distinguish the allied and auxiliary troops from those of the legion; by which it is inferred, that in early times such troops were arranged in cohorts instead of [[Illustrated Companion to the Latin Dictionary/Manipulus|maniples]]. Florus, iii. 21. Liv. ii. 64. Id. xxiii. 14. 4. Also, in some cases, for a troop or squadron of cavalry, but of what precise number is uncertain, Plin. ''Ep.'' x. 106. Virg. ''Aen.'' xi. 500. 5. ''Praetoria cohors''. A body of picked men, selected from the legionaries, who formed a sort of bodyguard to the [[Illustrated Companion to the Latin Dictionary/Consul|consul]], or commander under the republic; but became a permanent corps du garde under the emperors. See [[Illustrated Companion to the Latin Dictionary/Praetoriani|PRAETORIANUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Corps d'Armée]] ncoxidm6zbqpbmbzeph72r5kuciofie Illustrated Companion to the Latin Dictionary/Cohum 0 311973 2683735 2671611 2024-11-11T16:13:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683735 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'HUM'''. The rope or thong by which the yoke (''[[Illustrated Companion to the Latin Dictionary/Jugum|jugum]]'') is fastened to the pole (''[[Illustrated Companion to the Latin Dictionary/Temo|temo]]'') of a [[Illustrated Companion to the Latin Dictionary/Aratrum|plough]]. (Festus, ''s. v.'') It is very distinctly seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cohum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|annexed example |caption=Cohum/1.1}}, from a bas-relief discovered in the island of Magnensia.{TR: Correct is probably "Magnesia".} <gallery> File:Cohum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|Cohum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Bits, Bridle, Reins, and Harness]] e8z24a8v6a990s0j3t0bjq35vyzqkyo Illustrated Companion to the Latin Dictionary/Coliphium 0 311974 2683736 2671612 2024-11-11T16:13:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683736 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLIPH'IUM'''. A sort of food upon which wrestlers and persons in training for athletic exercises were dieted, in order to increase their muscular development, without adding superfluous flesh, upon the same principle as still pursued by our prize-fighters, &c. What the Roman ''coliphia'' were is not distinctly known; but they are generally supposed to have been a kind of bread cake, without leaven, and mixed with new cheese. Plaut. ''Pers.'' i. 3. 12. Juv. ii. 53. Schol. Vet. ''ad l.'' Mart. vii. 67. 12. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Gymnasium and Palaestra]] ll0adblz81b0xwrra9zt5goh4yevawt Illustrated Companion to the Latin Dictionary/Collare 0 311975 2683737 2671613 2024-11-11T16:13:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683737 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLA'RE'''. An iron collar put round the neck of runaway slaves, with a leading chain (''[[Illustrated Companion to the Latin Dictionary/Catulus|catulus]]'') attached to it, like a dog's chain and collar. (Lucil. ''Sat.'' xxix. 15. ed. Gerlach.) Prisoners of war were sometimes treated in the same way, as may be seen by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Collare 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|illustration |caption=Collare/1.1}}, representing a barbarian captive, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Antoninus. 2. A dog's collar. (Varro, ''R. R.'' ii. 9. 15.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Collare 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|example |caption=Collare/2.1}} is from a [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] pavement in one of the houses at Pompeii, and represents a watch-dog, with his collar and chain attached. <gallery> File:Collare 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|Collare/1.1 File:Collare 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 186.jpg|Collare/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 0oo8475mapy75nsjuyxxsoioq4a47gx Illustrated Companion to the Latin Dictionary/Colliciae 0 311976 2683738 2671614 2024-11-11T16:13:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683738 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLIC'IAE''' or '''COLLIQ'UIAE'''. Gutters, made with concave tiles, placed under the eaves of a house, for the purpose of carrying away the rain water from the roof, and conducting it into the ''[[Illustrated Companion to the Latin Dictionary/Impluvium|impluvium]]''. Festus, ''s.'' Inlicium. Vitruv. vi. 3. 2. Open drains or gutters in the country, for the purpose of carrying away the rain water from the lands into the ditches (''fossae''). Plin. ''H. N.'' xviii. 49. n. 2. Columell. ii. 8. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Water-courses]] [[Category:Classed Index/Timber-work and Roof]] ko3y8qkf12e94ok2wqcquezxew9wogc Illustrated Companion to the Latin Dictionary/Colliciaris 0 311977 2683740 2671615 2024-11-11T16:13:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683740 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLICIA'RIS''' sc. ''tegula''. A drain [[Illustrated Companion to the Latin Dictionary/Tegula|tile]], for making ''[[Illustrated Companion to the Latin Dictionary/Colliciae|colliciae]]''. Cato, ''R. R.'' xiv. 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] d6jp7duwt06am6xt648sj65dmhjd14t Illustrated Companion to the Latin Dictionary/Colliphium 0 311978 2683741 2671616 2024-11-11T16:13:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683741 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLIPH'IUM'''. See [[Illustrated Companion to the Latin Dictionary/Coliphium|COLIPHIUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] t03ouejt0fgjcxvbcozj8geci0q7du1 Illustrated Companion to the Latin Dictionary/Colliquiae 0 311979 2683742 2671617 2024-11-11T16:14:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683742 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLIQ'UIAE'''. See [[Illustrated Companion to the Latin Dictionary/Colliciae|COLLICIAE]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] mj6wavr80bx4ik94xe6kfr36os0s2c8 Illustrated Companion to the Latin Dictionary/Colluviarium 0 311980 2683743 2671618 2024-11-11T16:14:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683743 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLUVIA'RIUM'''. A sort of well or opening formed at certain intervals in the channel of an [[Illustrated Companion to the Latin Dictionary/Aquaeductus|aqueduct]], for the purpose of procuring a free current of air along its course; and also, perhaps, to facilitate the operation of clearing away any foul deposits left by the waters, by affording a ready access to every part of the duct. Vitruv. viii. 8. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Aqueducts]] lt3f3nnu1q81fthea5mld1p9n8fk212 Illustrated Companion to the Latin Dictionary/Collybistes 0 311981 2683744 2671619 2024-11-11T16:14:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683744 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLYBIS'TES''' or '''COLLYBIS'TA''' ({{lang|grc|κολλυβιστής}}). A Greek word Latinised; a money dealer. Hieron. ''Comment. Matth.'' c. 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] i0hpk3iyabkvqzmlet9h802hcqkyknx Illustrated Companion to the Latin Dictionary/Collybus 0 311982 2683745 2671621 2024-11-11T16:14:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683745 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COL'LYBUS''' ({{lang|grc|κόλλυβος}}). Properly, a Greek word, meaning a ''small coin''; whence it came to signify, both amongst the Greeks and Romans, the ''difference of exchange'', or ''agio'', as it is called, charged by the dealer for changing the money of one country into the currency of another. Cic. ''Att.'' xii. 6. Id. ''Verr.'' ii. 3. 78. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] hj91tz06bszdwb3vsulc71nsc7e0e5v Illustrated Companion to the Latin Dictionary/Collyra 0 311983 2683746 2671622 2024-11-11T16:14:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683746 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLY'RA''' ({{lang|grc|κολλύρα}}). A sort of bread or bun, of an oval form, which was eaten with broth or with gravy. Plaut. ''Pers.'' i. 3. 12. Compare ''ib.'' 15 and 17. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] nyhbs3mr8v6pnekiobuyk8px56vai0u Illustrated Companion to the Latin Dictionary/Collyris 0 311984 2683747 2671623 2024-11-11T16:15:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683747 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLY'RIS''' ({{lang|grc|κολλυρίς}}). Same as [[Illustrated Companion to the Latin Dictionary/Collyra|COLLYRA]]. Augustin. ''de Gent.'' 2. A head-dress worn by women, and supposed to have received its name from some resemblance in form to the bread or bun designated by the same term. (Tertull. ''Cult Foem.'' 7.) In a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] (''Mus. Borb.'' vi. 38.), there is represented a plate of bread or buns divided into separate segments of precisely the same form as those which appear on the head-dress worn by Faustina on an engraved gem (see the wood-cut ''s.'' [[Illustrated Companion to the Latin Dictionary/Caliendrum|CALIENDRUM]]; such a coincidence favours the conjecture that the painting affords a genuine example of the kind of bread, and the gem of the peculiar head-dress which went under the same name. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0bkhikg93odnzeyklyfj2oeo7sbnw5o Illustrated Companion to the Latin Dictionary/Collyrium 0 311985 2683748 2671624 2024-11-11T16:15:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683748 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLLY'RIUM''' ({{lang|grc|κολλύριον}}). A medical substance made up into the shape of a ''[[Illustrated Companion to the Latin Dictionary/Collyra|collyra]]'', composed of various ingredients, according to the nature of the remedy required, and applied externally for rubbing the parts affected, or for inserting into any hollow, such as the nostrils, &c. Celsus, v. 28. 12. Hor. ''Sat.'' i. 5. 50. Scrib. ''Comp.'' 142. Columell. vi. 30. 8. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Surgical Implements, etc.]] itl0d5r34x78w0nfdp9hqczxtiqdrll Illustrated Companion to the Latin Dictionary/Colobium 0 311986 2683749 2671625 2024-11-11T16:15:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683749 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLOB'IUM''' ({{lang|grc|κολόβιον}}). A [[Illustrated Companion to the Latin Dictionary/Tunica|tunic]] with short sleeves (from the Greek {{lang|grc|κολοβός}}, ''docked'' or ''curtailed'') which just covered the upper and fleshy part of the arm (Serv. ''ad'' Virg. ''Aen.'' ix. 616.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Colobium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 187.jpg|annexed example |caption=Colobium/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. This was the original and usual form of the tunic worn by the Romans of the republican age, at home, or in active exercise, as here represented; but abroad, or when in costume, as we might say, the [[Illustrated Companion to the Latin Dictionary/Toga|toga]] was thrown over it. <gallery> File:Colobium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 187.jpg|Colobium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Under-Clothing]] q94v7cwjtqmntztsb22qkbpefkg3t16 Illustrated Companion to the Latin Dictionary/Colonica 0 311987 2683750 2671626 2024-11-11T16:15:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683750 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLO'NICA'''. A ''farm-house''. Auson. ''Ep.'' iv. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 77r85zjhfq09r5nkfdvs2kbcdohfqbm Illustrated Companion to the Latin Dictionary/Colonus 0 311988 2683751 2671627 2024-11-11T16:15:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683751 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLO'NUS'''. A ''yeoman'' or ''farmer''; i. e. one who gains a livelihood by the cultivation of the soil, whether as a tenant farmer, or one who tills his own land. Varro, ''R. R.'' ii. ''Proem.'' 5. Columell. i. 7. Scaevola, ''Dig.'' 33. 7. 20. 2. A ''colonist''. Cic. ''N. D.'' iii. 19. Justin. xvi. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] b4gwmtgozmooaq4dv02hjjyfup4npwa Illustrated Companion to the Latin Dictionary/Colossus 0 311989 2683752 2671628 2024-11-11T16:15:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683752 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLOS'SUS''' ({{lang|grc|κολοσσός}}). A statue of gigantic dimensions, or very much beyond the proportions of nature; such, for instance, as the Colossus at Rhodes, which was above seventy feet high. Hygin. ''Fab.'' 233. Festus, ''s. v.'' Plin. ''H. N.'' xxxiv. 18. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 6lp5xj6xgonqdoa1z3bnexblj982pee Illustrated Companion to the Latin Dictionary/Colostra 0 311990 2683753 2671629 2024-11-11T16:16:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683753 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLOS'TRA''' (Plin. ''H. N.'' xi. 96. Mart. ''Ep.'' xiii. 38.); only another name for [[Illustrated Companion to the Latin Dictionary/Coagulum|COAGULUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] g1chpcpbqpopynh4ddoicakvhr7otnv Illustrated Companion to the Latin Dictionary/Columbarium 0 311991 2683754 2671630 2024-11-11T16:16:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683754 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUMBA'RIUM''' ({{lang|grc|περιστερεών}}). A ''dove-cote'' or ''pigeon-house''; which probably differed very little from those of the present day, with the exception of being frequently built upon a much larger scale; for as many as five thousand birds were sometimes kept in the same house. Varro, ''R. R.'' iii. 7. Pallad. i. 24. 2. ''Columbaria'' (plural); the ''pigeon-holes'', or separate cells in the cote for each pair of birds. Varro, ''R. R.'' iii. 7. 4. and 11. Columell. viii. 8. 3. 3. ''Columbaria'' (plural); the ''niches'' or pigeon-holes in a sepulchral chamber, in which the ashes of the dead contained in jars (''[[Illustrated Companion to the Latin Dictionary/Olla|ollae]]'') were deposited. (Inscript. ''ap.'' Spon. ''Miscell. Er. Ant.'' 19. p. 287. ''Ap.'' Fabretti, p. 9.) Each of these were adapted for the reception of a pair of jars, like doves in their nests, as exhibited by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Columbarium 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|annexed illustration |caption=Columbarium/3.1}}, copied from a sepulchral vault near Rome. The lids of the jars are seen above, and the names of the persons whose ashes they contained are inscribed underneath, against the face of the wall, into which the jars themselves are sunk. All the four walls of the sepulchre were covered with niches of this description, which sometimes amounted to one hundred and more. See [[Illustrated Companion to the Latin Dictionary/Sepulcrum|SEPULCRUM COMMUNE]], and illustration. 4. ''Columbaria'', plural ({{lang|grc|τρύπηματα}}). The ''oar-ports'', through which the [[Illustrated Companion to the Latin Dictionary/Remus|oars]] projected from the inside of a vessel (Isidor. ''Orig.'' xix. 2. 3. Compare Festus. ''s.'' Navalis Scribia); so called because they resembled the niches in a dove-cote, as plainly shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Columbarium 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 189.jpg|illustration |caption=Columbarium/4.1}}, representing two oar-ports on the side of a vessel, in the Vatican Virgil. This also accounts for the meaning of the word ''columbarius'' in a fragment of Plautus, where it signifies ''a [[Illustrated Companion to the Latin Dictionary/Remex|rower]]'', accompanied with a sentiment of depreciation. 5. ''Columbaria'', plural ({{lang|grc|ὀπαί}}). The cavities or holes in the walls of a building which form a bed for the heads of the tie-beams (''[[Illustrated Companion to the Latin Dictionary/Tignum|tigna]]'') to lie in. (Vitruv. iv. 2. 4.) See the illustration to [[Illustrated Companion to the Latin Dictionary/Materiatio|MATERIATIO]], letters ''d, d, d''. 6. ''Columbaria'' (plural). Openings formed in the axle of a particular description of tread-wheel (''[[Illustrated Companion to the Latin Dictionary/Tympanum|tympanum]]''), for raising water. The axle, in question, was a hollow cylinder, and the water raised by the revolutions of the wheel was conveyed into the axle through these apertures, and then discharged from its extremity into the receiving trough (Vitruv. x. 4.); but the whole process will be better understood by a reference to the article [[Illustrated Companion to the Latin Dictionary/Tympanum|TYMPANUM]], 5. <gallery> File:Columbarium 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|Columbarium/3.1 File:Columbarium 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 189.jpg|Columbarium/4.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Sepulchres]] [[Category:Classed Index/Oarage and Rowers]] [[Category:Classed Index/Timber-work and Roof]] huz88f8e1qn5i92wnempbp7ecz7jqvu Illustrated Companion to the Latin Dictionary/Columbar 0 311992 2683755 2671631 2024-11-11T16:16:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683755 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUM'BAR'''. A contrivance, something like the pillory, for confining the hands and head (Plaut. ''Rud.'' iii. 5. 60.); so termed from the resemblance which the apertures through which these parts projected, bore to the holes for nests in a dove-cote (''[[Illustrated Companion to the Latin Dictionary/Columbarium|columbarium]]''). It was employed for the punishment of slaves, and, in all probability, resembled the "wooden collar" of the Chinese, which is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Columbar 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|annexed engraving |caption=Columbar/1.1}}, from a drawing by Staunton. <gallery> File:Columbar 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|Columbar/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 14z115wtaikyihw73ksquxbxtrxy8zo Illustrated Companion to the Latin Dictionary/Columella 0 311993 2683756 2671632 2024-11-11T16:16:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683756 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUMEL'LA''' ({{lang|grc|στυλίς}}). A general diminutive of [[Illustrated Companion to the Latin Dictionary/Columna|COLUMNA]]. 2. ({{lang|grc|στηλίδιον}}). A small ''[[Illustrated Companion to the Latin Dictionary/Cippus|cippus]]'', or short pillar, erected over a grave as a tomb-stone. Cic. ''Leg.'' ii. 26. 3. ''Columella ferrea''. A strong iron pin or bolt, forming part of the ''trapetum'', or machine for bruising olives. (Cato, ''R. R.'' xx. 1. Id. xxii. 2.) See [[Illustrated Companion to the Latin Dictionary/Trapetum|TRAPETUM]], and the illustration, on which it is marked by the figure 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 2nawhxye0x4d20kgw2q9ug3tvjdlz90 Illustrated Companion to the Latin Dictionary/Columen 0 311994 2683757 2671633 2024-11-11T16:16:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683757 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COL'UMEN'''. The highest timber in the frame-work of a roof, forming the ridge piece to the whole. (Vitruv. iv. 2. 1.) See [[Illustrated Companion to the Latin Dictionary/Materiatio|MATERIATIO]] and the illustration, on which it is marked ''b, b''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Timber-work and Roof]] bojuxwrlv0vvsjeazw576leb70qvgry Illustrated Companion to the Latin Dictionary/Columnarium 0 311995 2683758 2671634 2024-11-11T16:17:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683758 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUMNA'RIUM'''. A Roman tax levied upon proprietors or occupants for the number of [[Illustrated Companion to the Latin Dictionary/Columna|columns]] contained in their houses, or other buildings belonging to them. Cic. ''Att.'' xiii. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ngwbh2epw2gukihopxfnjzgusej9rb9 Illustrated Companion to the Latin Dictionary/Columnarius 0 311996 2683759 2671635 2024-11-11T16:17:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683759 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUMNA'RIUS'''. A worthless fellow, or, perhaps, an insolvent debtor; i. e. literally one who had been summoned to receive punishment at the ''[[Illustrated Companion to the Latin Dictionary/Columna|columna Maenia]]''. Cael. ''ad'' Cic. ''Fam.'' viii. 9. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dj5wzyq7dsn4eattu908ldvf2k6hlyt Illustrated Companion to the Latin Dictionary/Columna 0 311997 2683760 2671636 2024-11-11T16:17:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683760 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUM'NA''' ({{lang|grc|κίων, στῦλος}}). A ''column'', employed in architecture to support the entablature and roof of an edifice. It is composed of three principal parts: the capital (''[[Illustrated Companion to the Latin Dictionary/Capitulum|capitulum]]''); the shaft (''[[Illustrated Companion to the Latin Dictionary/Scapus|scapus]]''); and the base (''[[Illustrated Companion to the Latin Dictionary/Spira|spira]]''). The column was, moreover, constructed in three principal styles or orders, each possessing characteristic forms and proportions of its own, distinctive of the order, but by unprofessional persons most readily distinguished by the difference in the capitals. 1. ''Dorica'', the Doric, shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Columna 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 189.jpg|engraving |caption=Columna/1.1}}, representing a view of the Parthenon, from Gwilt's "Encyclopaedia of Architecture," the oldest, most substantial, and heaviest of all, which has no base, and a very simple capital (see [[Illustrated Companion to the Latin Dictionary/Capitulum|CAPITULUM]], 1. and 2.). 2. ''Ionica'', the Ionic; the next in lightness, which is furnished with a base, and has its capital decorated with [[Illustrated Companion to the Latin Dictionary/Voluta|volutes]] (see [[Illustrated Companion to the Latin Dictionary/Capitulum|CAPITULUM]], 3. and 4.). 3. ''Corinthia'', the Corinthian, the lightest of all, which has a base and plinth below it, and a deep capital ornamented with foliage (see [[Illustrated Companion to the Latin Dictionary/Capitulum|CAPITULUM]], 5.). To these are sometimes added:{{mdash}}4. ''Tuscanica'', the Tuscan, only known from the account of Vitruvius, and which nearly resembles the Roman Doric; and 5. ''Composita'', the Composite, a mixed order, formed by combining the volutes of the Ionic with the foliage of the Corinthian. This most perfect and most beautiful of all architectural supports originated, as is generally the case, from the simplest beginnings. A few strong poles, or the straight trunks of trees, stuck into the ground, in order to support a cross-piece for a thatch of boughs or straw to rest upon, formed the first shaft (''[[Illustrated Companion to the Latin Dictionary/Scapus|scapus]]'') of a column. When a tile or slab of wood was placed under the bottom of the trunk to form a foundation, and prevent the shaft from sinking too deeply into the ground, the first notion of a base (''[[Illustrated Companion to the Latin Dictionary/Spira|spira]]'') was attained; and a similar one, placed on its top to afford a broader surface for the cross-beam or [[Illustrated Companion to the Latin Dictionary/Epistylium|architrave]] to rest upon, furnished the first capital. Thus these simple elements, elaborated by the genius and industry of succeeding ages, produced the several distinctive properties of the architectural orders. To explain the peculiar properties belonging to each order of columns is rather the province of the architect, than of a work of this nature; for it would require large drawings and minute details, scarcely requisite for the classical student or general reader. One point, however, is to be constantly borne in mind,{{mdash}}that the ''columna'' of ancient architecture always implied a ''real'', and not a ''fictitious'', support; for neither the Greeks nor the Romans, until the arts had declined, ever made use of columns, as the moderns do, in their buildings, as a superfluous ornament, or mere accessory to the edifice, but as a main and essentially constituent portion of the fabric, which would immediately fall to pieces if they were removed; and that the abusive application of coupled, clustered, incastrated, imbedded columns, &c., was never admitted in Greek architecture; for the chief beauty of the column consists in its ''isolation'', by means of which it presents an endless variety of views and changes of scene, with every movement of the spectator, whether seen in rank or in file. 2. ''Columna cochlis''. A column with a ''cockle'' or ''spiral staircase'' in the centre, for the purpose of ascending to the top. (P. Victor. ''de Reg. Urb. Rom.'' c. 8. and 9.) These were employed for various purposes; and more especially for ''honorary columns'', to support on their tops the statue of the person whose achievements or memory they were erected to commemorate. Two of the kind still remain at Rome, one constructed in honour of the Emperor Trajan, which is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Columna 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 190.jpg|engraving |caption=Columna/2.1}}, with a section by its side of part of the interior, to show the spiral staircase, and which, with the statue on the top, now supplanted by Pope Sixtus V., was 130 feet in height; the other, of a similar character, in honour of the Emperor M. Aurelius Antoninus. Both are covered externally by spiral bas-reliefs, representing the various wars carried on by these emperors, from which many figures have been selected to illustrate these pages. 3. ''Columna rostrata''. A column ornamented with images, representing the [[Illustrated Companion to the Latin Dictionary/Prora|prows]] (''[[Illustrated Companion to the Latin Dictionary/Rostrum|rostra]]'') of ships all down the shaft. (Virg. ''Georg.'' ii. 29. Servius, ''ad l.'') These were erected in commemoration of persons who had obtained a great naval victory; and the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Columna 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 191.jpg|example |caption=Columna/3.1}} represents the one set up in honour of C. Duilius (Plin. ''H. N.'' xxxiv. 11.) after his action with the Carthaginian fleet, B. C. 261, now preserved, together with part of the original inscription underneath, detailing the number of vessels and booty taken, in the [[Illustrated Companion to the Latin Dictionary/Capitolium|Capitol]] at Rome. 4. ''Columna Bellica''. A short column erected before the [[Illustrated Companion to the Latin Dictionary/Templum|temple]] of Bellona, situated near the ''[[Illustrated Companion to the Latin Dictionary/Porta|porta]] Carmentalis'' and ''[[Illustrated Companion to the Latin Dictionary/Circus|Circus]] Maximus'', against which the Romans in early times used to hurl a [[Illustrated Companion to the Latin Dictionary/Hasta|spear]] when about to declare war. Festus, ''s. v.'' Bellona. Ovid. ''Fast.'' vi. 206. 5. ''Columna Maenia''. A column erected in the Roman [[Illustrated Companion to the Latin Dictionary/Forum|forum]], to which slaves, thieves, and other offenders were bound, and publicly punished. Cic. ''Sext.'' 58. Id. ''Div. Verr.'' 16. Ascon. ''ib.'' 6. ''Columnae Herculis''. The ''columns of Hercules''; originally and properly, two large pyramidal columns, which the Phoenicians were accustomed to set up in the course of their extensive voyages, as light-houses and landmarks, whereby to recognise particular coasts upon any future visit, being respectively dedicated to Hercules and Astarte, their sun and moon. They are plainly shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Columna 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 191.jpg|annexed wood-cut |caption=Columna/6.1}}, from the device on a Tyrian coin, where the two columns, with the light-house in front, the conch underneath, which the master of the vessel sounded to announce his arrival in [[Illustrated Companion to the Latin Dictionary/Portus|port]] (see [[Illustrated Companion to the Latin Dictionary/Bucinator|BUCINATOR]]), and the tree representing the land, evidently explain the objects intended. Remains of such works, or others resembling them, are found in the West of England, in China, and in Africa, and are mentioned by Tacitus (''Germ.'' 34.), as existing in his day on the eastern bank of the Rhine, in the country of the Frisii (''Frisons''). By the Greeks and Romans, however, the two pyramidal mountains at the Straits of Gibraltar, Calpe and Abyla (''Gibraltar'' in Europe, and ''Ceuta'' in Africa) were termed the ''Columns of Hercules'', in consequence of the resemblance which they bear at a distance to the Phoenician columns described above, and a corresponding fable, to account for the name, was invented in favour of their own hero. Mela, i. 5. Plin. ''H. N.'', iii. ''Proem.'' 7. The ''king-post'', or ''crown-post'' in a timber roof, which supports the tie-beams (''[[Illustrated Companion to the Latin Dictionary/Capreolus|capreoli]]'') and rafters (''[[Illustrated Companion to the Latin Dictionary/Canterius|cantherii]]''), marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=D}} in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Columna 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 192.jpg|illustration |caption=Columna/7.1}}. Vitruv. iv. 2. 1. <gallery> File:Columna 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 189.jpg|Columna/1.1 File:Columna 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 190.jpg|Columna/2.1 File:Columna 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 191.jpg|Columna/3.1 File:Columna 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 191.jpg|Columna/6.1 File:Columna 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 192.jpg|Columna/7.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Timber-work and Roof]] [[Category:Classed Index/The Column]] 1ifttzd2128a5cnj1aqoldpqngou96y Illustrated Companion to the Latin Dictionary/Colum 0 311998 2683761 2671637 2024-11-11T16:17:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683761 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'LUM''' ({{lang|grc|ἠθμός}}). A ''colander'', or strainer made of basket-work, bullrushes, bast, or osiers (Cato, ''R. R.'' xi. 2. Columell. xi. 2. 70. Id. xii. 19. 4.), and in the form of an inverted cone, through which new made wine and oil (Columell. xii. 38. 7. Scrib. ''Comp.'' 156.), was passed after it had been squeezed out by the [[Illustrated Companion to the Latin Dictionary/Prelum|press beam]]. (Virg. ''Georg.'' ii. 242.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Colum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|example |caption=Colum/1.1}} introduced is from a Roman bas-relief, representing various processes connected with the vintage. 2. ''Colum nivarium''. A wine strainer made of metal, for cooling, diluting, and mixing the wine with snow at table. (Mart. ''Ep.'' xiv. 103.) It was used in the following manner. A lump of frozen snow being deposited in the strainer, and the strainer being placed upon the drinking cup, the wine was then poured upon the snow, with which it mixed itself, and filtered into the cup, through the perforations of the strainer, free from any sediment or impurities. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Colum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|example |caption=Colum/2.1}} represents an original of bronze discovered in Pompeii. 3. A basket for catching fish, like an eel or prawn basket; so termed, because when taken up, the water drains out of it, leaving the fish at the bottom, like the dregs in a strainer. Auson. ''Ep.'' iv. 57. Compare [[Illustrated Companion to the Latin Dictionary/Nassa|NASSA]]. <gallery> File:Colum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|Colum/1.1 File:Colum 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 188.jpg|Colum/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Wine Vessels]] [[Category:Classed Index/Manufacture of Oil and Wine]] 9t8n078uutln9rhsyu3p2e6z9f482oi Illustrated Companion to the Latin Dictionary/Coluria 0 311999 2683762 2671638 2024-11-11T16:17:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683762 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLU'RIA'''. Circular segments of stone placed one on the top of the other to form a [[Illustrated Companion to the Latin Dictionary/Columna|column]], when the column is made of different pieces instead of one entire block of marble. Sidon. ''Ep.'' ii. 2; but the reading is not certain. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Column]] bxd9w3ige0e4lqxmj02k378x0ew725c Illustrated Companion to the Latin Dictionary/Colus 0 312000 2683763 2671639 2024-11-11T16:17:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683763 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLUS''' ({{lang|grc|ἠλακάτη}}). A ''distaff''; commonly made out of a cane stick about a yard in length, slit at the top in such a manner that it would open, and form a sort of basket for containing the mass of wool or flax intended to be spun into threads, as represented by the right-hand figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Colus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 192.jpg|annexed wood-cut |caption=Colus/1.1}}, which is copied from an Egyptian original in the British Museum. The ring which surrounds it is intended to be put over the wool, as a sort of cap, which keeps the whole mass together. The peasantry of Italy make their distaffs of precisely the same form and materials at the present day. When the distaff was filled with wool, it was designated by such epithets as ''compta'' (Plin. ''H. N.'' viii. 74.), ''plena'' (Tibull. i. 3. 86.), or ''lana amicta'' (Catull. 64. 312.), and is shown by the left-hand figure, from a bas-relief on the [[Illustrated Companion to the Latin Dictionary/Forum|Forum]] of Nerva at Rome, which represents a female with the distaff in her left hand, the drawn thread (''[[Illustrated Companion to the Latin Dictionary/Stamen|stamen]]'') depending from it, and in the act of twisting the spindle (''[[Illustrated Companion to the Latin Dictionary/Fusus|fusus]]'') with the fingers of her right hand. Compare also the article [[Illustrated Companion to the Latin Dictionary/Neo|NEO]], in which the manner both of spinning, and of using these implements, is more fully detailed. <gallery> File:Colus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 192.jpg|Colus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Toilet, and Utensils of Females]] [[Category:Classed Index/Spinning]] jg1yhkixp8z16uqxv4xixgag8g3p64o Illustrated Companion to the Latin Dictionary/Colymbus 0 312001 2683764 2671640 2024-11-11T16:18:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683764 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COLYMB'US''' ({{lang|grc|κόλυμβος}}). In the Gloss of Isidorus, a tank (''[[Illustrated Companion to the Latin Dictionary/Lacus|lacus]]'') wherein clothes were washed; hence, a swimming or plunging bath. Lamprid. ''Hel.'' 23. Prudent. ''{{lang|grc|Περὶ στεφ.}}'' 12. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] rqvgf41ye19ybym0rk21i6asfim3anf Illustrated Companion to the Latin Dictionary/Comatorius 0 312002 2683765 2671641 2024-11-11T16:18:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683765 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMATO'RIUS'''. See [[Illustrated Companion to the Latin Dictionary/Acus|ACUS]], 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] rvxjmzdmt3brspbzq42cf73z8csej0n Illustrated Companion to the Latin Dictionary/Comatus 0 312003 2683766 2671642 2024-11-11T16:18:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683766 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMA'TUS''' ({{lang|grc|κομήτης}}). In a general sense, one who is possessed of a head of long thick hair, which is allowed to luxuriate in its natural growth (Mart. xii. 70. Suet. ''Cal.'' 35.); but the word is also specially used to characterize the Germans (Tertull. ''Virg. Veland.'' 10.) and the people of Transalpine Gaul, including Belgica, Celtica, and Aquitanica, all of which were comprised under the name of ''Gallia Comata'' (Mela, iii. 2. Plin. iv. 31. Lucan. i. 443.), in consequence of the profusion and abundance of their hair, and the manner in which it was arranged, uniformly represented by the Roman artists like the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Comatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 193.jpg|example |caption=Comatus/1.1}} here annexed, which is copied from a [[Illustrated Companion to the Latin Dictionary/Sarcophagus|sarcophagus]] discovered in the Villa Amendola, near Rome, and covered with bas-reliefs giving the details of a combat between the Romans and Gauls. <gallery> File:Comatus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 193.jpg|Comatus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Hair and Beard]] i0baae2p86fqxsckro7wuz4tj1tc72y Illustrated Companion to the Latin Dictionary/Coma 0 312004 2683767 2671643 2024-11-11T16:18:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683767 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMA''' ({{lang|grc|κόμη}}). The hair of the head; nearly synonymous with [[Illustrated Companion to the Latin Dictionary/Caesaries|CAESARIES]], but mostly with an implied sense of length and profusion; i. e. a fine head of long thick hair; whence we find the word applied to the mane of animals (Pallad. iv. 13. 2. Aul. Gell. v. 14. 2.); to the horse hair on the crest of a [[Illustrated Companion to the Latin Dictionary/Galea|helmet]] (Stat. ''Theb.'' viii. 389. and [[Illustrated Companion to the Latin Dictionary/Crista|CRISTA]]); and often connected with such epithets as ''intonsa'' (Cic. ''Tusc.'' iii. 26.), ''demissa'' (Prop. ii. 24. 52.), and the like. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Hair and Beard]] q2pae6suohq8rospypamms0jk5zv4yy Illustrated Companion to the Latin Dictionary/Comes 0 312005 2683768 2671644 2024-11-11T16:18:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683768 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMES''' ({{lang|grc|ἀκόλουθος}}). A companion or associate, generally; but more specially an attendant, or tutor, who accompanied his pupil to and from school, in his walks, &c. Suet. ''Aug.'' 98. ''Tib.'' 12. ''Claud.'' 35. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] fsgs5mvara0xyssqgcv64t3uuj6i8i6 Illustrated Companion to the Latin Dictionary/Comissatio 0 312006 2683769 2671645 2024-11-11T16:19:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683769 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMISSA'TIO''' ({{lang|grc|κῶμος, συμπόσιον}}). A revelling, feasting, or drinking bout, commencing after the ''[[Illustrated Companion to the Latin Dictionary/Coena|coena]]'', and often protracted to a late hour of the night. (Varro, ''L. L.'' vii. 89. Liv. xl 13. Cic. ''Cael.'' 15. Suet. ''Tit.'' 7.) Greek scenes of this nature are frequently represented on fictile vases. (Mus. Borb. v. 51. Millin. ''Vas. Ant.'' ii. 58. Tischbein. ii. 55. Wink. ''Mon. Ined.'' 200.), in which the lateness of the hour is indicated by the introduction of [[Illustrated Companion to the Latin Dictionary/Candelabrum|candelabra]], the festivity by the presence of Comus and winged [[Illustrated Companion to the Latin Dictionary/Genius|genii]], and the debauchery by the mixed company of courtesans, dancing, playing, and singing girls. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Meals]] 1ww0je0o1tlrop5ooopwmanbrv2fpo1 Illustrated Companion to the Latin Dictionary/Comissator 0 312007 2683770 2671647 2024-11-11T16:19:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683770 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMISSA'TOR''' ({{lang|grc|κωμαστής, συμπότης}}). A reveller, who forms one of the company at a ''[[Illustrated Companion to the Latin Dictionary/Comissatio|comissatio]]'', or ''wine party''. (Liv. xl. 9. Cic. ''Cael.'' 28.) It was not always usual for the ''comissator'' to dine (''coenare'') with his host; but he was often invited to come in and take his wine with the company after he had dined elsewhere; as Habinnas comes from the ''[[Illustrated Companion to the Latin Dictionary/Coena|coena]]'' of Scissa to the ''commissatio'' of Trimalchio{{mdash}}''Habinnas comissator intravit''. Pet ''Sat.'' 65. 3. Compare Liv. xl. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Meals]] kezgatan6lnwwwr0g2ts4kecpy720jj Illustrated Companion to the Latin Dictionary/Comitium 0 312008 2683771 2671648 2024-11-11T16:19:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683771 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMIT'IUM'''. An enclosed place abutting on the Roman [[Illustrated Companion to the Latin Dictionary/Forum|Forum]], and near the ''[[Illustrated Companion to the Latin Dictionary/Curia|Curia]]'', where the Comitia Centuriata were held and causes tried. (Varro, ''L. L.'' v. 155.) It was originally uncovered, in consequence of which the assemblies were often obliged to be dissolved when the weather was bad; but was roofed in, to obviate this inconvenience, during the second Punic war. (Liv. xxvii. 36.) Some lofty walls, still remaining under the Palatine hill, are supposed to be vestiges of this building. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] dg4oaijv62e6x090anm4ba8b2cndg23 Illustrated Companion to the Latin Dictionary/Commentaculum 0 312009 2683773 2671649 2024-11-11T16:19:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683773 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMMENTAC'ULUM''' or '''COMMOTAC'ULUM'''. A wand which the Roman priesthood carried in their sacrificial processions, wherewith to clear the way, and prevent the populace from closing too near upon them. Festus. ''s. v.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] pinuulkiwfqg9upmz2h4db72g95n75z Illustrated Companion to the Latin Dictionary/Compeditus 0 312010 2683774 2671650 2024-11-11T16:19:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683774 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMPEDI'TUS'''. Having [[Illustrated Companion to the Latin Dictionary/Compes|fetters]] or shackles upon the ''feet''; but the word more especially designates a slave who always wore, and worked in, fetters (Seneca, ''Tranq.'' c. 10. Plaut. ''Capt.'' v. i. 23. Cato, ''R. R.'' 56. Compare Ovid. ''Pont.'' i. 6. 31.), like the galley-slaves of modern Italy, whose chains are made precisely like those worn by the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Compeditus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 193.jpg|illustration |caption=Compeditus/1.1}}, from an engraved gem, which represents Saturn in fetters; an adjunct frequently given by the Romans to the statues of this deity, but from which they were removed during his festival in the month of September (Stat. ''Sylv.'' i. 6. 4.), when a temporary liberty was also allowed to the slaves in allusion to the happy condition which mankind were supposed to have enjoyed under his reign. <gallery> File:Compeditus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 193.jpg|Compeditus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] fao3hdyh4m5csfcnjmco2v9dzqdlaqq Illustrated Companion to the Latin Dictionary/Compes 0 312011 2683775 2671651 2024-11-11T16:20:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683775 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMPES''' ({{lang|grc|πέδη}}). A ''fetter'', or shackle for the feet; as shown by the [[Illustrated Companion to the Latin Dictionary/Compeditus|preceding wood-cut]], and the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Catulus|CATULUS]]. 2. A ring of silver or gold, worn by women round the bottom of the leg, just above the ankle, in the same manner as a bracelet is round the wrist (Plin. ''H. N.'' xxxiii. 54. Compare xxxiii. 12. Pet. ''Sat.'' 67. 7.), as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Compes 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|annexed engraving |caption=Compes/2.1}}, from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] of Ariadne. Ornaments of this nature were confined to females of the plebeian classes at Rome, to courtesans, dancing girls, and characters of that description, who went with bare feet, and partially exposed their legs; which would otherwise have been entirely concealed under the long and training drapery of the Roman ladies and matrons. For a similar reason, they are never represented in the Pompeian paintings on figures who wear shoes, but only when the foot and ankle is uncovered; but when Petronius, in the passage cited, places them on the legs of Fortuna above her shoes, it is to ridicule the vulgar ostentation of wealth in the wife of the parvenu by the adoption of an unusual custom. <gallery> File:Compes 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|Compes/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] qm2a09eaps248ennajhefuni9gm80zw Illustrated Companion to the Latin Dictionary/Compitum 0 312012 2683776 2671652 2024-11-11T16:20:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683776 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COM'PITUM'''. A place where two or more [[Illustrated Companion to the Latin Dictionary/Via|roads]] meet; more especially with reference to the country (Virg. ''Georg.'' ii. 382.), in contradistinction from ''[[Illustrated Companion to the Latin Dictionary/Trivium|trivium]]'', which applies more to the streets of a town. (Cic. ''Agr.'' i. 3.) It was customary to erect [[Illustrated Companion to the Latin Dictionary/Ara|altars]], shrines, and small [[Illustrated Companion to the Latin Dictionary/Templum|temples]] on these spots, at which religious rites in honour of the ''[[Illustrated Companion to the Latin Dictionary/Lares|Lares Compitales]]'', the deities who presided over cross-roads, were performed by the country people (Prop. iv. 3. 54.); whence the word ''compitum'' is sometimes used for a shrine erected on such a spot. (Grat. ''Cyneg.'' 483. Pers. iv. 28.) All these particulars are elucidated by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Compitum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|illustration |caption=Compitum/1.1}}, from a landscape [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii. <gallery> File:Compitum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|Compitum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Roads and Streets]] trwl10nhxfdnfms33pi14cuxb21jqcq Illustrated Companion to the Latin Dictionary/Compluvium 0 312013 2683777 2671653 2024-11-11T16:20:27Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683777 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COMPLU'VIUM'''. A large square opening in the centre of the roof which covered the four sides of an ''[[Illustrated Companion to the Latin Dictionary/Atrium|Atrium]]'' in Roman [[Illustrated Companion to the Latin Dictionary/Domus|houses]], and towards which these sides converged for the purpose of carrying down the rain into a reservoir (''[[Illustrated Companion to the Latin Dictionary/Impluvium|impluvium]]'') in the floor immediately under it; as is clearly shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Compluvium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|illustration |caption=Compluvium/1.1}}, representing the interior of a Pompeian Atrium restored. (Varro, ''L. L.'' v. 161. Festus, ''s.'' Impluvium. Vitruv. vi. 3. 6.) In a passage of Suetonius (''Aug.'' 92.), the whole of the open space, or area surrounded by the [[Illustrated Companion to the Latin Dictionary/Porticus|colonnade]], is designated the ''compluvium''. <gallery> File:Compluvium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 194.jpg|Compluvium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] 73r1308b12va76r4qoo1miusigvjs9d Illustrated Companion to the Latin Dictionary/Concaedes 0 312014 2683778 2671654 2024-11-11T16:20:38Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683778 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCAE'DES'''. A barricade made of trees cut down and placed across a [[Illustrated Companion to the Latin Dictionary/Via|road]] to impede the approach or pursuit of a hostile force. (Tac. ''Ann.'' i. 50. Vet. ''Mil.'' iii. 22.) On the [[Illustrated Companion to the Latin Dictionary/Columna|columns]] of Trajan and Antonine the Roman, as well as barbarian, soldiers are frequently represented in the act of felling trees for this and similar purposes. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Fortification]] czur9koed9x0exjd5szel06xtq67wwv Illustrated Companion to the Latin Dictionary/Concha 0 312015 2683779 2671655 2024-11-11T16:20:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683779 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CON'CHA''' ({{lang|grc|κόγχη}}). Strictly, a shell-fish, such as the muscle, pearl oyster, or murex; and, as various household utensils were made out of the shells of these fish, or in imitation of them, the name is commonly given to such objects; as to a salt-cellar (Hor. ''Sat.'' i. 3. 14.); a drinking cup (Juv. vi. 303.); a vase for unguents. Hor. ''Od.'' ii. 7. 22. Juv. vi. 419. 2. The ''conch'', or Triton's shell, which they are frequently represented by poets and artists as blowing in place of a trumpet (Plin. ''H. N.'' ix. 4. Lucan, ix. 394.), in which cases the shell more closely resembles the ''[[Illustrated Companion to the Latin Dictionary/Bucina|bucina]]'', as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Concha 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 195.jpg|annexed engraving |caption=Concha/2.1}} from a terra-cotta lamp. <gallery> File:Concha 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 195.jpg|Concha/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Wind Instruments]] 5lklxl5yksko9reu45rbav7dff1z89d Illustrated Companion to the Latin Dictionary/Conciliabulum 0 312016 2683780 2671656 2024-11-11T16:21:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683780 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCILIAB'ULUM'''. In a general sense, any place of public resort; but more especially a rendezvous where the country people were in the habit of meeting together at stated intervals, for the purpose of transacting business, holding markets, and settling disputes, thus answering very nearly to our ''market'' and ''assize-towns'', and places where fairs are appointed to be held. Festus ''s. v.'' Liv. vii. 15. Id. xxxiv. 1. and 56. Id. xl. 37. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 5onmw8g481djo19p8xxh17lfmobs8mv Illustrated Companion to the Latin Dictionary/Conclave 0 312017 2683781 2671657 2024-11-11T16:21:11Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683781 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCLA'VE'''. A general name, applied indiscriminately to any room or apartment in a [[Illustrated Companion to the Latin Dictionary/Domus|house]] which is not a public passage room, but might be locked with a key, whether a [[Illustrated Companion to the Latin Dictionary/Triclinium|dining-room]], bed-room, &c. Festus, ''s. v.'' Ter. ''Eun.'' iii. 5. 35. Id. ''Heaut.'' v. 1. 29. Cic. ''Rosc. Am.'' 23. Id. ''Or.'' ii. 86. Vitruv. vi. 3. 8. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Houses]] ngksm0a97tr6r7w1q1xab7d99u2qo77 Illustrated Companion to the Latin Dictionary/Concrepo 0 312018 2683782 2671658 2024-11-11T16:21:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683782 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CON'CREPO'''. See [[Illustrated Companion to the Latin Dictionary/Crepitus|CREPITUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 43t9pj2ygc9y3r45jy59opv2168o056 Illustrated Companion to the Latin Dictionary/Concubinatus 0 312019 2683783 2671659 2024-11-11T16:21:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683783 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCUBINA'TUS'''. Properly, an alliance between two persons of different sexes, in the nature of a marriage, which was not looked upon as immoral or degrading amongst the Romans, so long as each party remained single, though it had none of the legimitate consequences of a proper marriage attached to it. It usually occurred between persons of unequal rank or condition, but who still wished to live together, as between a senator and freed-woman; and, in effect, very closely resembled the so called ''morganatic'' marriages of crowned heads or princes with persons of inferior rank, which, by the laws of some countries, may be impolitic or illegal, but not immoral. Becker, ''Gallus''. Ulp. Dig. 25. 7. 1. Ib. 48. 5. 13. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] r54zcaqx9zqoq3moyk23v6b8fakesg3 Illustrated Companion to the Latin Dictionary/Concubina 0 312020 2683784 2671660 2024-11-11T16:21:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683784 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCUBI'NA'''. A female who had contracted the peculiar sort of alliance termed ''[[Illustrated Companion to the Latin Dictionary/Concubinatus|concubinatus]]''. Cic. ''Or.'' i. 40. Dig. 25. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Marriage]] t5shcxt7549rglhxmaw7ktrnz1xzxl8 Illustrated Companion to the Latin Dictionary/Concubinus 0 312021 2683785 2671661 2024-11-11T16:21:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683785 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONCUBI'NUS'''. A man who contracts the alliance termed ''[[Illustrated Companion to the Latin Dictionary/Concubinatus|concubinatus]]'' with a female. Catull. 61. 130. Quint. i. 2. 8. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] atvj7jrwdoy3np9vw5cqnj7ed7d755u Illustrated Companion to the Latin Dictionary/Condalium 0 312022 2683786 2671662 2024-11-11T16:22:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683786 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONDA'LIUM'''. A [[Illustrated Companion to the Latin Dictionary/Anulus|ring]] worn on the first joint (''[[Illustrated Companion to the Latin Dictionary/Condylus|condylus]]'', {{lang|grc|κόνδυλος}}) of the fore-finger. (Festus ''s.'' Condylus. Plaut. ''Trin.'' i. 3. 7. and 15.) The commentators and lexicographers infer from the passage of Plautus (''l. c.'') that rings of this description were peculiar to the slave class; but it does not appear that the ''condalium'', which Stasimus loses in the play, was his own; it might surely have been his master's; and the one in our {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Condalium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 195.jpg|engraving |caption=Condalium/1.1}} is on the right hand of a female in a bronze statue discovered at Herculaneum. There are, however, two statues in the Vatican (Visconti, ''Mus. Pio Clem.'' iii. 28. and 29.), both representing comic [[Illustrated Companion to the Latin Dictionary/Histrio|actors]] (one of them certainly a slave), who wear similar rings on the same joint of the fore-finger, but on the left hand. <gallery> File:Condalium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 195.jpg|Condalium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ornaments for the Person]] dlzdnbjp3ts7gym06xq4hlk7d9kgw4t Illustrated Companion to the Latin Dictionary/Conditivum 0 312023 2683787 2683356 2024-11-11T16:22:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683787 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONDITI'VUM'''. Seneca, ''Ep.'' vi. Same as [[Illustrated Companion to the Latin Dictionary/Conditorium|CONDITORIUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] kyi0fxy88awv31rbgflkvkr4wg0pvip Illustrated Companion to the Latin Dictionary/Conditorium 0 312024 2683789 2671664 2024-11-11T16:22:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683789 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONDITO'RIUM'''. An underground vault or [[Illustrated Companion to the Latin Dictionary/Sepultura|burying]]-place (''descendit in conditorium''. Pet. ''Sat.'' 111. 7.), in which a corpse was deposited in a coffin, without being reduced to ashes (Plin. ''H. N.'' vii. 16.); a practice prevalent amongst the Romans at the two extreme periods of their history, before the custom of burning had obtained, and after it had been relinquished. This is the strict meaning of the word, though it also occurs in a more general sense for a monument erected above ground (Plin. ''Ep.'' vi. 10. 5.); and in which [[Illustrated Companion to the Latin Dictionary/Olla|cinerary urns]] were also placed. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Conditorium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|illustration |caption=Conditorium/1.1}} represents the section and plan of a sepulchral chamber, excavated in the rock which forms the base of the Aventine hill, at a depth of forty feet below the surface; the centre shaft formed a [[Illustrated Companion to the Latin Dictionary/Scalae|staircase]] for descending into the [[Illustrated Companion to the Latin Dictionary/Sepulcrum|sepulchre]], which is a circular chamber, having an external corridor all round it, as shown by the groundplan in miniature at the left hand of the upper part of the engraving. It also contains niches for cinerary urns, which may have been made at a subsequent period. 2. ({{lang|grc|λάρναξ}}). The chest or coffin in which the dead body was encased, when placed in the vault. (Suet. ''Aug.'' 18. Plin. ''H. N.'' xxxvii. 7.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Conditorium 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|illustration |caption=Conditorium/2.1}} represents the coffin of L. Cornelius Scipio Barbatus, which was discovered in an underground sepulchre of the Cornelian family on the Appian way. The whole is carved in a grey-coloured stone of volcanic formation (''peperino'') with dentils, [[Illustrated Companion to the Latin Dictionary/Triglyphus|triglyphs]], and rosettes in the [[Illustrated Companion to the Latin Dictionary/Metopa|metopes]]; the top slab takes off as a lid; and on the side is engraved the {{Illustrated Companion to the Latin Dictionary/Image Location|text=following epitaph |imagelink=Media:Conditorium 2.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|following epitaph |caption=Conditorium/2.2}}, not only courious as identifying for whom the coffin was made, but as an authentic specimen of early Latinity.{{mdash}} 3. A magazine in which military engines were kept. Ammian. xviii. 9. 1. <gallery> File:Conditorium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|Conditorium/1.1 File:Conditorium 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|Conditorium/2.1 File:Conditorium 2.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 196.jpg|Conditorium/2.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Sepulchres]] 0ywe8ty3n5s35kbjvb0xwelp49uxn3w Illustrated Companion to the Latin Dictionary/Condus 0 312025 2683790 2671665 2024-11-11T16:22:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683790 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONDUS''', or ''Promus Condus''. See [[Illustrated Companion to the Latin Dictionary/Promus|PROMUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] j938h502obxuuqdhgjjrv5voipkj97u Illustrated Companion to the Latin Dictionary/Condylus 0 312026 2683791 2671666 2024-11-11T16:22:49Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683791 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CON'DYLUS'''. Same as [[Illustrated Companion to the Latin Dictionary/Condalium|CONDALIUM]]. Festus, ''s. v.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] exc2yqhruuwlqnvfksvcdi2p3d881m1 Illustrated Companion to the Latin Dictionary/Confarreatio 0 312027 2683792 2671667 2024-11-11T16:23:00Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683792 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONFARREA'TIO'''. One of the three forms of contracting marriage in use amongst the Romans; believed to have been the most ancient, as it was the most solemn form, for it partook of the nature of a religious ceremony, whereas the other two were merely civil contracts. It was solemnised in the presence of ten witnesses, the high priest, and [[Illustrated Companion to the Latin Dictionary/Flamen|Flamen Dialis]]; was accompanied by prayers, and the sacrifice of a sheep, the skin of which was spread over the chairs on which the bride and bridegroom sat. The name obtained from a custom belonging to it of carrying a flour cake (''far'') before the bride as she returned from the wedding. (Arnob. iv. 140. Serv. ''ad'' Virg. ''Georg.'' i. 31. ''Aen.'' iv. 374. Plin. ''H. N.'' xviii. 3.) An ancient marble, representing this ceremony, is engraved and described by Bartoli (''Admirand.'' pl. 58.), and by Lumisden (''Antiquities of Rome'', appendix iii.); but the figures are too numerous, and the details too minute, to bear a reduction adapted to these pages. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Marriage]] 7lvecs529hsphbox4akgkg0t2xe23xd Illustrated Companion to the Latin Dictionary/Confarreatus 0 312028 2683793 2671668 2024-11-11T16:23:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683793 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONFARREA'TUS'''. One who is married by the ceremony of ''[[Illustrated Companion to the Latin Dictionary/Confarreatio|confarreatio]]''. Tac. ''Ann.'' iv. 16. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 76z825w8s3ea5ax26qy0yddbfyinyyi Illustrated Companion to the Latin Dictionary/Congiarium 0 312029 2683794 2671669 2024-11-11T16:23:22Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683794 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONGIA'RIUM'''. A ''largess'', or donation, consisting of a number of ''[[Illustrated Companion to the Latin Dictionary/Congius|congii]]'' filled with wine, oil, salt, &c. (Liv. xxv. 2. Plin. ''H. N.'' xiv. 17. ''Ib.'' xxxi. 41.), which it was customary with the Roman kings, [[Illustrated Companion to the Latin Dictionary/Consul|consuls]], and emperors to distribute amongst the ''people'' at their own expense. (Suet. ''Nero'', 7. Plin. ''Paneg.'' 25.) This is the original and strict meaning of the term; but in process of time, donations of other things, even money (Suet. ''Aug.'' 41.), were designated by the same name, as well as a largess made to the soldiery (Cic. ''Att.'' xvi. 8.), though the proper name for that is ''[[Illustrated Companion to the Latin Dictionary/Donativum|donativum]]''. The manner of distributing these favours was as follows;{{mdash}}the donor sat upon an elevated tribunal (''[[Illustrated Companion to the Latin Dictionary/Suggestum|suggestum]]''), which the recipients approached one by one, and were presented with a token (''[[Illustrated Companion to the Latin Dictionary/Tessera|tessera]]''), upon which the amount to be received was written, and made payable upon presentment at the magazine of the giver; as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Congiarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 197.jpg|illustration |caption=Congiarium/1.1}}, from a bas-relief on the [[Illustrated Companion to the Latin Dictionary/Arcus|arch]] of Constantine at Rome; or, in some cases, the tokens were thrown down promiscuously amongst the crowd to be scrambled for, when they were expressly called ''[[Illustrated Companion to the Latin Dictionary/Missilia|missilia]]''. <gallery> File:Congiarium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 197.jpg|Congiarium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] a9yho59q2208byrxm1stwxah00h6w1z Illustrated Companion to the Latin Dictionary/Congius 0 312030 2683795 2671670 2024-11-11T16:23:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683795 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CON'GIUS'''. A Roman liquid measure, containing six ''[[Illustrated Companion to the Latin Dictionary/Sextarius|sextarii]]'', or twelve ''[[Illustrated Companion to the Latin Dictionary/Hemina|heminae]]'' (Rhemn. Fann. ''de Pond. et Mens.'' 70. Cato, ''R. R.'' 57.), the form and character of which is shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Congius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 197.jpg|annexed engraving |caption=Congius/1.1}}, from an original of the age of Vespasian, now known as the Farnese Congius. The large letters P. X. stand for ''pondo decem''. <gallery> File:Congius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 197.jpg|Congius/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] gb4rioikmvnp5eynsy5wbat3ixv60c2 Illustrated Companion to the Latin Dictionary/Conisterium 0 312031 2683796 2671671 2024-11-11T16:23:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683796 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONISTE'RIUM''' ({{lang|grc|κονίστρα}}). An apartment in the ''[[Illustrated Companion to the Latin Dictionary/Palaestra|palaestra]]'' or ''[[Illustrated Companion to the Latin Dictionary/Gymnasium|gymnasium]]'', the floor of which was covered over with fine sand ({{lang|grc|κόνις}}), or in which the bodies of the wrestlers were rubbed over with sand after being anointed. Vitruv. v. 11. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Gymnasium and Palaestra]] i6sfawynef6l8u8qnsdee5alaoz0cqh Illustrated Companion to the Latin Dictionary/Conopeum 0 312032 2683797 2671672 2024-11-11T16:23:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683797 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONO'PEUM''' or '''CONOPI'UM''' ({{lang|grc|κωνωπεών}}, {{lang|grc|κωνωπεῖον}}). A ''musquito net'', suspended over a sleeping couch, or over persons reposing out of doors, to keep off the gnats and other troublesome insects; the use of which originated in Egypt. Hor. ''Epod.'' ix. 16. Prop. iii. 11. 45. Varro, ''R. R.'' ii. 10. 8. Juv. vi. 80., in which passage the penultimate is long. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Beds and Couches]] 5umsc6unq3rz79w9yea82kvokk2srfb Illustrated Companion to the Latin Dictionary/Conquisitores 0 312033 2683798 2671673 2024-11-11T16:24:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683798 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONQUISITO'RES'''. Pressmasters, or recruiting officers; who were appointed to go and seek out certain citizens, selected by the [[Illustrated Companion to the Latin Dictionary/Consul|consul]] for conscripts, and compel them upon his authority to take the military oath, and enter the service; whereas, on common occasions, the citizens presented themselves voluntarily to be enrolled. Cic. ''Mil.'' 25. Liv. xxi. 11. Hirt. ''B. Alex.'' 2. Compare Cic. ''Prov. Cons.'' 2. Liv. xxiii. 32. xxv. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] 9p32csei5v61qofynm7bgz35g6q0x2r Illustrated Companion to the Latin Dictionary/Consecratio 0 312034 2683799 2671674 2024-11-11T16:24:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683799 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONSECRA'TIO''' ({{lang|grc|ἀποθέωσις, ἀφιέρωσις}}). The act of deification, or canonisation; by which ceremony a mortal was enrolled amongst the gods, and admitted to a participation in divine honours, a distinction usually conferred upon the Roman Emperors, but unknown under the republic. The chief part of this ceremony was performed in the Campus Martius, where a pyre of faggots and rough wood was raised, covered externally by an ornamental design, resembling a tabernacle of three or four stories, each of which lessened as they got higher, and were ornamented with statues, drapery, and other decorations. In the second story, a splendid couch, with a waxen image of the deceased lying on it, was deposited, and surrounded with all kinds of aromatic herbs. The whole mass was then ignited and an eagle let loose from the top story, which was believed to carry the soul up to heaven, as seen in the subjoined {{Illustrated Companion to the Latin Dictionary/Image Location|text=wood-cut |imagelink=Media:Consecratio 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|wood-cut |caption=Consecratio/1.2}}, from a bas-relief on the [[Illustrated Companion to the Latin Dictionary/Arcus|arch]] of Titus, representing the deification of that emperor. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=first wood-cut |imagelink=Media:Consecratio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|first wood-cut |caption=Consecratio/1.1}} shows the tabernacle, from a medal of Caracalla, which bears the inscription {{Illustrated Companion to the Latin Dictionary/Inscription|text=CONSECRATIO}} as a legend. Tac. ''Ann.'' xiii. 2. Suet. ''Dom.'' 2. Herodian. iv. 2. <gallery> File:Consecratio 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|Consecratio/1.2 File:Consecratio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|Consecratio/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Funeral Rites and Burial]] 1nnk8d7kfyb6jhtc6x7ahnvbxjk3svd Illustrated Companion to the Latin Dictionary/Constratum 0 312035 2683800 2671675 2024-11-11T16:24:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683800 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONSTRA'TUM'''. In general, any flooring made of planks: as, 1. ''Constratum navis'' (Pet. ''Sat.'' 100.), the ''deck of a ship'', which is very clearly expressed in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Constratum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|annexed engraving |caption=Constratum/1.1}}, from a bas-relief on the tomb of Munatius Plancus at Pompeii. 2. ''Constratum pontis'' (Liv. xxx. 10.), the flooring which affords a gangway over a bridge of boats, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Constratum 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|annexed example |caption=Constratum/1.2}}, from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Antoninus, or over a wooden bridge, as in the illustration to [[Illustrated Companion to the Latin Dictionary/Pons|PONS SUBLICIUS]]. <gallery> File:Constratum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|Constratum/1.1 File:Constratum 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 198.jpg|Constratum/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Parts and Ornaments of Vessels]] guxy708c45dsa5ejag40r7ortyuc84w Illustrated Companion to the Latin Dictionary/Consul 0 312036 2683801 2671676 2024-11-11T16:24:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683801 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONSUL''' ({{lang|grc|ὕπατος}}). A consul; one of the two chief [[Illustrated Companion to the Latin Dictionary/Magistratus|magistrates]] annually elected by the Roman people during the republican period, and nominally retained under the empire, though with very different and limited powers. The outward symbols of their authority were the ''[[Illustrated Companion to the Latin Dictionary/Fascis|fasces]]'', which were carried before them by twelve [[Illustrated Companion to the Latin Dictionary/Lictor|lictors]]; an ivory sceptre (''[[Illustrated Companion to the Latin Dictionary/Sceptrum|sceptrum]] eburneum'', or ''[[Illustrated Companion to the Latin Dictionary/Scipio|scipio]] eburneus''), with the image of an eagle on its top; and the embroidered [[Illustrated Companion to the Latin Dictionary/Toga|toga]] (''toga picta''), which, however, was only worn upon certain occasions: their ordinary civil costume being the ''toga'' and ''[[Illustrated Companion to the Latin Dictionary/Tunica|tunica]]'', with the ''[[Illustrated Companion to the Latin Dictionary/Clavus|latus clavus]]''; their military one, the ''[[Illustrated Companion to the Latin Dictionary/Paludamentum|paludamentum]]'', ''[[Illustrated Companion to the Latin Dictionary/Lorica|lorica]]'', and ''[[Illustrated Companion to the Latin Dictionary/Parazonium|parazonium]]''. Consequently, on works of art, they are represented without any very distinctive marks: either simply draped in the toga, or in the same military costume as other superior officers; as on the consular coins of Cn. Piso, and of Cinna, in Spanheim, vol. ii. pp. 88. 91. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] qqrrrtomoe5zsysyfxf08756rhqny6d Illustrated Companion to the Latin Dictionary/Contabulatio 0 312037 2683803 2671677 2024-11-11T16:24:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683803 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTABULA'TIO''' The long parallel folds in a loose garment, such as the ''[[Illustrated Companion to the Latin Dictionary/Toga|toga]]'', ''[[Illustrated Companion to the Latin Dictionary/Palla|palla]]'', ''[[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]'', &c., which hang down from the shoulders, and present the appearance of folding or lapping over one another, like a boarding of planks in a wooden building, as is plainly demonstrated by the lines at the back of the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed figure |imagelink=Media:Contabulatio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 199.jpg|annexed figure |caption=Contabulatio/1.1}}, from a fictile vase. Apul. ''Met.'' xi. p. 240. Compare Tertull. ''de Pall.'' 5. and [[Illustrated Companion to the Latin Dictionary/Corrugis|CORRUGIS]]. <gallery> File:Contabulatio 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 199.jpg|Contabulatio/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] cbvnsj8bpis0wsj44y5gvwdmi6yono8 Illustrated Companion to the Latin Dictionary/Contarii 0 312038 2683805 2671678 2024-11-11T16:25:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683805 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTA'RII''', and '''CONTA'TI''' ({{lang|grc|κοντόφοροι}}). Soldiers armed with the long pike styled ''contus''. Inscript. ''ap.'' Grut. 40. 2. and 3. Veget. ''Mil.'' iii. 6. Arrian. ''Tact.'' p. 15. See [[Illustrated Companion to the Latin Dictionary/Contus|CONTUS]], 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] 87mrh25b902d4edluorf3t58etnwii8 Illustrated Companion to the Latin Dictionary/Contignatio 0 312039 2683806 2671679 2024-11-11T16:25:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683806 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTIGNA'TIO'''. The wood-work of beams and joists which supports the [[Illustrated Companion to the Latin Dictionary/Pavimentum|flooring]] in a building of several stories (Vitruv. vi. 5. Pallad. i. 9.); whence also used to designate the floor or story itself. Caes. ''B. C.'' ii. 9. Liv. xxi. 62. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] h79ode53irxj1uddvbfvsvklvv9mrb8 Illustrated Companion to the Latin Dictionary/Contomonobolon 0 312040 2683807 2671680 2024-11-11T16:25:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683807 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTOMONOB'OLON'''. A game in which feats of leaping were displayed by men who made use of a pole (''[[Illustrated Companion to the Latin Dictionary/Contus|contus]]'') to assist their exertions. Imp. Justin. ''Cod.'' 3. 43. 3. Compare [[Illustrated Companion to the Latin Dictionary/Monobolon|MONOBOLON]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Feats of Strength or Dexterity]] otxhqifinjao6rx76praq6s72pf1ovb Illustrated Companion to the Latin Dictionary/Contubernales 0 312041 2683808 2671681 2024-11-11T16:25:33Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683808 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTUBERNA'LES''' ({{lang|grc|σύσκηνοι}}). ''Comrades'' or ''mess-mates''; i. e. soldiers who shared the same quarters, and lived together under the same [[Illustrated Companion to the Latin Dictionary/Contubernium|tent]]; each tent being occupied by ten men, with a subaltern (''[[Illustrated Companion to the Latin Dictionary/Decanus|decanus]]''), something like our sergeant or corporal, at their head. Festus. ''s. v.'' Veg. ''Mil.'' ii. 8. and 13. Cic. ''Ligar.'' 7. Hirt. ''Bell. Alex.'' 16. 2. Young men of distinguished families, who accompanied a general in his military expeditions, for the purpose of learning the art of war, were also termed his ''contubernales'', or ''on his staff''. Cic. ''Cael.'' 30. Suet. ''Jul.'' 42. 3. Hence, in a more general sense, any close or intimitate friends and acquaintances. Plin. ''Ep.'' iv. 27. 5. 4. Persons living together as man and wife, without being legally married; as slaves, or a freedman and a slave. Pet. ''Sat.'' 96. 7. Id. 57. 6. Columell. i. 8. 5. Id. xii. 3. 7. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Troops]] nkwvbitb0txzyhsws5blcn1g1207e4t Illustrated Companion to the Latin Dictionary/Contubernium 0 312042 2683809 2671682 2024-11-11T16:25:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683809 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTUBER'NIUM''' ({{lang|grc|συσκηνία}}). A military [[Illustrated Companion to the Latin Dictionary/Tentorium|tent]] in which ten soldiers and their corporal (''[[Illustrated Companion to the Latin Dictionary/Decanus|decanus]]'', or ''caput contubernii'') are quartered [[Illustrated Companion to the Latin Dictionary/Contubernales|together]] (Caes. ''B. C.'' iii. 76. Tac. ''Hist.'' i. 43.); whence, in a more general sense, any dwelling in which several persons live together (Suet. ''Cal.'' 10. Tac. ''Hist.'' iii. 74.); and especially, the abode of a pair of slaves, male and female. Columell. xii. 1. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Camp and Tents]] iqnw5vexcra5wz7szl3inkw1i6ae6t8 Illustrated Companion to the Latin Dictionary/Contus 0 312043 2683811 2671683 2024-11-11T16:25:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683811 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONTUS''' ({{lang|grc|κοντός}}). A long and strong pole, shod with iron, employed for punting; i. e. for pushing on a boat against the stream, instead of [[Illustrated Companion to the Latin Dictionary/Remus|rowing]], like our ''punt-pole''; as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Contus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 200.jpg|annexed engraving |caption=Contus/1.1}}, from the very ancient [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] pavement in the temple of Preneste (now ''Palestrina''). Virg. ''Aen.'' vi. 302. Eurip. ''Alcest.'' 262. 2. A pole of similar character, employed on board ship (Virg. ''Aen.'' v. 208.) for various purposes; to keep the vessel off the rocks or shore (Hom. ''Od.'' ix. 487.); for taking soundings (Festus. ''s.'' Percunctatio. Donat. ''ad'' Terent. ''Hec.'' i. 2. 2.); and similar uses. Every [[Illustrated Companion to the Latin Dictionary/Triremis|trireme]] was furnished with three such poles, of different sizes (Böck. ''Urk.'' p. 125.); and in the illustration at p. 91. (''s.'' [[Illustrated Companion to the Latin Dictionary/Bucinator|BUCINATOR]]), one of the sailors is observed to stand at the head of the vessel, which is just about to enter the [[Illustrated Companion to the Latin Dictionary/Portus|port]], with a ''contus'' in his hands. 3. A cavalry ''pike'' of very great weight and length (Non. ''s. v.'' p. 555. Arrian. ''Tact.'' p. 15., where it is distinguished by juxta-position from the ''lance'', {{lang|grc|λόγχη}}, ''[[Illustrated Companion to the Latin Dictionary/Lancea|lancea]]''), and resembling the Macedonian ''[[Illustrated Companion to the Latin Dictionary/Sarissa|sarissa]]'', except that it was not quite so long. (Veg. ''Mil.'' iii. 24.) It was the national weapon of the Sarmatians (Tac. ''Ann.'' vi. 35. Stat. ''Achill.'' ii. 418. Sil. Ital. xv. 684.); though occasionally adopted by the Greeks, and some of the Roman cavalry (Arrian. p. 16.); and was likewise employed by sportsmen in hunting wild beasts. (Grat. ''Cyneg.'' 117.) The length and strength of the weapon in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Contus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 200.jpg|illustration |caption=Contus/3.1}}, which represents Alexander at the battle of Issus, from the great [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] of Pompeii, favours the belief that we have in it a genuine specimen of the ''contus''. It may be remarked that only one half of its entire length is presented to the view, as the portion behind the hand, which is placed at the centre of gravity, has perished, from the mutilation of the original; and, likewise, that it is erroneously instanced as an example of the ''sarissa'', an arm which belonged to the ''infantry'', and was still more ponderous. <gallery> File:Contus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 200.jpg|Contus/1.1 File:Contus 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 200.jpg|Contus/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Spears and Missiles]] [[Category:Classed Index/Ship's Gear]] [[Category:Classed Index/Oarage and Rowers]] 8qrumdmjw5ubebyaxq3jzhhua1n7939 Illustrated Companion to the Latin Dictionary/Conus 0 312044 2683812 2671684 2024-11-11T16:26:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683812 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'NUS''' ({{lang|grc|κῶνος}}). Generally, anything of a conical figure; whence, in a more special sense:{{mdash}} 1. The metallic ridge on the scull piece of a [[Illustrated Companion to the Latin Dictionary/Galea|helmet]], to which the crest was affixed (Plin. ''H. N.'' x. 1. Virg. ''Aen.'' iii. 468.); for which the genuine Latin word is [[Illustrated Companion to the Latin Dictionary/Apex|APEX]]; which see. 2. A particular kind of [[Illustrated Companion to the Latin Dictionary/Solarium|sun dial]]; from its designation, supposed to have been described upon an elevation of conical form. Vitruv. ix. 8. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Dials and Time Pieces]] [[Category:Classed Index/Defensive Armour]] hec9n4h2qoljofa4k6e87deuutnh5hf Illustrated Companion to the Latin Dictionary/Convivium 0 312045 2683814 2671685 2024-11-11T16:26:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683814 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CONVIV'IUM''' ({{lang|grc|σύνδειπνον, ἑστίασις}}). A feast, or banquet; but at regular and proper hours, and without any implied notion of debauchery or excess; in which respect it differs from ''[[Illustrated Companion to the Latin Dictionary/Comissatio|comissatio]]'', which was a protracted revel after the ''convivium''. Cic. ''Senect.'' 13. Id. ''Verr.'' ii. 4. 27. Id. ''Offic.'' iii. 14. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Meals]] 9llmayx8m9e8yh0hzru82htr59845dj Illustrated Companion to the Latin Dictionary/Cooperculum 0 312046 2683815 2671686 2024-11-11T16:26:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683815 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COOPER'CULUM'''. Same as [[Illustrated Companion to the Latin Dictionary/Operculum|OPERCULUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] b3hhxampnjlqabmvlfcz67cvqlsdps4 Illustrated Companion to the Latin Dictionary/Coopertorium 0 312047 2683816 2671687 2024-11-11T16:26:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683816 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COOPERTO'RIUM'''. ''Loose clothing'', as a covering for animals, objects, or persons. Veg. ''Vet.'' iii. 77. Scaev. ''Dig.'' 34. 2. 39. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] r6mv00vta911sfxgso47sieroszpa9d Illustrated Companion to the Latin Dictionary/Copadia 0 312048 2683817 2671688 2024-11-11T16:26:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683817 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COPA'DIA'''. Delicacies for the table, or dainties for gourmands. Apic. vi. 1. vii. 6. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] 6vtfd5ad9i309grdozc3q31hrii1rzc Illustrated Companion to the Latin Dictionary/Copa 0 312049 2683818 2671689 2024-11-11T16:27:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683818 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CO'PA'''. A girl who frequents the taverns, where she gains a livelihood by dancing, singing, and playing for the amusement of the company. Suet. ''Nero'', 27. Virg. ''Copa'', 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] mx2178ddad1aajxzhbt4iimmne6wlwq Illustrated Companion to the Latin Dictionary/Cophinus 0 312050 2683819 2671690 2024-11-11T16:27:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683819 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COPH'INUS''' ({{lang|grc|κόφινος}}). A large kind of basket or ''hamper'', very generally employed in gardening and husbandry (Columell. xi. 3. 51.), as well as for other purposes. (Juv. ''Sat.'' iii. 14. Id. vi. 542.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cophinus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|illustration |caption=Cophinus/1.1}} annexed, which is copied from an engraved gem, probably represents a basket of this description; the flowers placed in it indicate its use, and the size is declared by there being two persons to support it. <gallery> File:Cophinus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|Cophinus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Baskets]] 0sn6m0hoiog4yt45liiov4n6cu5cv3x Illustrated Companion to the Latin Dictionary/Copis 0 312051 2683820 2671691 2024-11-11T16:27:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683820 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COP'IS''' ({{lang|grc|κόπις}}). A ''scimitar''; a sword with a convex edge (''leniter curvatus'', Curt. viii. 14.), and, consequently, better adapted for cutting than thrusting. It was more especially peculiar to the Eastern nations (Xen. ''Cyr.'' ii. 1. 9. vi. 2. 10.); and, accordingly, the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Copis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|example |caption=Copis/1.1}} here given is lying on the ground beside a wounded Phrygian, in a statue excavated at Pompeii. 2. The hunting knife (''culter venatorius'') in consequence of its having a convex edge (see the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Culter|CULTER]], 3.), is called by the same name in Apuleius, ''Met.'' xi. p. 243. <gallery> File:Copis 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|Copis/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Swords]] t9m5lf36l3szi45drwrf5et8lujd99z Illustrated Companion to the Latin Dictionary/Copona 0 312052 2683821 2671692 2024-11-11T16:27:34Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683821 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COPO'NA'''. See [[Illustrated Companion to the Latin Dictionary/Caupona|CAUPONA]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ivojpj43wque3mijyh1w8lita16c4u5 Illustrated Companion to the Latin Dictionary/Copo 0 312053 2683822 2671693 2024-11-11T16:27:44Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683822 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COPO'''. See [[Illustrated Companion to the Latin Dictionary/Caupo|CAUPO]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 72rzg7hpv1aiomujmiicqtk1sk591jt Illustrated Companion to the Latin Dictionary/Coprea 0 312054 2683824 2671694 2024-11-11T16:27:55Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683824 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COP'REA''' ({{lang|grc|κπρίας}}). A ''jester'' or ''buffoon''; a word first introduced under the Roman emperors (Suet. ''Tib.'' 61. ''Claud.'' 8. Dio Cass. xv. 28.); in whose palaces such characters were kept, like the kings' jesters of the middle ages. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] mcp84ml00d4bq7m5oyoa0tfhysszk2n Illustrated Companion to the Latin Dictionary/Copta 0 312055 2683825 2671695 2024-11-11T16:28:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683825 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COP'TA''' ({{lang|grc|κοπτή}}). A sort of hard cake or biscuit, which would keep for a long time, and might be transmitted to great distances. The island of Rhodes was famed for its manufacture. Mart. xiv. 68. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] ogc94ngs4558i20ybxgisymy1dmsj4m Illustrated Companion to the Latin Dictionary/Coptoplacenta 0 312056 2683826 2671696 2024-11-11T16:28:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683826 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COPTOPLACEN'TA''' ({{lang|grc|κοπτοπλακοῦς}}). Same as the [[Illustrated Companion to the Latin Dictionary/Copta|preceding]]. Pet. ''Sat.'' 40. Poet. Lat. Min. ''ap.'' Wernsdorf. tom. ii. p. 234. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] sgbhv9bn7umhoovbyoawg7jtaajg9ow Illustrated Companion to the Latin Dictionary/Copula 0 312057 2683827 2671697 2024-11-11T16:28:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683827 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COP'ULA'''. A ''leash'' for coupling sporting dogs, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Copula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|example |caption=Copula/1.1}}, from a bas-relief, representing the funeral of Meleager. Ov. ''Trist.'' v. 9. 2. A ''breast-collar'' attached to the traces, by which draught horses or mules drew their loads, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Copula 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|example |caption=Copula/2.1}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Herculaneum, after Ginzrot. Apul. ''Met.'' ix. p. 185. <gallery> File:Copula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|Copula/1.1 File:Copula 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 201.jpg|Copula/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Bits, Bridle, Reins, and Harness]] [[Category:Classed Index/Hunting]] q74g3yx1cto28sd9w1u8ze6to8vc2mo Illustrated Companion to the Latin Dictionary/Coquus 0 312058 2683828 2671698 2024-11-11T16:28:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683828 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COQUUS''' ({{lang|grc|μάγειρος}}). A ''cook'' (Mart. xiv. 220. Liv. xxxix. 6.); and in early times a ''maker of bread'' (Festus, ''s. v.'' Plin. ''H. N.'' xviii. 28.) It was not until U. C. 568., that the baker's became a distinct trade at Rome; and previously to this period each family ground their own flower, the cook making and baking the bread (Plin. ''l. c.'') The Greek {{lang|grc|μάγειρος}} was also originally employed in making bread for the family. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Bakers and Bread-making]] [[Category:Classed Index/Domestic Slaves]] 30y2xh4b3o4p3q76vajhxjhgehayyfw Illustrated Companion to the Latin Dictionary/Corax 0 312059 2683830 2671699 2024-11-11T16:28:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683830 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COR'AX''' ({{lang|grc|κόραξ}}). A Greek word, which occurs in a Latin form in Vitruvius, but only as a translation from Diades, who merely mentions it as the name of one of the military engines employed in the attack of fortified places, observing, at the same time, that it was very inefficient, and not worth the trouble of describing. (Vitruv. x. 13. 8.) Polybius also gives the same appellation to an engine employed by the Romans on board ship, and describes at length the manner in which it was constructed and applied. Polyb. i. 22. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Machines and Engines of War]] svkiku0z4lwohguzc51t0dvctn72oaj Illustrated Companion to the Latin Dictionary/Corbicula 0 312060 2683831 2683357 2024-11-11T16:29:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683831 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORBIC'ULA'''. (Pallad. ii. 10. 6.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Corbis|CORBIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0j33ybb1scklrozyczw0la3t1rr3pqf Illustrated Companion to the Latin Dictionary/Corbis 0 312061 2683832 2671701 2024-11-11T16:29:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683832 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COR'BIS'''. A basket of wicker-work, made in a pyramidical or conical shape (Varro, ''L. L.'' v. 139. Id. ''R. R.'' i. 22. 1. Isidor. ''Orig.'' xx. 9. Compare Arrian. ''Anab.'' v. 7. 8. {{lang|grc|πλέγμα ἐκ λύγου πυραμοειδές}}), and used for a variety of agricultural purposes, the particular application being generally marked by a characteristic epithet, as:{{mdash}} 1. ''Corbis messoria''; a basket used for measuring corn in the ear, as opposed to the ''[[Illustrated Companion to the Latin Dictionary/Modius|modius]]'', in which it was measured after it had been threshed out (Cic. ''Sext.'' 38. Cato, ''R. R.'' 136.); or in which the ears of corn (''spicas'') were collected by the reaper, when each ear was nicked off from the top of the stalk by a serrated instrument (see the illustration and description ''s.'' ''[[Illustrated Companion to the Latin Dictionary/Falx|Falx denticulata]]''), instead of being cut with the straw. Varro, ''R. R.'' i. 50. 1. Propert. iv. 11. 28. Ov. ''Met.'' xiv. 643. 2. ''Corbis pabulatorius''; a basket of the same character, which contained a certain measure of green food for cattle. Columell. vi. 3. 5. Id. xi. 2. 99. 3. ''Corbis constricta''; a basket of similar character, employed as a muzzle for horses (Veget. ''Mulom.'' iii. 23. 2.), but here the reading is doubtful; Schneider has ''[[Illustrated Companion to the Latin Dictionary/Curcuma|curcuma]]''. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Corbis 0.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 202.jpg|example |caption=Corbis/0.1}} introduced above is copied from a fresco [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] in the [[Illustrated Companion to the Latin Dictionary/Sepulcrum|sepulchre]] of the Nasonian family on the Flaminian Way, near Rome, where it appears several times in the hands of figures engaged in rural occupations; and is given as a genuine specimen of the Roman ''corbis'' or ''[[Illustrated Companion to the Latin Dictionary/Corbula|corbula]]'', on account of the uses to which it is there applied, its affinity in form to the descriptions cited at the head of this article, and because a basket of exactly the same shape and materials is now employed by the Neapolitan peasantry for similar purposes, and called by a diminutive of the same name, ''la corbella''. <gallery> File:Corbis 0.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 202.jpg|Corbis/0.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Baskets]] 2i7xemno853de4x16hrhtg65wtkl3rs Illustrated Companion to the Latin Dictionary/Corbita 0 312062 2683833 2671702 2024-11-11T16:29:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683833 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COR'BITA''' ({{lang|grc|πλοῖον σιταγωγόν}} or {{lang|grc|σιτηγόν}}). A merchantman; but more accurately, a ship employed solely for the transport of corn, and so termed, because it carried a ''[[Illustrated Companion to the Latin Dictionary/Corbis|corbis]]'' at the mast-head. (Festus, ''s. v.'') These were large and heavy sailing vessels (Plaut. ''Poen.'' iii. 1. 4. Lucil. ''ap.'' Non. ''s. v.'' p. 533. Compare Cic. ''Att.'' xvi. 6.), with two [[Illustrated Companion to the Latin Dictionary/Malus|masts]], as proved by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Corbita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 202.jpg|annexed example |caption=Corbita/1.1}} from a medal of Commodus, struck in commemoration of his having chartered a number of vessels to bring corn to Rome from Africa and Egypt, as narrated by Lampridius in his life. The ''corbis'' is seen at the top of the main mast; and it may be remarked that the modern name ''corvette'' originated in this word. <gallery> File:Corbita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 202.jpg|Corbita/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ships and Boats]] j9704srz37lqfg02szr2jhozq3eoi44 Illustrated Companion to the Latin Dictionary/Corbula 0 312063 2683834 2671703 2024-11-11T16:29:34Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683834 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COR'BULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Corbis|CORBIS]]; a small basket employed in fruit gathering (Cato, ''R. R.'' ii. 5.); as a bread basket (Caecil. ''ap.'' Non. ''s. v.'' p. 197.); and for carrying up dishes from the [[Illustrated Companion to the Latin Dictionary/Culina|kitchen]] to the dining room. Plaut. ''Aul.'' ii. 7. 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] chml1x41795ec1d35b8p1ra2t49wyld Illustrated Companion to the Latin Dictionary/Cordax 0 312064 2683836 2671704 2024-11-11T16:29:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683836 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORDAX''' ({{lang|grc|κόρδαξ}}). A dance of the old Greek comedy, at once highly ridiculous, and so indecent that it was considered a mark of drunkenness or great want of self-respect to dance it off the stage. (Pet. ''Sat.'' 52. 9. Hesych. ''s. v.'' Aristoph. ''Nub.'' 540.) A dance of this kind is represented on the marble tazza in the Vatican (Visconti, ''Mus. Pio-Clem.'' iv. 29.), where it is performed by ten figures, five Fauns, and five Bacchanals; but their movements, though extremely lively and energetic, are not marked by any particular indelicacy; certainly not so much as is exhibited in the Neapolitan ''tarantella'', which is thought to preserve the vestiges of the Greek ''cordax''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] eai3ync3i5rkp9mxp6wcilpki0xy54a Illustrated Companion to the Latin Dictionary/Coriarius 0 312065 2683837 2671705 2024-11-11T16:29:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683837 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORIA'RIUS'''. One who prepares hides and skins; a ''tanner'' or a ''carrier''. Plin. ''H. N.'' xvii. 6. Inscript. ''ap.'' Grut. 648. 8. and 283. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Shoe-makers and Leather-workers]] k7m3mtfdrq978q1jknig3g86e26vdal Illustrated Companion to the Latin Dictionary/Cornicen 0 312066 2683838 2671706 2024-11-11T16:30:06Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683838 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COR'NICEN''' ({{lang|grc|κεραταύλης}} or {{lang|grc|κεραύλης}}). A ''trumpeter''; i. e. who blows the large circular horn called ''[[Illustrated Companion to the Latin Dictionary/Cornu|cornu]]'', as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Cornicen 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 203.jpg|annexed illustration |caption=Cornicen/1.1}}, from the [[Illustrated Companion to the Latin Dictionary/Arcus|arch]] of Constantine at Rome. Liv. ii. 64. Juv. x. 214. <gallery> File:Cornicen 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 203.jpg|Cornicen/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Musicians]] n6ggynp1963vwxle2b9ja6a641d9e8n Illustrated Companion to the Latin Dictionary/Cornicularius 0 312067 2683839 2671707 2024-11-11T16:30:17Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683839 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORNICULA'RIUS'''. Strictly, a soldier who had been presented by his general with the ''[[Illustrated Companion to the Latin Dictionary/Corniculum|corniculum]]''; whence the name was given as a title to an assistant officer, or adjutant, who acted for the [[Illustrated Companion to the Latin Dictionary/Consul|consul]] or [[Illustrated Companion to the Latin Dictionary/Tribunus|tribune]]; probably because the person so promoted was always selected from amongst those who had received the above-named reward. Suet. ''Dom.'' 17. Val. Max. vi. 1. 11. 2. Hence the word came also to be applied in civil matters to a clerk or secretary, who acted as the assistant of a [[Illustrated Companion to the Latin Dictionary/Magistratus|magistrate]]. Cod. Theodos. 7. 4. 32. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Officers of the Army]] 28v1q75o7l05nx22sd5ia5wbu4afnl1 Illustrated Companion to the Latin Dictionary/Corniculum 0 312068 2683840 2671708 2024-11-11T16:30:28Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683840 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORNIC'ULUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cornu|CORNU]], any small horn; but, in a more special sense, an ornament bestowed upon meritorious soldiers by their commanding officer, as a mark of distinction (Liv. x. 44.), supposed to have been in the form of a horn, and worn upon the [[Illustrated Companion to the Latin Dictionary/Galea|helmet]], either as a support for the crest, like the left-hand figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Corniculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 203.jpg|engraving |caption=Corniculum/1.1}} annexed, from a bas-relief; or affixed to the sides, like the one on the right, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii. <gallery> File:Corniculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 203.jpg|Corniculum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Military Rewards, Badges, etc.]] gtw9ggc4bvv7drf0b169gyhs55lqd2d Illustrated Companion to the Latin Dictionary/Cornu copiae 0 312069 2683842 2671709 2024-11-11T16:30:39Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683842 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORNU CO'PIAE''' ({{lang|grc|κέρας Ἀμαλθείας}}). The ''horn of plenty''; a symbol composed of the primitive drinking-horn ([[Illustrated Companion to the Latin Dictionary/Cornu|CORNU]], 4.), filled with corn and fruit, to indicate the two kinds of nourishment essential to mankind, whence commonly employed by poets and artists as a symbol of Happiness, of Concord, and of Fortune. (Plaut. ''Pseud.'' ii. 3. 5. Compare Hor. ''Epist.'' i. 12. 29. ''Od.'' i. 17. 15. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cornu_copiae 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|example |caption=Cornu_copiae/1.1}} is from a terra-cotta lamp, where it accompanies an image of Fortune. <gallery> File:Cornu_copiae 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|Cornu copiae/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Classed Index-category missing]] 5e6a5pzj1shdfgrhuw5odwtng192el0 Illustrated Companion to the Latin Dictionary/Cornu 0 312070 2683843 2671710 2024-11-11T16:30:50Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683843 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORNU''', '''CORNUS''', or '''CORNUM''' ({{lang|grc|κέρας}}), originally, an animal's horn; whence specially applied to various other objects, either because they were made of horn, or resembled one in form; for instance: 1. A ''horn [[Illustrated Companion to the Latin Dictionary/Laterna|lantern]]''. Plaut. ''Amph.'' i. 1. 188. See [[Illustrated Companion to the Latin Dictionary/Laterna|LATERNA]]. 2. An ''oil cruet'', either made of horn, or out of a horn. Hor. ''Sat.'' ii. 2. 61. 3. A ''funnel'' made out of a horn. (Virg. ''Georg.'' iii. 509.) See [[Illustrated Companion to the Latin Dictionary/Infundibulum|INFUNDIBULUM]]. 4. A ''drinking-horn'' (Calpurn. ''Ecl.'' x. 48. Plin. ''H. N.'' xi. 45.), originally made out of a simple horn, but subsequently of different metals modelled into that form. When drinking, the horn was held above the head, and the liquor permitted to flow from it into the mouth through a small orifice at the sharp end, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cornu 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|illustration |caption=Cornu/4.1}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii. 5. An ornamental part of the [[Illustrated Companion to the Latin Dictionary/Galea|helmet]]. (Liv. xxvii. 33. Virg. ''Aen.'' xii. 89.) See [[Illustrated Companion to the Latin Dictionary/Corniculum|CORNICULUM]]. 6. ({{lang|grc|σάλπιγξ στρογγύλη}}). A very large trumpet; originally made of horn, but subsequently of bronze (Varro, ''L. L.'' v. 117. Ovid. ''Met.'' i. 98.), with a cross-bar, which served the double purpose of keeping it in shape, and of assisting the trumpeter to hold it steady while in use, as shown by the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Cornicen|CORNICEN]]. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cornu 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|example |caption=Cornu/6.1}} is copied from the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. 7. The horn of a [[Illustrated Companion to the Latin Dictionary/Lyra|lyre]] (''[[Illustrated Companion to the Latin Dictionary/Testudo|testudo]]''); and as there were two of these, one on each side of the instrument, the plural is more appropriately used. (Cic. ''N. D.'' ii. 59.) They were sometimes actually made with the horns of certain animals, as of the wild antelope (Herod. iv. 192.), which appear to be represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cornu 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|annexed example |caption=Cornu/7.1}}, from a painting at Pompeii. 8. A ''[[Illustrated Companion to the Latin Dictionary/Arcus|bow]]''; in like manner made with the horns of animals, joined together by a centre piece, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cornu 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|annexed example |caption=Cornu/8.1}}, from a fictile vase. In this sense both the singular and plural are used. Ovid. ''Met.'' v. 383. Virg. ''Ecl.'' x. 59. Suet. ''Nero'', 39. 9. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=extreme ends |imagelink=Media:Cornu 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|extreme ends |caption=Cornu/9.1}} of a yardarm, to which a square sail is attached; used in the plural, because there were two of them. Virg. ''Aen.'' iii. 549. ''Ib.'' v. 832. 10. Also in the plural. Ornaments affixed to each end of the stick upon which an ancient book or [[Illustrated Companion to the Latin Dictionary/Volumen|volume]] was rolled, in the same manner as now practised for maps, and projecting on either side beyond the margin of the roll. The precise character of these horns is not ascertained, nor in what respect they differed from the ''[[Illustrated Companion to the Latin Dictionary/Umbilicus|umbilici]]''; nor have any appendages appearing to correspond with the name been met with amongst the numerous MSS. discovered at Herculaneum. It is clear, however (from Ov. ''Trist.'' i. 1. 8. and Tibull. iii. 3. 13.), that all books were not decorated with them, but only such as were fitted up with more than ordinary taste and elegance. As the cylinder to which the horns were attached was fastened on to the bottom of the roll, the expression ''ad cornua'' is used to signify the end. Mart. xi. 107. Compare [[Illustrated Companion to the Latin Dictionary/Umbilicus|UMBILICUS]]. <gallery> File:Cornu 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|Cornu/4.1 File:Cornu 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|Cornu/6.1 File:Cornu 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|Cornu/7.1 File:Cornu 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|Cornu/8.1 File:Cornu 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 204.jpg|Cornu/9.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Drinking Cups]] [[Category:Classed Index/Stringed Instruments]] [[Category:Classed Index/Wind Instruments]] [[Category:Classed Index/Books and Writing Materials]] [[Category:Classed Index/Bows, Slings, etc.]] [[Category:Classed Index/The Rigging]] 7elg80kc26z9enc5vj95773cgapo8f4 Illustrated Companion to the Latin Dictionary/Corollarium 0 312071 2683844 2671711 2024-11-11T16:31:01Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683844 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COROLLA'RIUM'''. Also a diminutive from [[Illustrated Companion to the Latin Dictionary/Corona|CORONA]]; but more specially applied to a light wreath made of very ''thin leaves of metal'' plated or gilt, which the Romans used to give away as a present to favourite [[Illustrated Companion to the Latin Dictionary/Histrio|actors]]. Plin. ''H. N.'' xxi. 3. Varro, ''L. L.'' v. 178. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 65kq7nlgwqcm9u08420x8a2c2paqh57 Illustrated Companion to the Latin Dictionary/Corolla 0 312072 2683845 2671712 2024-11-11T16:31:12Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683845 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COROL'LA''' ({{lang|grc|στεφανίσκος}}). As a general diminutive of [[Illustrated Companion to the Latin Dictionary/Corona|CORONA]], means any kind of small chaplet or garland (Prop. ii. 34. 59. Catull. 63. 66.); but the word is used in a more special sense to designate a ''wreath of artificial flowers'' made out of thin horn shavings, tinged with different colours, to imitate the tints required, and worn in the winter season. Plin. ''H. N.'' xxi. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Head-bands]] dk9hiyoxk3ga3ujkbfk9pgk2b6rkzmn Illustrated Companion to the Latin Dictionary/Coronaria 0 312073 2683847 2671713 2024-11-11T16:31:23Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683847 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORONA'RIA'''. A female who makes [[Illustrated Companion to the Latin Dictionary/Corona|garlands]] and chaplets. Plin. ''H. N.'' xxi. 3. See [[Illustrated Companion to the Latin Dictionary/Coronarius|next illustration]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ovjnmyyfyyxvqddrxstm4ikwlyquiil Illustrated Companion to the Latin Dictionary/Coronarius 0 312074 2683848 2671714 2024-11-11T16:31:34Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683848 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORONA'RIUS''' ({{lang|grc|στεφανηπλόκος}}). One who makes and sells [[Illustrated Companion to the Latin Dictionary/Corona|garlands]], wreaths, chaplets, or crowns, of real or artificial flowers. (Front. ''ad'' M. Caes. ''Ep.'' i. 6. Plin. ''H. N.'' xxxiv. 26.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Coronarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|illustration |caption=Coronarius/1.1}} is from a Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|painting]], and represents male and female genii engaged in this operation. 2. ''Aurum coronarium''. A sum of gold sent by the provinces to a commander, for making a golden triumphal crown. (Cic. ''Pis.'' 37.) See [[Illustrated Companion to the Latin Dictionary/Corona|CORONA]], 1. (3.). 3. ''Opus coronarium''. ''Stucco-work'' employed in the decoration of cornices. Vitruv. vii. 6. [[Illustrated Companion to the Latin Dictionary/Corona|CORONA]], 14. and 15. <gallery> File:Coronarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|Coronarius/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Head-bands]] 5bglorfc6jzb5xo6f8b8xv4x7396riw Illustrated Companion to the Latin Dictionary/Coronatus 0 312075 2683849 2671715 2024-11-11T16:31:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683849 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORONA'TUS''' ({{lang|grc|στεφανηφόρος}}). Wearing a wreath, chaplet, or crown. See the illustrations to [[Illustrated Companion to the Latin Dictionary/Corona|CORONA]]. 2. Also, decorated with garlands or festoons; applied to things, as to ships (Ov. ''Fast.'' iv. 335.); to [[Illustrated Companion to the Latin Dictionary/Ara|altars]] (Prop. iii. 10. 19.); to cattle (Prop. iii. 1. 10. Id. iv. 1. 21.). == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] tb4ckjq4o8xycksup1nox01zlx833i1 Illustrated Companion to the Latin Dictionary/Corona 0 312076 2683850 2671716 2024-11-11T16:31:56Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683850 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORO'NA''' ({{lang|grc|στέφανος, κορωνίς}}). A ''wreath, garland'', or ''chaplet'', made of real or artificial flowers, leaves, &c., worn as an ornament upon the head; but not as a ''crown'' in our sense of the word, i. e. as an emblem of royalty; for amongst the ancients, a diadem (''[[Illustrated Companion to the Latin Dictionary/Diadema|diadema]]'') occupied the place of the modern crown. Of these there were a great many varieties, distinguished by the different materials or the designs in which they were made, and chiefly employed as rewards for public virtue, or ornaments for festive occasions. Under these two divisions, the principal ''coronae'' are enumerated in the following paragraphs:{{mdash}} 1. ''Corona triumphalis''. The ''triumphal crown''; of which there were three several kinds. (1.) ''A wreath of laurel leaves without the berries'' (Aul. Gell. v. 6. 1. Plin. ''H. N.'' xv. 39.), worn by the general during his [[Illustrated Companion to the Latin Dictionary/Triumphus|triumph]] in the manner shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed bust |imagelink=Media:Corona 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|annexed bust |caption=Corona/1.1}} of Antoninus, from an engraved gem. This being esteemed the most honourable of the three, was expressely designated ''laurea insignis''. (Liv. vii. 13.) (2.) A ''crown of gold'' made in imitation of laurel leaves, which was held over the head of the general during the triumph by a public officer (''servus publicus'', Juv. x. 41.) appointed for the purpose, and in the manner shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Corona 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|illustration |caption=Corona/1.2}}, from a bas-relief on the [[Illustrated Companion to the Latin Dictionary/Arcus|Arch]] of Titus, representing that emperor in his triumphal car at the procession for the conquest of Jerusalem, in which a winged figure of Victory poetically performs the part of the public officer. (3.) A crown of gold, and of considerable value, but merely sent as a present to the general who had obtained a triumph (Plut. ''Paul. Aemil.'' 34.), from the different provinces, whence it is expressely called ''provincialis''. Tertull. ''Coron. Mil.'' 13. 2. ''Corona ovalis''. A chaplet of ''myrtle'' worn by a general who had obtained the honour of an ovation. Aul. Gell. v. 6. Festus, ''s. v.'' 3. ''Corona oleagina''. A wreath of ''olive leaves'', which was conferred upon the soldiery, as well as their commanders, and was appropriated as a reward for those through whose counsels or instrumentality a triumph had been obtained, though they were not themselves present in the action. Aul. Gell. v. 6. 4. ''Corona obsidionalis''. A garland of ''grass and wild flowers'', whence also termed ''graminea'' (Liv. vii. 37.), gathered on the spot where a Roman army had been besieged, and presented by that army to the commander who had come to their relief, and broken the siege. Though the least in point of value, this was regarded as the most honourable of all the military rewards, and the most difficult to be obtained. Aul. Gell. v. 6. Festus, ''s. v.'' Plin. xxii. 4. 5. ''Corona civicia''. The ''civic crown''; a chaplet of ''oak leaves with the acorns'', presented to the Roman soldier who had saved the life of a comrade in battle, and slain his opponent. It was originally presented by the rescued comrade, and latterly by the emperor. (Plin. ''H. N.'' xvi. 3. Aul. Gell. v. 6. Tac. ''Ann.'' xv. 12.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Corona 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|illustration |caption=Corona/5.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, representing a young warrior with the civic wreath. 6. ''Corona muralis''. The ''mural crown''; decorated with the towers and turrets of a battlement, and given as a reward of valour to the soldier who was first in scaling the walls of a besieged city. (Liv. xxvi. 48. Aul. Gell. v. 6.) The character of this crown is known from the representations of the goddess Cybele, to whom it was ascribed by poets and artists, in order to typify the cities of the earth over which she presided. (Lucret. ii. 607{{mdash}}610. Ov. ''Fast.'' iv. 219.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Corona 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|example |caption=Corona/6.1}} is from a bas-relief found in a [[Illustrated Companion to the Latin Dictionary/Sepulcrum|sepulchre]] near Rome. 7. ''Corona castrensis'', or ''vallaris''. A crown of gold, ornamented with palisades (''[[Illustrated Companion to the Latin Dictionary/Vallum|vallum]]''), and bestowed upon the soldier who first surmounted the stockade, and forced an entrance into an enemy's camp. (Aul. Gell. v. 6. Val. Max. i. 8. 6.) Of this no authentic specimen exists. 8. ''Corona classica, navalis'', or ''rostrata''. A chaplet of gold designed to imitate the beaks of ships (''[[Illustrated Companion to the Latin Dictionary/Rostrum|rostra]]''), and presented to the admiral who had destroyed a hostile fleet, and, perhaps, also to the sailor who was the first to board an enemy's vessel. (Paterc. ii. 81. Virg. ''Aen.'' viii. 684. Plin. ''H. N.'' It is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed wood-cut |imagelink=Media:Corona 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|annexed wood-cut |caption=Corona/8.1}}, on the head of Agrippa, from a bronze medal. 9. ''Corona radiata''. The ''radiated crown''; set round with projecting rays, and properly assigned to the gods or deified heroes; whence it was generally assumed by the Roman emperors, and by some other persons who affected the attributes of divinity. (Stat. ''Theb.'' 1. 28.) Its character is shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Corona 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|annexed illustration |caption=Corona/9.1}}, on the head of Augustus, from one of the Marlborough gems. 10. ''Corona pactilis, plectilis'', or ''plexilis''. A festive garland worn merely as an ornament round the head, and composed of natural flowers with their leves adhering to the stalks, by which they were twisted and twined together, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Corona 10.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|annexed illustration |caption=Corona/10.1}}, representing a personification of Spring, from a marble bas-relief. Plin. ''H. N.'' xxi. 8. Aul. Gell. xviii. 2. Plaut. ''Bacch.'' 1. 1. 37. 11. ''Corona sutilis''. An ornamental garland for the head, made of flowers plucked from their stalks, and sewed together. It was the one worn by the [[Illustrated Companion to the Latin Dictionary/Salii|Salii]] at their festivals; and was originally composed of flowers of any description, but subsequently of the rose alone, the choicest leaves being selected from each blossom, and then sewn together. (Plin. ''H. N.'' xxi. 8.) It is represented in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Corona 11.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|annexed engraving |caption=Corona/11.1}}, on the head of a Roman empress, from an engraved gem. 12. ''Corona natalitia''. A wreath of laurel, ivy, or parsely, which the Romans were in the custom of suspending over the door of a house in which a birth had taken place, in the same way as the natives of Holland put up a rosette of lace upon similar occasions. Bartholin. ''de Puerp.'' p. 127. Compare Juv. ''Sat.'' ix. 85. 13. ''Corona longa'' ({{lang|grc|ὑποθυμίς, ὑποθυμιάς}}). A ''long wreath'' or ''festoon'' of flowers hung over the neck and chest, in the same way as the ''rosary'', of which it was the probable original, the rosary being still called "''la corona''" by the modern Italians; but, amongst the Greeks and Romans, it appears to have been more particularly employed as a festive decoration, and was used to ornament buildings as well as persons. (Ovid. ''Fast.'' iv. 738. Cic. ''Leg.'' ii. 24.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Corona 13.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|illustration |caption=Corona/13.1}} is from an ivory carving in the Florentine Gallery, supposed to represent M. Antony in the costume of a follower of Bacchus, and resembles exactly the description which Cicero gives of Verres, with a chaplet on his head, and a garland round his neck{{mdash}}''ipse autem coronam habebat unam in capite, alteram in collo.'' ''Verr.'' ii. 5. 11. 14. A ''cornice'', or projecting member, used to decorate walls, either as a finish on the top (see the next illustration), or for the purpose of making ornamental divisions on any part of the surface. Vitruv. v. 2. Id. vii. 3. 4. Plin. ''H. N.'' xxxvi. 59. 15. A particular ''member of the cornice'', which {{Illustrated Companion to the Latin Dictionary/Image Location|text=crowns |imagelink=Media:Corona 15.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|crowns |caption=Corona/15.1}} an entablature under the roof, still called by our architects the ''corona''. It is that particular member which has a broad flat face situated between the ''[[Illustrated Companion to the Latin Dictionary/Sima|cyma recta]]'' above, and the ''[[Illustrated Companion to the Latin Dictionary/Cymatium|cymatium]]'', or bed moulding, below, from which it has a bold projection. (Vitruv. iv. 3. 6.) The Roman architects, unlike ours, do not appear to have appropriated any distinct word to express collectively all the members of which a cornice is composed; consequently, they did not regard the cornice as an entire portion of an entablature, but as several distinct members, which are always enumerated separately: viz. the ''[[Illustrated Companion to the Latin Dictionary/Sima|sima]]; cymatium in summo; corona; cymatium in imo''. Hesychius, however, uses the Greek {{lang|grc|κορωνίς}} in a collective sense, as equivalent to our ''cornice''. <gallery> File:Corona 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|Corona/1.1 File:Corona 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 205.jpg|Corona/1.2 File:Corona 5.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|Corona/5.1 File:Corona 6.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|Corona/6.1 File:Corona 8.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|Corona/8.1 File:Corona 9.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 206.jpg|Corona/9.1 File:Corona 10.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|Corona/10.1 File:Corona 11.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|Corona/11.1 File:Corona 13.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|Corona/13.1 File:Corona 15.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 207.jpg|Corona/15.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Head-bands]] [[Category:Classed Index/Ornaments for the Person]] [[Category:Classed Index/Military Rewards, Badges, etc.]] [[Category:Classed Index/The Pediment]] 6374cu81j7jflllafj2qpt5vfv1yhvq Illustrated Companion to the Latin Dictionary/Corrigia 0 312077 2683852 2671717 2024-11-11T16:32:07Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683852 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORRIG'IA''' ({{lang|grc|ἱμάς, σφαιρωτήρ}}). A ''shoe-string'' and ''boot-lace'' (Cic. ''Div.'' ii. 40.); which were sometimes made of dog's skin. (Plin. ''H. N.'' xxx. 12.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=examples |imagelink=Media:Corrigia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|examples |caption=Corrigia/1.1}} are from Pompeian [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]]. <gallery> File:Corrigia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|Corrigia/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feet]] g1koj4pgrv6n81jwy10zuzg79qdva5l Illustrated Companion to the Latin Dictionary/Corrugis 0 312078 2683853 2671718 2024-11-11T16:32:18Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683853 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORRU'GIS'''. Literally ''wrinkled''; but it is applied to the plaits of a loose garment (''sinus corrugis'', Nemes. ''Cyneg.'' 93.), produced by tieing a girdle round it (see the figures in the [[Illustrated Companion to the Latin Dictionary/Coronarius|opposite column]]); or to the irregular and transverse folds created by throwing up a portion over the shoulder, instead of leaving it pendant, as seen on the right side of the figure ''s.'' [[Illustrated Companion to the Latin Dictionary/Contabulatio|CONTABULATIO]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] tnzhcp726zhhf0zzjf4kz8c1e3zg2pp Illustrated Companion to the Latin Dictionary/Corsae 0 312079 2683855 2671719 2024-11-11T16:32:29Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683855 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORSAE'''. Fillets or mouldings employed to decorate the external face of a marble door-post. (Vitruv. iv. 6.) See the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Antepagmentum|ANTEPAGMENTUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Doors]] o25q81mytffsi68pimlqw1ly7p229tj Illustrated Companion to the Latin Dictionary/Cortinale 0 312080 2683856 2671720 2024-11-11T16:32:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683856 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORTINA'LE'''. A cellar in which new-made wine was boiled down in caldrons (''[[Illustrated Companion to the Latin Dictionary/Cortina|cortinae]]''). Columell. i. 6. 19. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Manufacture of Oil and Wine]] qajcu3z0wu1gy9wajr7x0udyqu7fafo Illustrated Companion to the Latin Dictionary/Cortina 0 312081 2683857 2671721 2024-11-11T16:32:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683857 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORTI'NA'''. A deep circular vessel, or ''caldron'', employed for boiling meat, melting pitch (Plin. ''H. N.'' xvi. 22.), making paint (Id. xxxv. 42.), and a variety of other purposes, for which its form and character rendered it convenient, and which, when placed over the fire, was either raised upon a trivet, or supported upon large stones put under it. (Plin. ''H. N.'' xxxvi. 65.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cortina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|example |caption=Cortina/1.1}} is copied from a bronze original found at Pompeii. 2. ({{lang|grc|ὅλμος, κύκλος, ἐπίθημα τοῦ τρίποδος}}). The ''lid'' or covering placed over the caldron or hollow part of the Delphic [[Illustrated Companion to the Latin Dictionary/Tripus|tripod]] (Virg. ''Aen.'' vi. 347. Prudent. ''Apoth.'' 506. ''tripodas cortina tegit'', Jul. Pollux. x. 81.), upon which the priestess sat to receive the divine afflatus, and pronounce her responses. It had the form of a half globe, and is frequently represented in that manner by [[Illustrated Companion to the Latin Dictionary/Scalptor|sculptors]], lying by itself upon the ground at the feet of Apollo; but when placed upon the caldron, the two together made a complete globe; as shown in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cortina 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|illustration |caption=Cortina/2.1}}, from a bas-relief upon an [[Illustrated Companion to the Latin Dictionary/Ara|altar]] in the Villa Borghese. In the original, the raven, sacred to Apollo, is sitting on its top; in one of Hamilton's vases, Apollo himself is seen sitting upon the cup, without any lid, and in another, upon a lid like the present. 3. An altar in the form of a tripod, made of marble, bronze, or the precious metals, often intended to be dedicated as an offering in the [[Illustrated Companion to the Latin Dictionary/Templum|temples]] of the gods, and likewise preserved as a piece of ornamental furniture in the houses of great and wealthy persons. (Plin. ''H. N.'' xxxiv. 8. Suet. ''Aug.'' 52. Compare Mart. xii. 66.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cortina 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|illustration |caption=Cortina/3.1}} is copied from an original of marble in the Vatican. 4. The vault or ceiling over the stage in a [[Illustrated Companion to the Latin Dictionary/Theatrum|theatre]], from its resemblance to the covering of the tripod, No. 2. Sever. ''Aetn.'' 294. <gallery> File:Cortina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|Cortina/1.1 File:Cortina 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 208.jpg|Cortina/2.1 File:Cortina 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|Cortina/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] [[Category:Classed Index/Implements of Worship and Sacrifice]] kk14e0lundlh8ffc11ydbzdb3t90hjx Illustrated Companion to the Latin Dictionary/Cortinula 0 312082 2683859 2671722 2024-11-11T16:33:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683859 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORTIN'ULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cortina|CORTINA]]. Ammian. xxix. 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] peagf4buiu0lvklko2wy98ln3e0fggr Illustrated Companion to the Latin Dictionary/Corvus 0 312083 2683860 2671723 2024-11-11T16:33:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683860 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORVUS''' ({{lang|grc|κόραξ}}). The name given to several machines employed in naval and military operations, and in the attack or defence of fortified places; each of which was so called either from its resemblance in form to the raven's beak, or from the manner of its application, like the raven darting down, and carrying off its prey; consequently, the word may be translated as a ''crane'', a ''grappling-iron'', a ''crow-bar'', as best suits the context in the passages where it occurs. Quin. Curt. iv. 2. Id. iv. 4. Vitruv. x. 19. 2. A cutting instrument used in [[Illustrated Companion to the Latin Dictionary/Chirurgus|surgical]] operations, because the blade was shaped like a raven's beak. Celsus, vii. 19. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Surgical Implements, etc.]] [[Category:Classed Index/Machines and Engines of War]] chhom9nv98zjgllq4ox7ssqtnvh5ija Illustrated Companion to the Latin Dictionary/Corycaeum 0 312084 2683861 2671724 2024-11-11T16:33:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683861 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORYCAE'UM'''. An apartment in the [[Illustrated Companion to the Latin Dictionary/Gymnasium|gymnasium]] and in large [[Illustrated Companion to the Latin Dictionary/Balineae|bathing establishments]], such as the Roman [[Illustrated Companion to the Latin Dictionary/Thermae|Thermae]], appropriated for playing a particular kind of game, which consisted in buffetting backwards and forwards a large sack ({{lang|grc|κώρυκος}}), filled with fig grains, olive husks, bran, or sand, suspended from the ceiling. Anthyll. ''ap.'' Oribas. ''Coll. Med.'' 6. Vitruv. v. 11. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Gymnasium and Palaestra]] mf97ap1y2f15deke1j5fqudwjygojnc Illustrated Companion to the Latin Dictionary/Corymbium 0 312085 2683862 2671725 2024-11-11T16:33:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683862 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORYM'BIUM'''. A wig of false hair, dressed in imitation of the ''corymbus'' (Pet. ''Sat.'' 110. 1. and 5.),{{mdash}}a fashion which is explained in the [[Illustrated Companion to the Latin Dictionary/Corymbus|next article]], No. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] bewqjf25vk3e1cmzvwgx61oavdrt7hz Illustrated Companion to the Latin Dictionary/Corymbus 0 312086 2683863 2671726 2024-11-11T16:33:45Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683863 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORYM'BUS''' ({{lang|grc|κόρυμβος}}). A ''bunch of ivy berries'', and likewise of other kinds of fruit which grow in the same conical-shaped clusters; afterwards, a [[Illustrated Companion to the Latin Dictionary/Corona|wreath]] or chaplet made with the ''leaves and clusters of the ivy'', which the ancients used as a festive ornament on many occasions, but especially as an appropriate decoration for Bacchus and his followers, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Corymbus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|annexed illustration |caption=Corymbus/1.1}}, from a marble bust, supposed to represent Ariadne. Tibull. i. 7. 45. Prop. ii. 30. 39. Juv. vi. 52. 2. A peculiar manner of arranging the hair, more especially characteristic of the early population of Athens (Heraclid. ''ap.'' Athen. xii. 5. Compare [[Illustrated Companion to the Latin Dictionary/Crobylus|CROBYLUS]]), and of the female sex amongst them. (Schol. ''ad'' Thucyd. i. 6.) It was produced by turning the hair backwards all round the head, and drawing it up to a point at the top, where it was tied with a band, so as to have a sort of resemblance in general form to a cluster of ivy berries, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Corymbus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|example |caption=Corymbus/2.1}}, from a bas-relief in Greek marble. When the hair was too long or too abundant to be tied thus simply, it was fastened in a double bow across the top of the head, as in the well-known statue of Apollo Belvedere, and a bust of Diana in the British Museum. In Cicero (''Ep. Att.'' xiv. 3.) Corymbus is a proper name, arising out of the custom of arranging the hair in the manner described. Ernesti, ''Clav. Cic.'' ''s. v.'' 3. The elevated ornament on the stern of a ship (Val. Flacc. i. 272.); for which the special name is [[Illustrated Companion to the Latin Dictionary/Aplustre|APLUSTRE]]; which see. <gallery> File:Corymbus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|Corymbus/1.1 File:Corymbus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 209.jpg|Corymbus/2.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Hair and Beard]] d4ljfwfanaq5f6q8etm2p62wb9ez2vt Illustrated Companion to the Latin Dictionary/Corytus 0 312087 2683864 2671727 2024-11-11T16:33:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683864 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CORY'TUS''' ({{lang|grc|γωρυτός}}). Properly, and accurately a ''bow-case'' (Serv. ''ad'' Virg. ''Aen.'' x. 168.), as contradistinguished from the quiver for arrows (''[[Illustrated Companion to the Latin Dictionary/Pharetra|pharetra]]''); although the same case was sometimes used to carry both the [[Illustrated Companion to the Latin Dictionary/Arcus|bow]] and [[Illustrated Companion to the Latin Dictionary/Sagitta|arrows]], when it is distinguished by a characteristic epithet (''sagittiferi coryti'', Sil. Ital. xv. 773.). An example of both kinds is given in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Corytus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|engraving |caption=Corytus/1.1}}, the simple bow-case from a fictile vase, the one containing the bow and arrows from an engraved gem. <gallery> File:Corytus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|Corytus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Bows, Slings, etc.]] cfznv0l3u5szzcn1jyb3zs18b4ls2pb Illustrated Companion to the Latin Dictionary/Cosmetae 0 312088 2683865 2671729 2024-11-11T16:34:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683865 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COSME'TAE'''. ''Ladies' maids''; slaves whose duty it was to attend the toilet of the Roman ladies, and assist in dressing and adorning their mistresses. Juv. ''Sat.'' vi. 477. Heindorf. ''ad'' Hor. ''Sat.'' i. 2. 98. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] o2luw9qronz0n98r0s3po50i3lfyf5m Illustrated Companion to the Latin Dictionary/Cos 0 312089 2683866 2671730 2024-11-11T16:34:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683866 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COS''' ({{lang|grc|ἀκόνη}}). A ''hone, whetstone'', or ''grindstone''; worked with water and oil (Plin. ''H. N.'' xxxvi. 47.), and by the same sort of machinery as now employed. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cos 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|illustration |caption=Cos/1.1}}, from an engraved gem, represents Cupid sharpening his [[Illustrated Companion to the Latin Dictionary/Sagitta|arrows]] on a grindstone, exactly as described by Horace (''Od.'' ii. 8. 15. ''ardentes acuens sagittas Cote cruenta''). <gallery> File:Cos 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|Cos/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Miscellaneous Domestic Furniture and Utensils]] d3ytpuj549sha5p4x5ajy9esc4fcgp6 Illustrated Companion to the Latin Dictionary/Cothurnatus 0 312090 2683867 2671731 2024-11-11T16:34:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683867 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COTHURNATUS'''. Wearing the ''[[Illustrated Companion to the Latin Dictionary/Cothurnus|cothurnus]]'', as explained and illustrated in the [[Illustrated Companion to the Latin Dictionary/Cothurnus|next word]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Actors, Mimics, Dancers, and Dancing]] cxghvj6wd8h0kv0hlpu8fh3gmfk3jk6 Illustrated Companion to the Latin Dictionary/Cothurnus 0 312091 2683869 2671732 2024-11-11T16:34:40Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683869 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COTHURNUS''' ({{lang|grc|κόθορνος}}). A ''high boot'' of Greek original, usually worn by [[Illustrated Companion to the Latin Dictionary/Venator|huntsmen]], and persons addicted to the sports of the field. It was a leather boot, enveloping the entire foot (whence ''cothurno calceatus'', Plin. ''H. N.'' vii. 19.) and leg as far as the calf (Serv. ''ad'' Virg. ''Aen.'' i. 337. Herod. vi. 125.), was laced up the front, and turned over with a fall down at the top, besides possessing the characteristic peculiarity of not being made right and left, as the foot coverings of the ancients usually were, but with a straight sole (''solo perpetuo'', Sidon. Apoll. ''Carm.'' ii. 400.), so that each boot could be worn indifferently on either foot (''utroque aptus pedi'', Serv. ''ad'' Virg. ''Bucol.'' vii. 32.); hence the frequent application of the word in the singular, whilst the ''[[Illustrated Companion to the Latin Dictionary/Calceus|calcei]]'' and other coverings made in pairs mostly occur in the plural. All these peculiarities are distinctly apparent in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cothurnus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|illustration |caption=Cothurnus/1.1}}, representing on a larger scale the boots worn by the fowler exhibited at p. 67. ''s.'' [[Illustrated Companion to the Latin Dictionary/Auceps|AUCEPS]]. 2. A boot of the same description, but more elaborately ornamented, and commonly translated ''buskin'', is occasionally assigned by the Greek artists to some of their divinities, especially to Diana, Bacchus, and Mercury; and by the Romans, in like manner, to the goddess Roma, and to their emperors, as a sign of divinity. Thus they were assumed by M. Antony, when he affected the character and attributes of Bacchus (Vell. Pat. ii. 82.); but they were not worn by the Roman as a part of his ordinary costume; for Cicero (''Phil.'' iii. 6.) reproaches the insolence of one Tuditanus who appeared in public ''cum [[Illustrated Companion to the Latin Dictionary/Palla|palla]] et cothurnis''. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cothurnus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 211.jpg|illustration |caption=Cothurnus/2.1}} affords a specimen of a ''cothurnus'' of this nature, from a marble figure of the goddess Roma. 3. The Roman poets also make use of the word ''cothurnus'', as a translation of the Greek {{lang|grc|ἐνδρομίς}} (see [[Illustrated Companion to the Latin Dictionary/Endromis|ENDROMIS]], 3.). In this manner it is applied by Virgil (''Aen.'' i. 341.), Nemesian (''Cyneg.'' 90.), and Sidonius Apollinaris (''Carm.'' ii. 400.), which last passage minutely describes the {{lang|grc|ἐνδρομίς}}, but not the ''cothurnus''. 4. A boot worn by tragic [[Illustrated Companion to the Latin Dictionary/Histrio|actors]] on the [[Illustrated Companion to the Latin Dictionary/Theatrum|stage]] (Virg. ''Ecl.'' viii. 10. Servius ''ad l.''), having a cork sole several inches thick, for the purpose of increasing their stature (compare Juv. ''Sat.'' vi. 633.), and giving them a more imposing appearance; whence the word also came to signify a grand and dignified style. It was in order to conceal the unsightly appearance of such a chaussure, that the tragic actors always wore long robes reaching to the ground, as seen in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cothurnus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 211.jpg|illustration |caption=Cothurnus/4.1}} annexed, from a marble bas-relief of the Villa Albani, representing a company of stage-players, though here the artist has left the ''cothurni'' uncovered, in order to identify the character of the actor. <gallery> File:Cothurnus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 210.jpg|Cothurnus/1.1 File:Cothurnus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 211.jpg|Cothurnus/2.1 File:Cothurnus 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 211.jpg|Cothurnus/4.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feet]] bqjev6gabc8ei2w1ab2rdjzrlxaf2g3 Illustrated Companion to the Latin Dictionary/Coticula 0 312092 2683870 2671733 2024-11-11T16:34:52Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683870 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COTIC'ULA'''. Diminutive of ''[[Illustrated Companion to the Latin Dictionary/Cos|Cos]]''; a touch-stone for assaying gold and silver. Plin. ''H. N.'' xxxiii. 43. 2. A small [[Illustrated Companion to the Latin Dictionary/Mortarium|mortar]], made of the same hard kind of stone as that used for hones and grindstones. Plin. ''H. N.'' xxxi. 45. Id. xxxvii. 54. Isidor. ''Orig.'' iv. 11. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] i9le6r0yjqptj8tl17ckgbzqrvsrw9p Illustrated Companion to the Latin Dictionary/Cottabus 0 312093 2683871 2671734 2024-11-11T16:35:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683871 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COTT'ABUS''' ({{lang|grc|κότταβος}}). A game of Sicilian origin, and a very favourite after-dinner amusement amongst the young men of Athens. It was played in various ways, more or less complicated; but the simple and ordinary manner consisted in casting the heel-tap of a wine cup into a large metal vessel, or upon the floor, whilst the player affected to discover the sincerity of his mistress's affections by the particular sound of the splash produced by the wine in its fall; hence the word is applied to sounds of similar kind, but produced by other means, as the lash of a [[Illustrated Companion to the Latin Dictionary/Flagellum|whip]]. Plaut. ''Trinc.'' iv. 3. 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Games of Chance]] nomyv24xbq52xhahbpqk6fo9wjwm4a1 Illustrated Companion to the Latin Dictionary/Cotula 0 312094 2683872 2671735 2024-11-11T16:35:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683872 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COT'ULA''' or '''COT'YLA''' ({{lang|grc|κοτύλη}}). A small measure of capacity, containing the half of a ''[[Illustrated Companion to the Latin Dictionary/Sextarius|sextarius]]''. (Mart. ''Ep.'' viii. 71.) It was especially employed by medical practitioners, and had a graduated scale marked upon the sides, like those used by our apothecaries, dividing it into twelve equal parts, each of which was termed an ''[[Illustrated Companion to the Latin Dictionary/Uncia|uncia]]'', 1 oz. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Surgical Implements, etc.]] g91twig9zzi6ai9igq9ph8pjzwmzqo0 Illustrated Companion to the Latin Dictionary/Covinarius 0 312095 2683873 2671736 2024-11-11T16:35:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683873 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COVINA'RIUS'''. One who fights from a war-car of the kind called ''[[Illustrated Companion to the Latin Dictionary/Covinus|covinus]]''. Tac. ''Agr.'' 35. and 36. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 6vfmivc9lw7nc0o293xh2zb8otkns4s Illustrated Companion to the Latin Dictionary/Covinus 0 312096 2683874 2671737 2024-11-11T16:35:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683874 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''COVI'NUS'''. A war-car employed by the Belgae and ancient Britons, the precise character of which is not ascertained, beyond the fact that it was armed with scythes, and probably had a covering over head. Mela, iii. 6. Lucan. i. 426. Sil. Ital. xvii. 417. 2. A travelling carriage adopted by the later Romans, after the model of the Belgian car; and which, from a passage of Martial (''Ep.'' xii. 24.), it is inferred, was driven by the owner, who sat inside, and not by a coachman. In the same passage, it is also distinguished from the ''[[Illustrated Companion to the Latin Dictionary/Carruca|carruca]]'' and ''[[Illustrated Companion to the Latin Dictionary/Esseda|essedum]]'', but without any particulars. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Carriages]] 4dgvwy6bxl3lpgmgvl9wg63q7vhyp2y Illustrated Companion to the Latin Dictionary/Crater 0 312097 2683875 2671738 2024-11-11T16:35:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683875 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRA'TER''' ({{lang|grc|κρατήρ}}). A capacious bowl or vessel, containing wine and water mixed together, out of which the drinking goblets were filled, and handed round to each individual at table; for the ancients seldom drank their wine [[Illustrated Companion to the Latin Dictionary/Merum|neat]]. (Non. ''s. v.'' p. 545. Ovid. ''Fast.'' v. 522. Virg. ''Aen.'' i. 728.) It was made of various materials, from earthenware up to the precious metals; and in different forms, according to the taste of the designer, but always with a wide open mouth, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Crater 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 212.jpg|example |caption=Crater/1.1}}, from a bronze original discovered at Pompeii. At meal time it was brought into the eating-room, and placed upon the ground, or on a stand, and the cup-bearer (''[[Illustrated Companion to the Latin Dictionary/Pincerna|pincerna]]'', ''[[Illustrated Companion to the Latin Dictionary/Pocillator|pocillator]]'') took the mixed liquor from it with a ladle (''[[Illustrated Companion to the Latin Dictionary/Cyathus|cyathus]]''), out of which he replenished the cups (''[[Illustrated Companion to the Latin Dictionary/Poculum|pocula]]'', ''[[Illustrated Companion to the Latin Dictionary/Calix|calices]]'', &c.), and handed them to the guests. In the representations of Greek banquets (see the examples quoted ''s.'' [[Illustrated Companion to the Latin Dictionary/Comissatio|COMISSATIO]]), the ''crater'' is placed upon the ground in front of the tables; in an ivory carving of a Bacchanalian scene (Buanorotti, ''Med.'' p. 451.), it stands likewise upon the ground, while a winged genius pours the wine into it from an ''[[Illustrated Companion to the Latin Dictionary/Amphora|amphora]]''; and in a marble bas-relief, representing a similar subject (Bartoli, ''Adm.'' p. 45.), a Faun fills it in like manner from a wine skin (''[[Illustrated Companion to the Latin Dictionary/Uter|uter]]''). 2. The crater of a volcanic mountain (Plin. ''H. N.'' iii. 14. Lucret. vi. 702.); which is produced by the cinders and other matters discharged into the air from the mouth of the volcano, falling down all round the top, when they naturally form a deep circular basin, through which the eruption finds its vent. <gallery> File:Crater 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 212.jpg|Crater/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Wine Vessels]] eed55d10n8a8vuu3rprnkpbks9svxd3 Illustrated Companion to the Latin Dictionary/Crates 0 312098 2683876 2671740 2024-11-11T16:35:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683876 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRA'TES''' ({{lang|grc|ταρσός}}). Our ''crate''; a stand, frame, or basket, made with hurdles, or like a hurdle; also a hurdle itself; all of which were employed by the ancients in many different ways, as the same objects still are amongst ourselves. Varro, Cato, Columell. Virg. Hor. Caes. &c. 2. Same as [[Illustrated Companion to the Latin Dictionary/Carnarium|CARNARIUM]]. Juven. xi. 82. 3. ''Sub crate necari''. To be executed under the hurdle; an unusual method of punishment, sometimes adopted by the Romans (Liv. i. 51. Id. iv. 50.), in which the condemned was laid under a hurdle, and crushed by a weight of stones thrown upon it. Plaut. ''Poen.'' v. 2. 65. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Miscellaneous Domestic Furniture and Utensils]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] nfhp01akiihe3nmfodx7j1pips4v83m Illustrated Companion to the Latin Dictionary/Craticius 0 312099 2683877 2671741 2024-11-11T16:36:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683877 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRATIC'IUS'''. Made with [[Illustrated Companion to the Latin Dictionary/Crates|hurdles]], or hurdle-wise. See [[Illustrated Companion to the Latin Dictionary/Paries|PARIES]], 1. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 49t9zxrjkfcbnwbddrtm3cltnocrm53 Illustrated Companion to the Latin Dictionary/Craticula 0 312100 2683879 2671742 2024-11-11T16:36:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683879 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRATI'CULA''' ({{lang|grc|ταρῥίον}}). Diminutive of [[Illustrated Companion to the Latin Dictionary/Crates|CRATES]]; whence, in a more special sense, a ''gridiron'' (Cato, ''R. R.'' 13. 2. Mart. ''Ep.'' xiv. 221.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Craticula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 212.jpg|example |caption=Craticula/1.1}} is taken from an original of bronze found in a tomb at Paestum, but without the handle, which is restored in the engraving, from a similar specimen painted in a [[Illustrated Companion to the Latin Dictionary/Sepulcrum|sepulchre]] of the Christian era on the Via Tiburtina. <gallery> File:Craticula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 212.jpg|Craticula/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] 2letn4xzjyuo0yd42p2x9fb6vsi5zvw Illustrated Companion to the Latin Dictionary/Creagra 0 312101 2683880 2671743 2024-11-11T16:36:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683880 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREAG'RA''' ({{lang|grc|κρεάγρα}}). A Greek word Latinized (Marc. Cap.), for which the proper Latin term is [[Illustrated Companion to the Latin Dictionary/Harpago|HARPAGO]]; which see. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] qfymp3d3rnav6ibhxqeuvi4q9nai736 Illustrated Companion to the Latin Dictionary/Cremium 0 312102 2683881 2671744 2024-11-11T16:36:41Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683881 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREM'IUM''' ({{lang|grc|φρύγανον}}). Small wood, or ''underwood'', for burning; especially employed in bakers' [[Illustrated Companion to the Latin Dictionary/Furnus|ovens]]. Columell. xii. 19. 3. Ulp. ''Dig.'' 32. 35. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Fires and Fuel]] 9edk5fgpy7u8jvu6sksz9hcfpy20kur Illustrated Companion to the Latin Dictionary/Crepiculum 0 312103 2683883 2671745 2024-11-11T16:36:51Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683883 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPIC'ULUM''', '''CREPID'ULUM''', '''CREPIT'ULUM'''. An ornament for the head worn by females, supposed to have acquired its name from the jingling sound it made with every motion of the wearer; but nothing definite is known respecting it, and the readings are doubtful. Festus, ''s. v.'' Tertull. ''de Pall.'' 4. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] bd3n630295v00k2oonmukoie8fzhc79 Illustrated Companion to the Latin Dictionary/Crepidarius 0 312104 2683884 2671746 2024-11-11T16:37:02Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683884 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPIDA'RIUS'''. One who followed the trade of making ''[[Illustrated Companion to the Latin Dictionary/Crepida|crepidae]]''. Aul. Gell. xiii. 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Shoe-makers and Leather-workers]] tubs2tw09cxv14ipbgspowq3y0s14i5 Illustrated Companion to the Latin Dictionary/Crepidatus 0 312105 2683886 2671747 2024-11-11T16:37:13Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683886 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPIDA'TUS'''. Wearing shoes of the kind called ''crepidae''; properly characteristic of the Greeks, and used with the ''[[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]]'' or the ''[[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]''. (Cic. ''Pis.'' 38. Suet. ''Dom.'' 4. [[Illustrated Companion to the Latin Dictionary/Crepida|CREPIDA]].) The well-known statue of the Belvedere Apollo, which has the ''chlamys'' on its left arm, will furnish an example. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0y9ilqsihubj5p4yu60zqprs9nw2bgn Illustrated Companion to the Latin Dictionary/Crepida 0 312106 2683887 2671748 2024-11-11T16:37:24Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683887 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREP'IDA''' ({{lang|grc|κρηπίς}}). Usually translated a slipper, which gives a very imperfect, as well as incorrect, notion of the word. The ''crepida'' consisted of a thick sole welted on to a low piece of leather, which only covered the side of the foot, but had a number of eyes (''[[Illustrated Companion to the Latin Dictionary/Ansa|ansae]]'') on its upper edge, through which a flat thong (''[[Illustrated Companion to the Latin Dictionary/Amentum|amentum]]'') was passed to bind it on the foot, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=preceding wood-cut |imagelink=Media:Crepida 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|preceding wood-cut |caption=Crepida/1.1}} from a Greek marble; or sometimes loops (''ansae'') only were welted to the sole, as in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Crepida 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|annexed example |caption=Crepida/1.2}}, also from a Greek statue, through which the ''amentum'' was interlaced, in different and fanciful patterns, across the instep, and as high as the ankle. It was properly characteristic of the Greek national costume, was adopted by both sexes, and considered the proper chaussure to be worn with the ''[[Illustrated Companion to the Latin Dictionary/Pallium|pallium]]'', and with the ''[[Illustrated Companion to the Latin Dictionary/Chlamys|chlamys]]''; consequently, on the fictile vases and other works of art, when figures are clad in the above-named garments, and not bare-footed, as in the heroic style, their feet are commonly protected by coverings of a similar description to those introduced above. Hor. ''Sat.'' i. 3. 127. Pers. i. 127. Liv. xxix. 19. Suet. ''Tib.'' 13. Aul. Gell. xiii. 21. 3. 2. ''Crepida carbatina''. See [[Illustrated Companion to the Latin Dictionary/Carbatinae|CARBATINA]]. <gallery> File:Crepida 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|Crepida/1.1 File:Crepida 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|Crepida/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Feet]] 2w6umdligs9ynn8p3o7dyas9v1ycwn2 Illustrated Companion to the Latin Dictionary/Crepido 0 312107 2683888 2671749 2024-11-11T16:37:35Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683888 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPI'DO''' ({{lang|grc|κρηπίς}}). Any raised basement upon which other things are built or supported, as of a [[Illustrated Companion to the Latin Dictionary/Templum|temple]], [[Illustrated Companion to the Latin Dictionary/Ara|altar]], [[Illustrated Companion to the Latin Dictionary/Obeliscus|obelisk]], &c. Plin. ''H. N.'' xxxvi. 14. Compare Cic. ''Orat.'' 67. 2. A wall built as a margin or embankment along the side of a river, [[Illustrated Companion to the Latin Dictionary/Portus|port]], or basin of water, to form a quay, against which ships were moored, and passengers or merchandise landed or embarked. Cic. ''Verr.'' ii. 5. 7. Quint. Curt. iv. 5. Id. v. 1. 3. The ''trottoir'', or ''raised causeway'' for foot passengers on the side of a Roman road or [[Illustrated Companion to the Latin Dictionary/Via|street]]. (Juv. v. 8. Pet. ''Sat.'' 9. 2.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Crepido 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|illustration |caption=Crepido/3.1}} represents a street, with its road-way and foot-pavement, in the city of Pompeii. 4. In architecture, the projecting members of a cornice, or other ornaments in a building. <gallery> File:Crepido 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 213.jpg|Crepido/3.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Roads and Streets]] [[Category:Classed Index/Mouldings, Ornaments, and Basement]] fay04nfni8isf8dqe6fh3ob53mwgubg Illustrated Companion to the Latin Dictionary/Crepidula 0 312108 2683889 2671750 2024-11-11T16:37:46Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683889 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPID'ULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Crepida|CREPIDA]]; whence especially applied to those worn by females. Plaut. ''Pers.'' iv. 2. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 09uz22is6pgk505i40sqse47oph6x0f Illustrated Companion to the Latin Dictionary/Crepitaculum 0 312109 2683890 2671751 2024-11-11T16:37:57Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683890 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPITAC'ULUM'''. A little ''rattle'', with [[Illustrated Companion to the Latin Dictionary/Tintinnabulum|bells]] attached, to make a jingling sound; especially a ''child's rattle''. (Quint. ix. 4. 66. Capell. i. 4. Compare Lucret. v. 230. where the diminutive, ''crepitacillum'', is used.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Crepitaculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|example |caption=Crepitaculum/1.1}} represents an original found at Pompeii. 2. Martial (''Ep.'' xiv. 54.), and Apuleius (''Met.'' xi. p. 240.), give the same designation to the Egyptian ''[[Illustrated Companion to the Latin Dictionary/Sistrum|sistrum]]'', which was only another kind of rattle; see that word and the illustration. <gallery> File:Crepitaculum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|Crepitaculum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Instruments which are clashed or beaten]] 2ezsl2kg7gu61tryd7ypibn9q8c8ggu Illustrated Companion to the Latin Dictionary/Crepitus 0 312110 2683891 2671752 2024-11-11T16:38:08Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683891 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREP'ITUS''', sc. ''digitorum''; or ''concrepare digitis''. A snapping of the fingers by pressing the tip of the thumb (hence ''pollex argutus'', Mart. vi. 89.) firmly against the middle finger, a gesture employed by the ancients for making a sign to attract observation (Cic. ''Agr.'' ii. 30.); particularly as a summons to their slaves (Pet. ''Sat.'' 27. 5. Mart. ''Ep.'' xiv. 19. Id. iii. 82.); and, in general, as a mark of contemptuous indifference; which latter expression is implied by the figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=engraving |imagelink=Media:Crepitus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|engraving |caption=Crepitus/1.1}}, representing a drunken Faun, from a statue found at Herculaneum, as it were in the act of exclaiming, "Eat, drink, and be merry; all else is not worth this snap of the fingers." <gallery> File:Crepitus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|Crepitus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Classed Index-category missing]] 5v3ixjt9k831me0qnb6xkuorf9a50f1 Illustrated Companion to the Latin Dictionary/Crepundia 0 312111 2683892 2671753 2024-11-11T16:38:19Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683892 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CREPUN'DIA''' ({{lang|grc|σπάργανα}}). ''Children's playthings''; consisting of a variety of miniature objects, such as [[Illustrated Companion to the Latin Dictionary/Crepitaculum|rattles]], [[Illustrated Companion to the Latin Dictionary/Pupa|dolls]], little swords, hatchets, &c., and other toys similar to those given to children at the present day. But the Greeks and Romans also included under the same name little tokens of the same description which they used to tie round their children's necks. (Plaut. ''Mil.'' v. 6.) for ornaments, or amulets, and also to serve as a means of recognition for those who were exposed, or put out to nurse. (Plaut. ''Cist.'' iv. 1. 13. Cic. ''Brut.'' 91. Soph. ''Oed. T.'' 1035.) Several of these are enumerated by Plautus (''Rud.'' iv. 4. 111{{mdash}}126. ''Ep.'' v. i. 34.), and are seen round the neck of a child in a statue of the Pio-Clementine Museum, copied in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=preceding engraving |imagelink=Media:Crepundia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|preceding engraving |caption=Crepundia/1.1}}, of the same character as he mentions: {{mdash}} viz. a half moon (''[[Illustrated Companion to the Latin Dictionary/Lunula|lunula]]''), on the top of the right shoulder; then a double axe (''[[Illustrated Companion to the Latin Dictionary/Securicula|securicula]] ancipes''); next a bucket (''[[Illustrated Companion to the Latin Dictionary/Situla|situla]] argenteola''); a sort of flower, not mentioned; a little sword (''[[Illustrated Companion to the Latin Dictionary/Ensiculus|ensiculus]] aureolus''); a little hand (''manicula''); then another half-moon; a dolphin, instead of the little sow (''[[Illustrated Companion to the Latin Dictionary/Sucula|sucula]]'') mentioned by Plautus; with a recurrence of the same objects. <gallery> File:Crepundia 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 214.jpg|Crepundia/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Nursery, and Sports of Children]] 8qkom88f72cm344dqu2nbh36qtiks2b Illustrated Companion to the Latin Dictionary/Creta 0 312112 2683893 2671754 2024-11-11T16:38:30Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683893 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRE'TA'''. The same as [[Illustrated Companion to the Latin Dictionary/Calx|CALX]] and [[Illustrated Companion to the Latin Dictionary/Linea|LINEA ALBA]]. Plin. ''H. N.'' viii. 65. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] jp9v78rh43s3yqov2jejmwyxh3alhe5 Illustrated Companion to the Latin Dictionary/Cribellum 0 312113 2683895 2671755 2024-11-11T16:38:41Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683895 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRIBELLUM''' ({{lang|grc|κοσκίνιον}}). Diminutive of [[Illustrated Companion to the Latin Dictionary/Cribrum|CRIBRUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 2lqu8mqas7u2f5yc3pchhe4b1ghazfg Illustrated Companion to the Latin Dictionary/Cribrum 0 312114 2683896 2671756 2024-11-11T16:38:52Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683896 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRI'BRUM''' ({{lang|grc|κόσκινον}}). A ''sieve''; made of [[Illustrated Companion to the Latin Dictionary/Membrana|parchment]] perforated with holes, or of horse-hair, thread, papyrus, or rushes, interwoven, so as to leave interstices between each plat. The Romans sifted their flour through two kinds of sieves, called respectively ''excussoria'' and ''pollinaria'', the latter of which gave the finest flour, termed ''pollen''. Sieves of horse-hair were first made by the Gauls; those of linen by the Spaniards; and of papyrus and rushes by the Egyptians. (Plin. ''H. N.'' xviii. 28. Cato, ''R. R.'' 76. 3. Pers. ''Sat.'' 3. 112.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cribrum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|example |caption=Cribrum/1.1}} is from a bas-relief on the [[Illustrated Companion to the Latin Dictionary/Columna|Column]] of Trajan. <gallery> File:Cribrum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|Cribrum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Bakers and Bread-making]] m1w0ikx1myl8ioghm9m1af6aun074me Illustrated Companion to the Latin Dictionary/Crinale 0 312115 2683897 2671757 2024-11-11T16:39:03Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683897 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRINA'LE'''. A large [[Illustrated Companion to the Latin Dictionary/Pecten|comb]] of convex form (''curvum'', Ovid. ''Met.'' v. 52.), made to fit the back of the head, where it was placed to keep the back hair close down to the head, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Crinale 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|annexed engraving |caption=Crinale/1.1}}, from a small bronze figure, representing one of the Sabine women in the arms of a Roman soldier. (Guasco, ''delle Ornatrici'', p. 69.) It will be understood that the long ends of the hair have fallen from their place by the violence of the struggle in which the figures had been engaged; and it may be remarked, that the women of Rome and its neighbourhood still wear a comb of the same kind, which they call "''lo spicciatojo''." <gallery> File:Crinale 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|Crinale/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Toilet, and Utensils of Females]] hhp1klo3vak05b8ty2fxw1mi88u401d Illustrated Companion to the Latin Dictionary/Crinis 0 312116 2683898 2671758 2024-11-11T16:39:14Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683898 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRI'NIS''' ({{lang|grc|θρίξ}}). Any hair; then especially the hair of the head; more particularly implying a head of hair in its natural state and growth; i. e. not cut, nor artificially dressed. Hence, ''crinis passus'', dishevelled hair, which is left to hang down to its full length, as was usual with the women of antiquity when afflicted with any great calamity (Liv. i. 13. and see the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Praeficae|PRAEFICAE]]); ''crinis sparsus'', hair which streams wildly from the head, characteristic of persons under violent exertions, or possessed by any furious passion or impulse. Ovid. ''Met.'' i. 542. and the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Baccha|BACCHA]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Hair and Beard]] gm9nzel7q9xe8k6btay1vu8py0ardil Illustrated Companion to the Latin Dictionary/Crinitus 0 312117 2683900 2671759 2024-11-11T16:39:25Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683900 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRINI'TUS'''. Having long and flowing [[Illustrated Companion to the Latin Dictionary/Crinis|hair]], which is suffered to hang down at its natural length, such as the figures introduced ''s.'' [[Illustrated Companion to the Latin Dictionary/Acersecomes|ACERSECOMES]] and [[Illustrated Companion to the Latin Dictionary/Camillus|CAMILLUS]]. Ennius ''ap.'' Cic. ''Acad.'' ii. 28. Mart. ''Ep.'' xii. 49. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] ql113dd0ube1a7ywikw4y6ti2x8dcfr Illustrated Companion to the Latin Dictionary/Cristatus 0 312118 2683901 2671760 2024-11-11T16:39:36Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683901 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRISTA'TUS'''. Applied to [[Illustrated Companion to the Latin Dictionary/Galea|helmets]], distinguishes those which were fitted with a crest (''[[Illustrated Companion to the Latin Dictionary/Crista|crista]]'') from the mere scull-cap (''[[Illustrated Companion to the Latin Dictionary/Cudo|cudo]]''), which had neither [[Illustrated Companion to the Latin Dictionary/Apex|ridge-piece]] nor crest. (Liv. ix. 40. Ovid. ''Met.'' viii. 25.) Compare the [[Illustrated Companion to the Latin Dictionary/Crista|preceding wood-cuts]] with the illustration to CUDO. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] hylsvb0nt7iohcgogarlec225d7t9b3 Illustrated Companion to the Latin Dictionary/Crista 0 312119 2683902 2671761 2024-11-11T16:39:47Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683902 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRISTA''' ({{lang|grc|λόφος}}). The ''crest of a [[Illustrated Companion to the Latin Dictionary/Galea|helmet]]''; which was affixed to an elevated ridge (''[[Illustrated Companion to the Latin Dictionary/Apex|apex]]'') on the top of the [[Illustrated Companion to the Latin Dictionary/Cudo|scull-cap]]. (Virg. ''Aen.'' xii. 89. Liv. x. 39. Plin. ''H. N.'' vii. 57.) Both the ''apex'' and ''crista'' are often included under the latter term; but the real difference between the two words is that given. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Crista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|illustration |caption=Crista/1.1}} here introduced affords an example of three Roman helmets, with their crests composed of feathers, from a group originally belonging to the [[Illustrated Companion to the Latin Dictionary/Arcus|Arch]] of Trajan, but now inserted on the Arch of Constantine, near the [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|Coliseum]]. The Greek crests were more usually made of horse-hair, with the entire tail falling down behind, as a protection to the nape of the neck and back, like the left-hand figure in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=following engraving |imagelink=Media:Crista 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 216.jpg|following engraving |caption=Crista/1.2}}, from a fictile vase; and they sometimes added as many as three crests to one helmet, like the right-hand figure in the engraving, from a statue of Minerva. <gallery> File:Crista 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 215.jpg|Crista/1.1 File:Crista 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 216.jpg|Crista/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Defensive Armour]] p2695f6bzcz2786y8p7k1a4me1hiunb Illustrated Companion to the Latin Dictionary/Crobylus 0 312120 2683903 2671762 2024-11-11T16:39:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683903 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRO'BYLUS''' ({{lang|grc|κρωβύλος}} or {{lang|grc|κρώβυλος}}). Designates a particular manner of arranging the hair, which was characteristic of the earliest inhabitants of Athens (Thucyd. i. 6.), and some uncivilized nations (''crobylus barbarorum'', Tertull. ''Virg. Veland.'' 10.). It was effected by drawing back the hair from the roots all round the head, and fastening it in a knot, or with a tie at the top; and the same fashion prevailed amongst both sexes of the Greeks: but the term ''crobylus'' had an especial reference to the men; ''[[Illustrated Companion to the Latin Dictionary/Corymbus|corymbus]]'', on the contrary, to the women. (Schol. ''ad'' Thucyd. ''l. c.'') Yet Thucydides and Heraclides of Pontus (''ap.'' Athen. xii. 5.) use the two words {{lang|grc|κρώβυλος}} and {{lang|grc|κόρυμβος}} as convertible terms, and both descriptive of the male adjustment. It is, moreover, an unfounded statement to say, as some of the interpreters have done, that the fashion was peculiar to "elderly persons." Thucydides, in narrating the progress of the Greeks towards civilization in dress and manners, remarks that certain antiquated customs, and amongst them that of the ''crobylus'', had but lately been given up by some of the old people. But age is always the most averse to change, and the last to adopt new fashions; and many will remember a similar instance in modern Europe to that mentioned by Thucydides, where some few of the oldest people continued to wear their pig-tails long after they had been generally laid aside by the younger portion of the community. Besides, the Greek artists frequently give a coiffure of this kind to Apollo, Bacchus, and youthful persons, as in our {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Crobylus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 216.jpg|example |caption=Crobylus/1.1}}, from a bronze figure of a boy discovered at Herculaneum. The precise set of the hair is not given with sufficient distinctness; but in the original it is clearly seen to be turned back and tied up in the same manner as that more plainly shown by the head of the female illustrating the words [[Illustrated Companion to the Latin Dictionary/Corymbus|CORYMBUS]]. <gallery> File:Crobylus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 216.jpg|Crobylus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Hair and Beard]] rwb74bym7gb8bi2v16z3r1vw2g207ib Illustrated Companion to the Latin Dictionary/Crocota 0 312121 2683904 2671763 2024-11-11T16:40:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683904 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CROCO'TA''' ({{lang|grc|κροκωτόν}}). A rich saffron-coloured robe, or gala dress, worn by the Greek women at the Dionysiac festivals; and from them adopted by the ladies of Rome (Non. ''s. v.'' p. 549. Plaut. ''Fragm. ap.'' Non. ''s.'' Strophium, p. 538.); by the priests of Cybele (Apul. ''Met.'' viii. p. 172.); and also by some individuals who affected a feminine and foppish style of dress. Cic. ''Harusp. Respons.'' 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] d9f9z7xtak9z27ul7bwzvb80kboh845 Illustrated Companion to the Latin Dictionary/Crocotula 0 312122 2683905 2671764 2024-11-11T16:40:20Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683905 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CROCO'TULA''' ({{lang|grc|κροκώτιον}}). Diminutive of the [[Illustrated Companion to the Latin Dictionary/Crocota|preceding]]. Plaut. ''Epid.'' ii. 2. 49. Virg. ''Catalect.'' v. 21. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 4ea50hifiwbolv8oqt6w4v3lvtthlyl Illustrated Companion to the Latin Dictionary/Crotalistria 0 312123 2683906 2671765 2024-11-11T16:40:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683906 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CROTALIS'TRIA'''. A female performer on the ''[[Illustrated Companion to the Latin Dictionary/Crotalum|crotala]]''. Prop. iv. 8. 39. See the [[Illustrated Companion to the Latin Dictionary/Crotalum|next wood-cut]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Musicians]] huh0w70yynrwuforwgmp0owew5qn1l1 Illustrated Companion to the Latin Dictionary/Crotalium 0 312124 2683907 2671766 2024-11-11T16:40:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683907 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CROTAL'IUM''' ({{lang|grc|κροτάλιον}}). Literally, a small rattle; a sort of pet or fancy name by which the Roman ladies designated a pendant to their [[Illustrated Companion to the Latin Dictionary/Inauris|ear-rings]], when formed by two or more drop pearls (''[[Illustrated Companion to the Latin Dictionary/Elenchus|elenchi]]''), sufficiently large to produce a sharp crackling sound (like that of the ''[[Illustrated Companion to the Latin Dictionary/Crotalum|crotalum]]''), when shaken against each other by the motions of the wearer. (Pet. ''Sat.'' 67. 9. Plin. ''H. N.'' ix. 56.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Crotalium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|example |caption=Crotalium/1.1}} represents an original ear-ring found at Pompeii. <gallery> File:Crotalium 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|Crotalium/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] iqze21vnakb3y4fus39t3lgpgptz3fp Illustrated Companion to the Latin Dictionary/Crotalum 0 312125 2683908 2671767 2024-11-11T16:40:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683908 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CROT'ALUM''' ({{lang|grc|κρόταλον}}). A sort of musical instrument especially employed in the worship of Cybele (Apul. ''Met.'' viii. p. 170.), and frequently used to form an accompaniment for dancing. (P. Scipio ''ap.'' Macrob. ''Sat.'' ii. 10. Virg. ''Copa'', 2.) It consisted of two split canes, or hollow pieces of wood or metal, joined together by a straight handle, as in the right-hand figure of the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Crotalum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|annexed engraving |caption=Crotalum/1.1}}, from a [[Illustrated Companion to the Latin Dictionary/Musivum|mosaic]] pavement in a tomb excavated in the Villa Corsini. When played, one of these was held in each hand, and snapped together with the fingers, so as to produce a crisp rattling sound, like the [[Illustrated Companion to the Latin Dictionary/Crusmata|castanets]], as shown by the female figure in the illustration, from a bas-relief of the Villa Borghese. <gallery> File:Crotalum 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|Crotalum/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ornaments for the Person]] [[Category:Classed Index/Instruments which are clashed or beaten]] ocvlt1rpd7j5ci7xqq9vg4z62wg1drc Illustrated Companion to the Latin Dictionary/Cruciarius 0 312126 2683909 2671768 2024-11-11T16:41:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683909 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUCIA'RIUS'''. A criminal executed upon the cross (''[[Illustrated Companion to the Latin Dictionary/Crux|crux]]'') by hanging (Pet. ''Sat.'' 112. 5. ''cruciarii parentes detraxerunt pendentem''); hence, a worthless fellow, like our ''gallows-bird''. Apul. ''Met.'' x. p. 215. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 3jdz5040oyvwv10q2llcy70ueo3pqai Illustrated Companion to the Latin Dictionary/Crucifixus 0 312127 2683910 2671769 2024-11-11T16:41:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683910 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUCIFIX'US'''. Or, separately, ''cruci fixus''; nailed to the cross, in the manner we understand by the term ''crucified''. Quint. vii. 1. 3. Plin. ''H. N.'' viii. 18. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] 8y1vkyuwa4b27lmnrd2vf72gshpjvub Illustrated Companion to the Latin Dictionary/Crumena 0 312128 2683911 2671770 2024-11-11T16:41:25Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683911 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUME'NA''' ({{lang|grc|βαλάντιον}}). A leathern pouch for carrying money, slung over the neck by a strap (Plaut. ''Asin.'' iii. 3. 67 Id. ''Truc.'' iii. 1. 7.), so as to hang in front of the person, or at his back; whence Ballio, in Plautus (''Pseud.'' i. 2. 38.), tells the slave to walk in front, that he might keep an eye upon the ''crumena'', which was slung behind him. It was from the practice of carrying money about in this manner, that the Greek expression {{lang|grc|βαλαντιότομος}}, equivalent to our ''cut-purse'', derived its origin and meaning. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Crumena 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|illustration |caption=Crumena/1.1}} is from a figure on a bronze lamp. <gallery> File:Crumena 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 217.jpg|Crumena/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:Classed Index/Purses and Bags]] db70dda6669i38zzvp2t9oa9znxfp0e Illustrated Companion to the Latin Dictionary/Cruppellarius 0 312129 2683913 2671771 2024-11-11T16:41:36Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683913 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUPPELLA'RIUS'''. A Celtic word employed by the Gauls to designate a particular class of men who fought as [[Illustrated Companion to the Latin Dictionary/Gladiatores|gladiators]], clothed from head to foot in an entire suit of armour. (Tac. ''Ann.'' i. 43. Lamprid. ''Alex. Sev.'' 56.) Men thus accoutred were termed ''[[Illustrated Companion to the Latin Dictionary/Cataphractus|cataphracti]]'' or ''[[Illustrated Companion to the Latin Dictionary/Clibanarii|clibanarii]]'' by the Persians, and ''cruppellarii'' by the Gauls. See the illustration ''s.'' [[Illustrated Companion to the Latin Dictionary/Cataphractus|CATAPHRACTI]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Gladiators]] flrpjzixbmbhvtw7eze0dkihua8wn7z Illustrated Companion to the Latin Dictionary/Crusmata 0 312130 2683914 2671772 2024-11-11T16:41:47Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683914 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUS'MATA''' or '''CRU'MATA''' ({{lang|grc|κρούματα}} or {{lang|grc|κρούσματα}}). ''Castanets''; in ancient times, as well as our own, peculiarly characteristic of the Spanish nation (Mart. ''Ep.'' vi. 71.), though the same instruments were also played by the women of Greece and Italy, as is proved by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Crusmata 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 218.jpg|annexed illustration |caption=Crusmata/1.1}}, from a fictile vase; and by a bas-relief of the Capitoline Museum (iii. 36.), in which a female is represented with the same instrument in her right-hand, and the ''[[Illustrated Companion to the Latin Dictionary/Scabellum|scabillum]]'' under her left foot. <gallery> File:Crusmata 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 218.jpg|Crusmata/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Instruments which are clashed or beaten]] shbzrg5ty1xhdxlhshay8pxmixbpn3u Illustrated Companion to the Latin Dictionary/Crustae 0 312131 2683915 2671773 2024-11-11T16:41:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683915 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUS'TAE'''. Figures or images in ''low-relief'', embossed upon plate, as contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Emblema|emblemata]]'', which were in high-relief. Cic. ''Verr.'' ii. 4. 23. Paul. ''Dig.'' 34. 2. 33. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sculpture, etc.]] ccbah7eua86a10hsjgwuqp81s5llygo Illustrated Companion to the Latin Dictionary/Crustarius 0 312132 2683917 2671774 2024-11-11T16:42:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683917 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUSTA'RIUS'''. An artist who designed, and modelled ''[[Illustrated Companion to the Latin Dictionary/Crustae|crustae]]'' for gold and silver plate. (Plin. ''H. N.'' xxxiii. 55.) They were sold at Rome in shops appropriated for that particular branch of trade, called ''crustariae [[Illustrated Companion to the Latin Dictionary/Taberna|tabernae]]''. Festus, ''s. v.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Sculpture, etc.]] r7piy1xqz4mi3qm72ruwtn3mo3yohot Illustrated Companion to the Latin Dictionary/Crustularius 0 312133 2683918 2671775 2024-11-11T16:42:20Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683918 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUSTULA'RIUS'''. One who makes and sells ''[[Illustrated Companion to the Latin Dictionary/Crustulum|crustula]]''. Senec. ''Ep.'' 56. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Pastrycooks and Confectioners]] mjjoqa47tncrshva2ruh2b8t5docyno Illustrated Companion to the Latin Dictionary/Crustulum 0 312134 2683919 2671776 2024-11-11T16:42:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683919 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUS'TULUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Crustum|CRUSTUM]]. Any small piece of pastry or cake, such as a pastrycook's tart; especially given to children. Hor. ''Sat.'' i. 1. 25. Juv. ''Sat.'' ix. 5. and Schol. Vet. ''ad l.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] 1kisp2jgzzp8tn55xfnl4es1bvxt6ls Illustrated Companion to the Latin Dictionary/Crustum 0 312135 2683920 2671777 2024-11-11T16:42:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683920 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUS'TUM'''. A fragment, or broken piece of bread, cake, or pastry. Hence the English ''crust''. Hor. ''Ep.'' i. 1. 78. Virg. ''Aen.'' vii. 114. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Viands]] q10hmicglmu5msxzfio3p163uzqaz7a Illustrated Companion to the Latin Dictionary/Crux 0 312136 2683921 2671778 2024-11-11T16:42:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683921 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRUX'''. One of the machines or contrivances employed by the ancients for inflicting capital punishment upon criminals and slaves. It was made and applied in two different ways. Originally, it was an upright pole with a sharp point at the top (Greek {{lang|grc|σταυρός, σκόλοψ}}), upon which the victim was ''impaled'', as still practised in the East; a mode of punishment indicated by the expression ''in crucem suffigere'' (Justin. xviii. 7. Hirt. ''B. Afr.'' 66.), or ''in crucem sedere'' (Maecen. ''ap.'' Senec. ''Ep.'' 101.); but, subsequently, it was fitted with a transverse piece of wood, like our ''cross'', upon which the condemned was [[Illustrated Companion to the Latin Dictionary/Crucifixus|fastened with nails]], or bound with ropes, and then left to perish, a mode of execution expressed by such phrases as ''[[Illustrated Companion to the Latin Dictionary/Crucifixus|cruci figere]]'', or ''affigere'', and the like. (Tac. ''Ann.'' xv. 44. Pet. ''Sat.'' iii. 5.) It would also appear from other passages (Plin. ''H. N.'' xiv. 3. ''pendere in cruce'', Pet. ''Sat.'' 112. 5.), that criminals were likewise hung upon it, as upon a ''gibbet'', or ''gallows''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Prison, and Instruments of Punishment]] g15agv1msdylh9z1qss97wzv0djwq8w Illustrated Companion to the Latin Dictionary/Crypta 0 312137 2683923 2671779 2024-11-11T16:43:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683923 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRYP'TA''' ({{lang|grc|κρύπτη}}, or {{lang|grc|κρυπτή}}). The original of our word ''crypt''; which, however, gives a very incorrect notion of the object conveyed to the Greek and Roman mind by the same term. The ancient ''crypta'' comes nearest to our ''cloister'', which it closely resembled; being, in fact, a long narrow gallery, on the level of the ground (not subterranean, as commonly supposed), inclosed by walls on both sides, and receiving its light from rows of [[Illustrated Companion to the Latin Dictionary/Fenestra|windows]], in one or both of the side walls which inclosed it. Structures of this kind were frequently built as public edifices for the convenience of the population; in the pleasure grounds of wealthy individuals (Seneca, ''Ira'', 111. 18.); as adjuncts to great mansions; to the promenades connected with a [[Illustrated Companion to the Latin Dictionary/Theatrum|theatre]] (Suet. ''Cal.'' 58.); and very commonly, as we learn from numerous inscriptions (Muratori, ''Inscript.'' p. 481. 4. Rheines. ''Syntagm. Inscript.'' ii. 28.) were attached to the side of a ''[[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]'' or ''open'' colonnade; being intended as agreeable places of resort, when the heat of the season or inclemency of the weather rendered shelter acceptable to an idle and luxurious population. Even the [[Illustrated Companion to the Latin Dictionary/Praetoriani|Praetorian guards]] had a ''crypta'' adjacent to their permanent camp at Rome, which was demolished by the orders of Hadrian, when he attempted to reform the discipline of the corps. (Spart. ''Hadr.'' 10.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Crypta 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 219.jpg|annexed illustration |caption=Crypta/1.1}}, compared with the one which follows, will afford a correct idea of the real nature of the ancient crypt. It represents the ground-plan of a public edifice constructed by the priestess Eumachia{TR: "Emachia" -> "Eumachia"} at Pompeii, consisting of a ''crypta'', ''[[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]'', and ''[[Illustrated Companion to the Latin Dictionary/Chalcidicum|chalcidicum]]'', all which members are enumerated in an inscription affixed to the outside wall over the principal entrance. The three corridors or cloisters marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=A A A}} constitute the ''crypta''. They are surrounded on three of the sides by a blank wall, decorated with fresco [[Illustrated Companion to the Latin Dictionary/Pictura|paintings]]; on the inside are observed the windows which opened upon an adjoining colonnade (''porticus''), marked {{Illustrated Companion to the Latin Dictionary/Inscription|text=B B B B}}, which, in its turn, surrounds a large central area, {{Illustrated Companion to the Latin Dictionary/Inscription|text=C}}. Considerable remains of a similar structure are still to be seen on the site of ancient Capua, contiguous to the [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatre]]; and an example of these cloisters, annexed to a theatre, is shown in the fragment containing the plan of Pompey's theatre, ''s.'' [[Illustrated Companion to the Latin Dictionary/Theatrum|THEATRUM]] 2. Enclosed cloisters of the same description, as far as relates to design and locality, were usually constructed, instead of open colonnades, round the inner court-yards of Roman villas and farm-houses, for the purpose of storing grain, fruits, and such produce as required to be kept free from damp, and yet not altogether excluded from air. Vitruvius, therefore, in giving a design for a model villa, very wisely recommends covered galleries (''cryptae'') to be constructed in the interior of farm buildings for such produce; and the stabling, as well as magazines for less perishable commodities, to be situated in the open front court (''[[Illustrated Companion to the Latin Dictionary/Vestibulum|vestibulum]]''). (Vitruv. vi. 5. 2. Compare Varro, ''R. R.'' i. 57.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Crypta 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 219.jpg|illustration |caption=Crypta/1.2}} represents a view of the remains of the suburban villa of L. Arrius Diomedes at Pompeii, and shows very clearly the character and style of these appurtenances. On the left hand only a portion of the foundations remain; but the right wing and centre are nearly entire, with a part of the first story of the villa behind it. From this there is a [[Illustrated Companion to the Latin Dictionary/Scalae|staircase]], still entire, leading down into the ''crypta'', which, it will not fail to be observed, is not a subterranean cellar, but on the level of the ground, and with windows opening into a square court, originally surrounded by the other stories built over the cloisters. 3. When the windows were closed with their [[Illustrated Companion to the Latin Dictionary/Foricula|wooden shutters]], the whole corridor would form a long, narrow, dark vault; whence the word, in poetical and metaphorical language, was transferred in a ''secondary'' sense to subterranean passages of various kinds: thus the main ''sewer'', which passed down the Suburra, in continuation of the ''[[Illustrated Companion to the Latin Dictionary/Cloaca|cloaca Maxima]]'' at Rome is termed ''crypta'' Suburrae (Juv. v. 106.); the ''tunnel'', which passes under the cliffs between Naples and Pausilippo, now the "Grotto of Pausilipo," is designated ''crypta Neapolitana'' (Pet. ''Fragm.'' 13. Seneca, ''Ep.'' 57.); and the ''crypta'', in front of which Quartilla offers her sacrifice (Pet. ''Sat.'' 16. 3.) may refer to this same grotto, or to a cloister attached to her house and gardens, like those described above. 4. The stalls for the horses and chariots in a [[Illustrated Companion to the Latin Dictionary/Circus|circus]] (Sidon. ''Carm.'' xxiii. 319.) See the illustration and article, [[Illustrated Companion to the Latin Dictionary/Carcer|CARCER]], 2. <gallery> File:Crypta 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 219.jpg|Crypta/1.1 File:Crypta 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 219.jpg|Crypta/1.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Houses]] 0nfnp3t3tlytxm4hefl1r2lu5lx4uys Illustrated Companion to the Latin Dictionary/Cryptoporticus 0 312138 2683924 2671780 2024-11-11T16:43:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683924 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CRYPTOPOR'TICUS'''. The term always employed by the younger Pliny when speaking of a structure similar to what is described under the [[Illustrated Companion to the Latin Dictionary/Crypta|last word]]. It appears to have been only another name, more fully descriptive, for CRYPTA; or, if there was any real distinction between the two, it may be, that when the gallery had [[Illustrated Companion to the Latin Dictionary/Fenestra|windows]] on both sides, as was the case with those in Pliny's villas, it possessed a considerable resemblance to the colonnade (''[[Illustrated Companion to the Latin Dictionary/Porticus|porticus]]''), and was consequently distinguished by the name ''crypto-porticus''; when there were windows only on one side, and a blank wall on the other, such as those represented in the [[Illustrated Companion to the Latin Dictionary/Crypta|two preceding illustrations]], it would be more appropriately designated by the name of ''crypta'' simply. Plin. ''Ep.'' ii. 17. 16. seqq. Id. v. 6. 27{{mdash}}28. Id. vii. 21. 2. Id. ix. 36. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Houses]] 1vygnpi1bqvn0tm6rvkuw694iee0r83 Illustrated Companion to the Latin Dictionary/Ctesibica machina 0 312139 2683925 2671781 2024-11-11T16:43:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683925 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CTESIB'ICA MACH'INA'''. A ''double-actioned forcing-pump'', invented by Ctesibius of Alexandria, who lived in the age of Ptolemy Euergetes (Vitruv. ix. 8. 2. Plin. ''H. N.'' vii. 38.), and constructed upon the principle now employed for our fire-engines. The machine is described at length by Vitruvius (x. 7.), from the writings of its inventor, which are now lost; and a pump of similar character, but improved construction, probably after a model of Hero, the pupil of Ctesibius, was discovered near Civita Vecchia, in the last century; but as that does not contain all the parts mentioned by Vitruvius, a representation of it is inserted under its Greek name [[Illustrated Companion to the Latin Dictionary/Sipho|SIPHO]], where the component parts of which it consists are explained from the description of Hero. In this place, only a {{Illustrated Companion to the Latin Dictionary/Image Location|text=conjectural diagram |imagelink=Media:Ctesibica_machina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 220.jpg|conjectural diagram |caption=Ctesibica_machina/1.1}} of the ''machina Ctesibica'' is introduced, designed by Perrault in accordance with the account of Vitruvius; but it will enable the reader, from a comparison of the two together, to form an accurate idea of the nature of these machines, and the difference between them. The parts mentioned by Vitruvius are:{{mdash}}''[[Illustrated Companion to the Latin Dictionary/Catinum|catinus]]'', the cup, {{Illustrated Companion to the Latin Dictionary/Inscription|text=A}}, which was not employed by Hero, who, instead of it, uses an upright tube ({{lang|grc|σωλὴν ὄρθιος}}); ''[[Illustrated Companion to the Latin Dictionary/Modiolus|modioli gemelli]]'', {{Illustrated Companion to the Latin Dictionary/Inscription|text=B B}}, the two boxes, or cases, in which the pistons (''regulae'') act, corresponding with the {{lang|grc|δύο πυξίδες}} of Hero; ''[[Illustrated Companion to the Latin Dictionary/Embolus|emboli masculi]]'', two suckers ({{Illustrated Companion to the Latin Dictionary/Inscription|text=C C}}), same as {{lang|grc|ἐμβολεῖς}}, Hero; ''fistulae in furcillae figura'', two connecting pipes in the form of a fork, which in the pump of Hero are supplied by a single horizontal tube ({{lang|grc|δωλήν}}); and ''[[Illustrated Companion to the Latin Dictionary/Paenula|paenula]]'', the ''cowl'' ({{Illustrated Companion to the Latin Dictionary/Inscription|text=D}}), placed over the cup to compress the water at the foot of the hose; not used by Hero. The operation of the machine is easily understood. It was placed over the reservoir, and both pistons worked together, the one being depressed while the other was drawn up; as the sucker ({{Illustrated Companion to the Latin Dictionary/Inscription|text=C}}) rises, it draws up a supply of water through an opening at the bottom of the cylinder ({{Illustrated Companion to the Latin Dictionary/Inscription|text=B}}), which is furnished with a moveable lid (marked by dotted lines in the engraving), that opens as the water flows in, but closes of its own accord immediately that the piston is pressed down again; and this pressure forces the water through the forked pipe into the ''catinus'' ({{Illustrated Companion to the Latin Dictionary/Inscription|text=A}}), the bottom of which, in like manner, is furnished with moveable lids over each pipe, alternately opening and shutting with each stroke of the pistons, which, as they move alternately up and down, force up the water in a ''continuous'' stream through the ''paenula'' ({{Illustrated Companion to the Latin Dictionary/Inscription|text=D}}) into a pipe or hose affixed to the top of it, and made to any length required. <gallery> File:Ctesibica_machina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 220.jpg|Ctesibica machina/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] neo6ezkewd9d7lzjx1r7hxft95d11h4 Illustrated Companion to the Latin Dictionary/Cubicularius 0 312140 2683926 2671782 2024-11-11T16:43:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683926 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUBICULA'RIUS'''. A slave whose service was confined to the sitting and dwelling-rooms (''[[Illustrated Companion to the Latin Dictionary/Cubiculum|cubicula]]'') of a [[Illustrated Companion to the Latin Dictionary/Domus|Roman house]]; he waited in the antechamber, and announced his master's visitors, &c. Cic. ''Verr.'' ii. 3. 4. Id. ''Att.'' vi. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Domestic Slaves]] 9wkdb0bgx2ygpe1i3k5rinieqh07mhv Illustrated Companion to the Latin Dictionary/Cubiculum 0 312141 2683927 2671783 2024-11-11T16:43:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683927 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUBIC'ULUM'''. Literally, a room furnished with a sofa or bed; whence it became a general term for any such room in a [[Illustrated Companion to the Latin Dictionary/Domus|private house]], whether used as a sitting or sleeping-room (Plin. ''Ep.'' i. 3. 1. ''cubicula nocturna et diurna'', Id. ii. 17. 21. Plaut. ''Most.'' iii. 2. 7.); for the Romans were much in the habit of reposing upon sofas in the day-time at their studies, meals, siestas, and receptions. 2. The emperor's box at the [[Illustrated Companion to the Latin Dictionary/Circus|Circus]] or [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatre]], wherein he reclined in state to view the games (Suet. ''Nero'', 12. Plin. ''Paneg.'' 51), instead of sitting on the open ''[[Illustrated Companion to the Latin Dictionary/Podium|podium]]'', as was usual in more simple times. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Houses]] m4vbxa5kxcx2kxl2ieb94j9d80fbmri Illustrated Companion to the Latin Dictionary/Cubile 0 312142 2683928 2671785 2024-11-11T16:43:58Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683928 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUBI'LE''' ({{lang|grc|κοίτη}}). In general, any place to lie down in, as a [[Illustrated Companion to the Latin Dictionary/Lectus|bed]], or the [[Illustrated Companion to the Latin Dictionary/Dormitorium|room]] in which the bed is: whence more especially used to designate ''the marriage-bed'' (Virg. ''Aen.'' viii. 412. Eur. ''Med.'' 151.); a sleeping-room (Cic. ''Cat.'' iv. 8. Suet. ''Nero'', 25.); and, indeed, like ''cubitorium'', any one of the small apartments in a [[Illustrated Companion to the Latin Dictionary/Domus|private house]] usually occupied by the master or his family. Plin. ''H. N.'' xv. 10. ''salutatorium''; Plin. ''Paneg.'' 63. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 9xvuyrjgdd5zjzhbvigx155e2kljmm2 Illustrated Companion to the Latin Dictionary/Cubital 0 312143 2683929 2671786 2024-11-11T16:44:09Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683929 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUBITAL'''' ({{lang|grc|ὑπαγκώνιον}}). A bolster or cushion for the elbow to rest upon, when the figure is otherwise in a recumbent position, such as was used for the convenience of invalids (Hor. ''Sat.'' ii. 3. 255.), or by persons when reclining at their meals (see [[Illustrated Companion to the Latin Dictionary/Accubo|ACCUBO]]). The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cubital 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 221.jpg|illustration |caption=Cubital/1.1}} is from a figure on the top of an Etruscan tomb. <gallery> File:Cubital 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 221.jpg|Cubital/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Beds and Couches]] gftdumzyn7y7lnjszftc6nd5clhtvo2 Illustrated Companion to the Latin Dictionary/Cubitoria 0 312144 2683930 2671787 2024-11-11T16:44:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683930 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUBITO'RIA''', sc. ''vestimenta''. (Pet. ''Sat.'' 30. 11.) Same as [[Illustrated Companion to the Latin Dictionary/Coenatoria|COENATORIAE]] ''vestes''. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] t55vsplxrw14601kplrhf6ps8twmjlw Illustrated Companion to the Latin Dictionary/Cucullio 0 312145 2683931 2671788 2024-11-11T16:44:31Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683931 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUCUL'LIO''' or '''CUCU'LIO'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Cucullus|CUCULLUS]]; the diminutive expressing inferiority of quality, rather than of dimensions. Lamprid. ''Elag.'' 32. ''mulionico''; Capitol. ''Ver.'' 4. ''vulgari viatorio''; Cato, ''R. R.'' ii. 3. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 1z7sjyij3rxo4ypnlfi2pl02w15uyua Illustrated Companion to the Latin Dictionary/Cucullus 0 312146 2683932 2671789 2024-11-11T16:44:42Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683932 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUCUL'LUS'''. A piece of paper rolled into the shape of a funnel, in which the chemists and other tradespeople of Rome used to wrap the powders and drugs bought by their customers (Mart. ''Ep.'' iii. 2.), precisely as the grocer and chandler's shopkeeper do at the present day. 2. From similarity in form to the preceding, a ''hood'' or ''cowl'' attached to some other garment, such as the ''[[Illustrated Companion to the Latin Dictionary/Lacerna|lacerna]], [[Illustrated Companion to the Latin Dictionary/Sagum|sagum]], [[Illustrated Companion to the Latin Dictionary/Paenula|paenula]]'', &c., which could be drawn up over the head, to serve instead of a hat; and was commonly worn by slaves, rustics, fishermen, and persons whose occupations exposed them to the weather at all seasons, like the cowl of the Capuchin friars, and modern Neapolitan fishermen. (Columell. xi. 1. 21. Mart. ''Ep.'' xi. 98. 10. Juv. vi. 118. Pallad. i. 43. 4.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=above illustration |imagelink=Media:Cucullus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|above illustration |caption=Cucullus/2.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, representing a group of common people drinking in a tavern (''[[Illustrated Companion to the Latin Dictionary/Caupona|caupona]]''). When it was desired to uncover the head, the cowl was pushed back, and rested on the upper part of the back, in the manner shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=second engraving |imagelink=Media:Cucullus 2.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|second engraving |caption=Cucullus/2.2}}, representing another of the figures in the same group. The first of these illustrates Cicero's description of M. Antony (''Phil.'' ii. 31.), ''domum venit capite involuto''; the latter one, the ''caput aperuit'', of the same passage. 3. ''Cucullus Bardaicus'' (Jul. Cap. ''Pertinax'', 8.); same as [[Illustrated Companion to the Latin Dictionary/Bardocucullus|BARDOCUCULLUS]]. 4. ''Cucullus Liburnicus'' (Mart. ''in Lemmate'', xiv. 139.); same as [[Illustrated Companion to the Latin Dictionary/Bardocucullus|BARDOCUCULLUS]]. 5. ''Cucullus Santonicus'' (Juv. viii. 145.); same as [[Illustrated Companion to the Latin Dictionary/Bardocucullus|BARDOCUCULLUS]]; from the town of ''Saintes'' in France, where the manufacture of these articles was introduced from Illyria. <gallery> File:Cucullus 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|Cucullus/2.1 File:Cucullus 2.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|Cucullus/2.2 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Outward Apparel]] [[Category:Classed Index/Surgical Implements, etc.]] f2wq2t5k2v1zbpuaueps518vkcnxcua Illustrated Companion to the Latin Dictionary/Cucuma 0 312147 2683933 2671790 2024-11-11T16:44:53Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683933 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUC'UMA'''. A vessel employed for boiling water, making decoctions, and similar purposes, the precise form and character of which there are no materials for determining. (Pet. ''Sat.'' 135. 4. Id. 136. 2.) The word, however, is still retained in the colloquial language of the modern Romans, in which "''la cucuma''" means a vessel for boiling water. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] ooyzmtszkkf3l20amv9erz3ikuqhjyn Illustrated Companion to the Latin Dictionary/Cucurbita 0 312148 2683934 2671791 2024-11-11T16:45:04Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683934 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUCUR'BITA''' and '''CUCURBIT'ULA''' ({{lang|grc|κολοκύνθη, σικύα}}). A ''pumpkin'', or ''gourd''; thence, a ''cupping-glass'', which the ancients made out of those fruits (Juv. ''Sat.'' xiv. 58.), as well as of horn or bronze. (Celsus, ii. 11.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cucurbita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|example |caption=Cucurbita/1.1}} represents an ancient original made out of a pumpkin, now preserved in the Vatican Library, and published by Rhodius. <gallery> File:Cucurbita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|Cucurbita/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Classed Index-category missing]] syn1hqwg5ykbqe093k79u48sg0oskyj Illustrated Companion to the Latin Dictionary/Cudo 0 312149 2683935 2671792 2024-11-11T16:45:15Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683935 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CU'DO''' or '''CU'DON''' ({{lang|grc|καταῖτυξ, λιτός περικεφάλαιος}}). The simplest form of [[Illustrated Companion to the Latin Dictionary/Galea|helmet]], consisting of a mere ''scull-cap'', without any ridge-piece (''[[Illustrated Companion to the Latin Dictionary/Apex|apex]]'') or crest (''[[Illustrated Companion to the Latin Dictionary/Crista|crista]]'') (hence, {{lang|grc|ἄφαλος τε καὶ ἄλοφος}}, Hom. ''Il.'' x. 258.), made out of leather or the skin of wild animals (Sil. Ital. viii. 493.), and fastened under the chin by a thong ({{lang|grc|ὀχεύς}}). It was worn by some of the Roman light-armed troops (Polyb. vi. 22.); is ascribed to Diomedes by Homer, and is frequently seen in Greek representations of that hero, from one of which in bronze the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed example |imagelink=Media:Cudo 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|annexed example |caption=Cudo/1.1}} is taken. <gallery> File:Cudo 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 222.jpg|Cudo/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Defensive Armour]] 1j56q9cbky3jaq7fmq8nm9hwou0d4pi Illustrated Companion to the Latin Dictionary/Culcita 0 312150 2683936 2671793 2024-11-11T16:45:26Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683936 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUL'CITA''' ({{lang|grc|τύλη, στρωμνή}}). A mattrass for a sofa, couch, or [[Illustrated Companion to the Latin Dictionary/Lectus|bed]], stuffed with wadding, wool, or feathers (Varro, ''L. L.'' v. 167. Pet. ''Sat.'' 38. Cic. ''Tusc.'' iii. 19. Seneca, ''Ep.'' 87.); which, consequently, was sometimes very soft, like our feather beds, and at others, like our wool and hair mattrasses, sufficiently hard not to take an impression from the body resting upon it. (Seneca, ''Ep.'' 108.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Culcita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|illustration |caption=Culcita/1.1}} is from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii. <gallery> File:Culcita 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|Culcita/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Beds and Couches]] hefhqo0ax90ynqlwnwz3wz2nr07vtuk Illustrated Companion to the Latin Dictionary/Culeus 0 312151 2683937 2671794 2024-11-11T16:45:37Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683937 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CU'LEUS''' or '''CUL'LEUS'''. A very large sack made of pig's-skin or leather, and employed by the Romans for the transport of wine or oil (Nepos, ''Eum.'' 8. Plin. ''H. N.'' vii. 19. Cato, ''R. R.'' xi. 1.), as represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Culeus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|annexed illustration |caption=Culeus/1.1}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, which shows the manner of transporting it on a cart frame, of emptying its contents into smaller vessels (''[[Illustrated Companion to the Latin Dictionary/Amphora|amphorae]]''), and how it was filled; viz. by the neck at the top, which was then tied up with a cord. A contrivance of precisely the same kind is still employed in Italy for the transport and sale of oil. The size of this will likewise account for another use to which it was applied by the ancient Romans, for sewing parricides in. Cic. ''Q. Fr.'' i. 2. 2. 2. Also a liquid measure; the largest used by the Romans, containing twenty ''amphorae'', or 118 gallons, and particularly employed in estimating the produce of a vineyard or olive ground. Rhemn. Fann. ''de Pond. et Mens.'' 86. Varro, ''R. R.'' 1. 2. 7. <gallery> File:Culeus 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|Culeus/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Manufacture of Oil and Wine]] gy7i9he9r6a5nnezunzegpfezgulewf Illustrated Companion to the Latin Dictionary/Culigna 0 312152 2683938 2671795 2024-11-11T16:45:48Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683938 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CULIG'NA''' ({{lang|grc|κυλίχνη}}). A vessel for wine, the exact nature of which is not ascertained. Cato, ''R. R.'' 132. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] gydkptg5co5htumt24mza4hlrlhe6g3 Illustrated Companion to the Latin Dictionary/Culina 0 312153 2683939 2671796 2024-11-11T16:45:59Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683939 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CULI'NA'''. A kitchen. (Cic. ''Fam.'' xv. 18. Pet. ''Sat.'' 2. 1. Seneca, ''Ep.'' 114.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Culina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|illustration |caption=Culina/1.1}} represents a kitchen stove in the house of Pansa at Pompeii, with some cooking utensils upon it, as discovered when first excavated; viz. a strainer (''[[Illustrated Companion to the Latin Dictionary/Colum|colum]]''), a kitchen knife (''[[Illustrated Companion to the Latin Dictionary/Culter|culter coquinaris]]''), and an implement for dressing eggs (supposed ''[[Illustrated Companion to the Latin Dictionary/Apalare|apalare]]''); below is the ground-plan of a kitchen in the same city, from the house of the Quaestor, distributed into the following parts. Immediately on the left hand of the entrance there is a semicircular sink (1) , and on the right a [[Illustrated Companion to the Latin Dictionary/Scalae|staircase]] (2), which probably led up to the store-rooms; fronting the entrance are the remains of the [[Illustrated Companion to the Latin Dictionary/Latericius|brickwork]] which formed the stove (3), similarly constructed to the elevation above; and adjoining this is another small chamber (4), which we might call the back kitchen, with a [[Illustrated Companion to the Latin Dictionary/Latrina|privy]] (5) at its furthest extremity; a convenience, which, singularly enough, is generally found adjacent to the kitchens in the houses of Pompeii. <gallery> File:Culina 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 223.jpg|Culina/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Kitchen and Cooking Utensils]] [[Category:Classed Index/The Houses]] 9zspla7uiopeu1fh4o1k3uhq52yi25p Illustrated Companion to the Latin Dictionary/Cultellus 0 312154 2683940 2671797 2024-11-11T16:46:10Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683940 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CULTEL'LUS''' ({{lang|grc|μαχαιρίς, μαχαίριον}}). Diminutive of [[Illustrated Companion to the Latin Dictionary/Culter|CULTER]]; and employed in nearly the same senses, only designating a lesser description of each kind. But the ''cultellus'' is never so small as our pocket and pen-knife (''[[Illustrated Companion to the Latin Dictionary/Scalprum|scalprum]]''); for Juvenal designates a ''carving-knife'' by the diminutive (''Sat.'' v. 122.); Ulpian (''Dig.'' 9. 2. 11.), a [[Illustrated Companion to the Latin Dictionary/Tonsor|barber]]'s ''razor''; and the ''cultellus'' of Horace (''Ep.'' i. 7. 51.), which people used to clean and pare their nails with, was the same as the barber's instrument, which is expressly name for that purpose by Valerius Maximus (iii. 2. 15.), ''cultellum tonsorium quasi unguium resecandorum causa poposcit''. 2. ''Cultellus ligneus''. A wedge of wood; which is sharper at the edge than at the back, like the blade of a ''[[Illustrated Companion to the Latin Dictionary/Culter|culter]]''. Vitruv. vii. 3. 2. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Knives]] lnwyu4e929v7exb0aqevn10njakykzx Illustrated Companion to the Latin Dictionary/Culter 0 312155 2683941 2671798 2024-11-11T16:46:21Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683941 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUL'TER''' ({{lang|grc|μάχαιρα}}). The name given by the ancients to several different implements employed in cutting, which were made with a single edge, broadish back, and a sharp point; all of which were used for domestic or agricultural, and not military, purposes, excepting when descriptive of the barbarous ages, or to characterize the assassin rather than the soldier. Our ''knife'' is, perhaps, the nearest translation, but the ancient ''culter'' is mostly applied to the largest class of instruments, which pass by the name of knives amongst us. The several kinds, with the epithets which distinguished them, are enumerated below. 2. ''Culter coquinaris''. A ''cook's knife'' or ''kitchen-knife'' (Varro, ''ap.'' Non. ''s. v.'' p. 195.), for cutting up meat. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Culter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|illustration |caption=Culter/1.1}} is from an original discovered in a [[Illustrated Companion to the Latin Dictionary/Culina|kitchen]] at Pompeii. [[Illustrated Companion to the Latin Dictionary/Lanius|Butchers]] also made use of a similar implement for the same purpose. Liv. iii. 48. Herod. ii. 61. 2. The knife employed by the ''[[Illustrated Companion to the Latin Dictionary/Cultrarius|cultrarius]]'' at a sacrifice for cutting the victim's throat (Plaut. ''Rud.'' i. 2. 45.); and by the butchers in the slaughter-house (Varro, ''R. R.'' ii. 5.11.); frequently represented on sepulchral bas-reliefs, from one of which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed specimen |imagelink=Media:Culter 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|annexed specimen |caption=Culter/2.1}} is taken, where the inscription {{Illustrated Companion to the Latin Dictionary/Inscription|text=CULTRARI OSSA}} identifies the instrument. Compare the engraving ''s.'' [[Illustrated Companion to the Latin Dictionary/Cultrarius|CULTRARIUS]], in which it is seen in use. 3. ''Culter venatorius''. A ''[[Illustrated Companion to the Latin Dictionary/Venator|huntsman]]'s knife'', carried from a belt round the waist, with which he despatched his prey at close quarters (Pet. ''Sat.'' 40. 5. Suet. ''Aug.'' 19.); similar to that used by the men who fought with wild beasts in the [[Illustrated Companion to the Latin Dictionary/Amphitheatrum|amphitheatre]]; see the first illustration to [[Illustrated Companion to the Latin Dictionary/Bestiarius|BESTIARIUS]]. The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Culter 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|example |caption=Culter/3.1}} is copied from an engraved gem. 4. The sharp edge, or flat part of the blade in a vine-dresser's pruning-hook (''[[Illustrated Companion to the Latin Dictionary/Falx|falx vinitoria]]''), which, in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed engraving |imagelink=Media:Culter 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|annexed engraving |caption=Culter/4.1}}, from an old MS. of Columella, lies between the handle and the hook at the top (Columell. iv. 25. 3.), and which was particularly brought into use for lopping and cutting off. 5. ''Culter tonsorius''. A sort of knife or razor which [[Illustrated Companion to the Latin Dictionary/Tonsor|barbers]] used for shaving. (Cic. ''Off.'' ii. 7. Pet. ''Sat.'' 108. 11. Plin. ''H. N.'' vii. 59.) Also designated by the diminutive ''[[Illustrated Companion to the Latin Dictionary/Cultellus|cultellus]]'', and probably having a blade with a point shaped like the [[Illustrated Companion to the Latin Dictionary/Venator|huntsman]]'s knife (No. 3.), for it was used for keeping the nails clean. Hor. ''Ep.'' i. 7. 51. compared with Val. Max. iii. 2. 15. 6. A knife made of bone or ivory, for eating fruit with (Columell. xii. 45. 4.); also termed ''cultellus''. Plin. ''H. N.'' xii. 54. 7. The ''coulter'' of a [[Illustrated Companion to the Latin Dictionary/Aratrum|plough]]; formed like the blade of a large knife, and inserted vertically in front of the share (''[[Illustrated Companion to the Latin Dictionary/Vomer|vomer]]''. Plin. ''H. N.'' xviii. 48.), as is clearly shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Culter 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|annexed illustration |caption=Culter/7.1}}, from an engraved gem. 8. ''In cultrum collocatus''. A technical expression in use amongst Roman architects and mechanics, when speaking of objects placed upon their smallest sides or narrowest edges; as of bricks or stones in a building set upon their sides, instead of laid in the usual manner, with their broadest surfaces upwards. (Vitruv. x. 5.) The modern Italians make use of a similar metaphor, "''per coltello''," when they wish to express the same kind of arrangement. <gallery> File:Culter 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|Culter/1.1 File:Culter 2.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|Culter/2.1 File:Culter 3.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|Culter/3.1 File:Culter 4.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 224.jpg|Culter/4.1 File:Culter 7.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|Culter/7.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Provision Dealers]] [[Category:Classed Index/The Plough]] [[Category:Classed Index/Knives]] b0w26ius47mdtnagpokb3k8vvbfl5go Illustrated Companion to the Latin Dictionary/Cultrarius 0 312156 2683942 2671799 2024-11-11T16:46:32Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683942 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CULTRA'RIUS'''. The minister or servant of an officiating priest, who despatched the victim at a sacrifice, by cutting its throat with a knife (''[[Illustrated Companion to the Latin Dictionary/Culter|culter]]''), as contradistinguished from ''[[Illustrated Companion to the Latin Dictionary/Popa|popa]]'', who knocked it down with a blow of the axe (''[[Illustrated Companion to the Latin Dictionary/Securis|securis]]'') or mallet (''[[Illustrated Companion to the Latin Dictionary/Malleus|malleus]]''). (Suet. ''Cal.'' 32. Inscript. ''ap.'' Grut. 640. 11.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=illustration |imagelink=Media:Cultrarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|illustration |caption=Cultrarius/1.1}}, from a very beautiful marble bas-relief discovered at Pompeii, represents an old woman and a Faun about to offer up a pig in sacrifice, the former in the character of a priestess, the latter as a ''cultrarius'', cutting its throat. <gallery> File:Cultrarius 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|Cultrarius/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Ministers and Attendants]] 3x2336hqq712ejwb23r3j8qamubv522 Illustrated Companion to the Latin Dictionary/Culullus 0 312157 2683943 2671800 2024-11-11T16:46:43Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683943 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CULUL'LUS'''. According to the Scholiasts on Horace, an earthenware ''[[Illustrated Companion to the Latin Dictionary/Calix|calix]]'' employed by the pontifices and [[Illustrated Companion to the Latin Dictionary/Vestales|Vestals]] in their sacrificial rites; but commonly used in a general sense for any kind of drinking-cup. Acron. and Porphyr. ''ad'' Hor. ''Od.'' i. 31. 11. Hor. ''A. P.'' 434. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 6d2st6zapizn47o9yi31u2bkifsa7xf Illustrated Companion to the Latin Dictionary/Cumera 0 312158 2683944 2671801 2024-11-11T16:46:54Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683944 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUM'ERA'''. A sort of tub, pan, or basket with a convex lid, used by the country people for keeping corn in. Festus, ''s.'' Cumerum. Hor. ''Sat.'' i. 1. 53. Id. ''Epist.'' i. 7. 30. Acrod. ''ad ll.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Miscellaneous Domestic Furniture and Utensils]] clo9flzp3r2xfq9ukm5aotehonevmha Illustrated Companion to the Latin Dictionary/Cumerum 0 312159 2683945 2671802 2024-11-11T16:47:05Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683945 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUM'ERUM'''. A covered vase, or, perhaps, basket, carried by the ''[[Illustrated Companion to the Latin Dictionary/Camillus|camillus]]'' in a marriage procession (Varro, ''L. L.'' vii. 34.), and containing the necessaries (''utensilia'') of the bride. Festus, ''s. v.'' == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Marriage]] smn0rsvdx71m2nqa09hqyvn78veq7z1 Illustrated Companion to the Latin Dictionary/Cunabula 0 312160 2683946 2671803 2024-11-11T16:47:16Z CalRis25 911425 Project RICH-2K: Remove heading to change article from initial version into production version and replace it with a template 2683946 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} {{Illustrated Companion to the Latin Dictionary/RICH-1849}} '''CUNA'BULA'''. A ''child's cradle''. (Cic. ''Div.'' i. 36. Plaut. ''Amph.'' v. 1. 55. Serv. ''ad'' Virg. ''Ecl.'' iv. 23. Arnob. ''adv. Gent.'' iv.) The {{Illustrated Companion to the Latin Dictionary/Image Location|text=example |imagelink=Media:Cunabula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|example |caption=Cunabula/1.1}} is from a very ancient MS. of Genesis, published by Lambeccius (''Comment. Bibl. Caes.'' iii. 29.); but ancient cradles were also commonly made in the shape of a trough or boat, as in the [[Illustrated Companion to the Latin Dictionary/Cunaria|next illustration]]; whence a Greek name for the same is {{lang|grc|σκάφη}}. Athen. xiii. 85. 2. Hence the place in which any living thing is born: a birth-place (Prop. iii. 1. 27.); a bird's nest (Plin. ''H. N.'' x. 51.); a bee-hive. Virg. ''Georg.'' iv. 66. <gallery> File:Cunabula 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 225.jpg|Cunabula/1.1 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/The Nursery, and Sports of Children]] p4bsfdwzg59tr9d32sw7old69mro010 User:Atcovi/Criminology 2024 Fall Research Paper 2 313569 2684049 2682746 2024-11-12T00:06:52Z Atcovi 276019 2684049 wikitext text/x-wiki '''Topic''': Exploring pedophilia through nature vs nurture, while assessing it through 2 theories from the eyes of Lombroso (Atavist theory) and the social learning theory. Provide peer reviews for both, then provide a final input on which one is more plausible to explain pedophilia and the sexual crimes attached with it. <center>'''''Pedophila Through Nature vs. Nurture'''''</center> Pedophilia is, as defined by notable Canadian sexologist and forensic psychologist Micheal C. Seto in his 2009 review of pedophilia, the "persistent sexual interest in prepubescent children [children generally younger than 13]"<ref>{{Cite journal|last=Seto|first=Michael C.|date=2009-04-01|title=Pedophilia|url=https://www.annualreviews.org/doi/10.1146/annurev.clinpsy.032408.153618|journal=Annual Review of Clinical Psychology|language=en|volume=5|issue=1|pages=391–407|doi=10.1146/annurev.clinpsy.032408.153618|issn=1548-5943}}</ref>. ICD-11 (the 11th revision of the International Classification of Diseases) requires, in order for a pedophilia diagnosis to be made, that the individual has consistent sexual thoughts, urges, and illusions of pre-pubertal children & to have either acted on these urges or be clearly distraught by these feelings. The diagnosee cannot be a child (pre-pubertal) and extreme caution is urged when assessing an adolescene for this disorder<ref name="ICD-11">{{cite web|url=https://icd.who.int/browse11/l-m/en#/http%3a%2f%2fid.who.int%2ficd%2fentity%2f517058174|title=ICD-11 for Mortality and Morbidity Statistics|date=2024|publisher=[[World Health Organization]]/[[ICD-11]]|at=See section 6D32 Pedophilic disorder|access-date=November 6, 2024|quote=Pedophilic disorder is characterized by a sustained, focused, and intense pattern of sexual arousal—as manifested by persistent sexual thoughts, fantasies, urges, or behaviours—involving pre-pubertal children. In addition, in order for Pedophilic Disorder to be diagnosed, the individual must have acted on these thoughts, fantasies or urges or be markedly distressed by them. This diagnosis does not apply to sexual behaviours among pre- or post-pubertal children with peers who are close in age.}}</ref>. Pedophilia is problematic, dangerous, and is a contributing factor behind many sexual crimes done against children. To assess the reason behind the development of pedophilia, it is essential to first cover the nature vs. nurture debate in criminology. The nature vs. nurture debate concerns which origin is more likely to be the source and cause of criminal behavior as one reaches an age where they can be held responsible for their behavior. The "nature" aspect puts fault on one's genetic predispositions, or the chance of developing certain traits due to one's genes<ref>{{Cite web|url=https://library.fiveable.me/key-terms/introduction-brain-behavior/genetic-predisposition|title=Genetic predisposition - (Intro to Brain and Behavior) - Vocab, Definition, Explanations {{!}} Fiveable|website=library.fiveable.me|access-date=2024-11-07}}</ref>. On the other hand, the "nurture" aspect is concerned with one's upbringing and environmental living conditions. Throughout history, several theories have been posed on whether nature or nurture play a bigger role in one's development into embracing a criminal lifestyle. In this review, two theories will be analyzed and applied regarding pedophilia. The first theory is atavism, as applied to the field of criminology, by 1800s Italian criminologist Cesare Lombroso. Cesare Lombroso proposed that a criminal can be identified by physical features that are a result of an evolutive degression. Criminals possess physical features, or atavistic anomalies, that are abnormal and distinct from normal human begins, with these atavistic anomalies closely resembling a "savage" or a "primitive man"<ref name=":0">{{Cite journal|last=Ellwood|first=Charles|date=1912-01-01|title=Lombroso's Theory of Crime|url=https://scholarlycommons.law.northwestern.edu/jclc/vol2/iss5/6/|journal=Journal of Criminal Law and Criminology|volume=2|issue=5|pages=716}}</ref><ref name=":1">{{Cite book|url=https://www.worldcat.org/title/on1285696621|title=Criminology|last=Siegel|first=Larry J.|date=2023|publisher=Cengage|isbn=978-0-357-62474-6|edition=Eighth edition|location=Boston, MA|oclc=on1285696621}}</ref>. According to Lombroso, these traits could be darker skin, a bulky jaw, sharper teeth, ears akin to a monkey, and an insensitivity to pain<ref name=":1" /><ref>{{Cite journal|last=Mazzarello|first=Paolo|date=2011|title=Cesare Lombroso: an anthropologist between evolution and degeneration|url=https://pubmed.ncbi.nlm.nih.gov/21729591/|journal=Functional Neurology|volume=26|issue=2|pages=97–101|issn=0393-5264|pmc=3814446|pmid=21729591}}</ref>. One could derive these traits via either "indirect heredity", where the criminal's lineage were afflicted by monstrous illnesses (such as mental illnesses) and these traits were passed down to the criminal, or "direct heredity", where these criminal traits were given to the criminal directly from their parents<ref name=":1" />. Despite Lombroso's atavist theory being rejected on the grounds of having been inspired by racist underpinnings & and maintaining little to no scientific backing, Lombroso laid out an important road to studying the criminals themselves rather than just the crime<ref name=":0" />. ----On the other hand, the social learning theory states that people are not inherently criminals, but exhibit criminal-like behavior due to their upbringing or environment. Individuals witness criminal behavior and perceive the reward higher than the consequences. Notable psychologists, such as Albert Bandura, advocated for this theory. An example of this theory being demonstrated is like a son who watches his father abuse his mother and goes on to model his father's behavior when dealing with his significant other and his children<ref name=":1" />. The social learning theory expanded upon the "tremendous complexity of human responsiveness" by adding an additional element to the learning process: learning via rewards and consequences<ref>{{Cite book|title=Social learning theory|last=Bandura|first=Albert|date=1977|publisher=Prentice-Hall|isbn=978-0-13-816751-6|series=Prentice-Hall series in social learning theory|location=Englewood Cliffs, New Jersey}}</ref>. The social learning theory is more accepted compared to the atavist theory by Lombroso. The nature vs. nurture debate in criminology has been a heated topic in the world of psychology & criminology for centuries. Another popular take on the debate, as propagated by geneticists, is that neither origin is solely responsible for criminal behavior, and that criminal behavior is a combination of both nature and nurture done in a very "complex and not yet fully understood [way]", which leads to offensive and law-breaking behavior. Some scientists, surprisingly enough, believe that the debate is "unhelpful" and "outdated", yet the debate ravages on. Certain researchers hesitate to take a stance, fearing that leaning to one-side over the other may leave the door open to biased narrators who may use the debate to spread false agendas. For example, if someone were to believe that nature is responsible for crime vs. nurture, this could lead to a resurgence in racist propaganda disguised as "scientific discourse". Alternatively, placing an emphasis on nurture could close the door for improvement for those riddled in poverty and other environmental disadvantages<ref>{{Cite journal|last=Levitt|first=Mairi|date=2013-12-12|title=Perceptions of nature, nurture and behaviour|url=https://lsspjournal.biomedcentral.com/articles/10.1186/2195-7819-9-13|journal=Life Sciences, Society and Policy|volume=9|issue=1|pages=13|doi=10.1186/2195-7819-9-13|issn=2195-7819|pmc=PMC4513026}}</ref>. As detailed, there is significant controversy regarding which side of the nature vs. nurture debate is correct, but what is the scientific consensus concerning nature vs. nurture for pedophilia? Which side is more responsible for the disorder at hand and what are some measures that can be taken depending on whether nature or nurture is the culprit? ---- == References == {{Reflist}} [[Category:Atcovi's Work]] g4j4hyugecyirjtf7o3hit25i2m6yuu 2684082 2684049 2024-11-12T01:32:17Z Atcovi 276019 2684082 wikitext text/x-wiki '''Topic''': Exploring pedophilia through nature vs nurture, while assessing it through 2 theories from the eyes of Lombroso (Atavist theory) and the social learning theory. Provide peer reviews for both, then provide a final input on which one is more plausible to explain pedophilia and the sexual crimes attached with it. <center>'''''Pedophila Through Nature vs. Nurture'''''</center> Pedophilia is, as defined by notable Canadian sexologist and forensic psychologist Micheal C. Seto in his 2009 review of pedophilia, the "persistent sexual interest in prepubescent children [children generally younger than 13]"<ref>{{Cite journal|last=Seto|first=Michael C.|date=2009-04-01|title=Pedophilia|url=https://www.annualreviews.org/doi/10.1146/annurev.clinpsy.032408.153618|journal=Annual Review of Clinical Psychology|language=en|volume=5|issue=1|pages=391–407|doi=10.1146/annurev.clinpsy.032408.153618|issn=1548-5943}}</ref>. ICD-11 (the 11th revision of the International Classification of Diseases) requires, in order for a pedophilia diagnosis to be made, that the individual has consistent sexual thoughts, urges, and illusions of pre-pubertal children & to have either acted on these urges or be clearly distraught by these feelings. The diagnosee cannot be a child (pre-pubertal) and extreme caution is urged when assessing an adolescene for this disorder<ref name="ICD-11">{{cite web|url=https://icd.who.int/browse11/l-m/en#/http%3a%2f%2fid.who.int%2ficd%2fentity%2f517058174|title=ICD-11 for Mortality and Morbidity Statistics|date=2024|publisher=[[World Health Organization]]/[[ICD-11]]|at=See section 6D32 Pedophilic disorder|access-date=November 6, 2024|quote=Pedophilic disorder is characterized by a sustained, focused, and intense pattern of sexual arousal—as manifested by persistent sexual thoughts, fantasies, urges, or behaviours—involving pre-pubertal children. In addition, in order for Pedophilic Disorder to be diagnosed, the individual must have acted on these thoughts, fantasies or urges or be markedly distressed by them. This diagnosis does not apply to sexual behaviours among pre- or post-pubertal children with peers who are close in age.}}</ref>. Pedophilia is problematic, dangerous, and is a contributing factor behind many sexual crimes done against children. To assess the reason behind the development of pedophilia, it is essential to first cover the nature vs. nurture debate in criminology. The nature vs. nurture debate concerns which origin is more likely to be the source and cause of criminal behavior as one reaches an age where they can be held responsible for their behavior. The "nature" aspect puts fault on one's genetic predispositions, or the chance of developing certain traits due to one's genes<ref>{{Cite web|url=https://library.fiveable.me/key-terms/introduction-brain-behavior/genetic-predisposition|title=Genetic predisposition - (Intro to Brain and Behavior) - Vocab, Definition, Explanations {{!}} Fiveable|website=library.fiveable.me|access-date=2024-11-07}}</ref>. On the other hand, the "nurture" aspect is concerned with one's upbringing and environmental living conditions. Throughout history, several theories have been posed on whether nature or nurture play a bigger role in one's development into embracing a criminal lifestyle. In this review, two theories will be analyzed and applied regarding pedophilia. The first theory is atavism, as applied to the field of criminology, by 1800s Italian criminologist Cesare Lombroso. Cesare Lombroso proposed that a criminal can be identified by physical features that are a result of an evolutive degression. Criminals possess physical features, or atavistic anomalies, that are abnormal and distinct from normal human begins, with these atavistic anomalies closely resembling a "savage" or a "primitive man"<ref name=":0">{{Cite journal|last=Ellwood|first=Charles|date=1912-01-01|title=Lombroso's Theory of Crime|url=https://scholarlycommons.law.northwestern.edu/jclc/vol2/iss5/6/|journal=Journal of Criminal Law and Criminology|volume=2|issue=5|pages=716}}</ref><ref name=":1">{{Cite book|url=https://www.worldcat.org/title/on1285696621|title=Criminology|last=Siegel|first=Larry J.|date=2023|publisher=Cengage|isbn=978-0-357-62474-6|edition=Eighth edition|location=Boston, MA|oclc=on1285696621}}</ref>. According to Lombroso, these traits could be darker skin, a bulky jaw, sharper teeth, ears akin to a monkey, and an insensitivity to pain<ref name=":1" /><ref>{{Cite journal|last=Mazzarello|first=Paolo|date=2011|title=Cesare Lombroso: an anthropologist between evolution and degeneration|url=https://pubmed.ncbi.nlm.nih.gov/21729591/|journal=Functional Neurology|volume=26|issue=2|pages=97–101|issn=0393-5264|pmc=3814446|pmid=21729591}}</ref>. One could derive these traits via either "indirect heredity", where the criminal's lineage were afflicted by monstrous illnesses (such as mental illnesses) and these traits were passed down to the criminal, or "direct heredity", where these criminal traits were given to the criminal directly from their parents<ref name=":1" />. Despite Lombroso's atavist theory being rejected on the grounds of having been inspired by racist underpinnings & and maintaining little to no scientific backing, Lombroso laid out an important road to studying the criminals themselves rather than just the crime<ref name=":0" />. ----On the other hand, the social learning theory states that people are not inherently criminals, but exhibit criminal-like behavior due to their upbringing or environment. Individuals witness criminal behavior and perceive the reward higher than the consequences. Notable psychologists, such as Albert Bandura, advocated for this theory. An example of this theory being demonstrated is like a son who watches his father abuse his mother and goes on to model his father's behavior when dealing with his significant other and his children<ref name=":1" />. The social learning theory expanded upon the "tremendous complexity of human responsiveness" by adding an additional element to the learning process: learning via rewards and consequences<ref>{{Cite book|title=Social learning theory|last=Bandura|first=Albert|date=1977|publisher=Prentice-Hall|isbn=978-0-13-816751-6|series=Prentice-Hall series in social learning theory|location=Englewood Cliffs, New Jersey}}</ref>. The social learning theory is more accepted compared to the atavist theory by Lombroso. The nature vs. nurture debate in criminology has been a heated topic in the world of psychology & criminology for centuries. Another popular take on the debate, as propagated by geneticists, is that neither origin is solely responsible for criminal behavior, and that criminal behavior is a combination of both nature and nurture done in a very "complex and not yet fully understood [way]", which leads to offensive and law-breaking behavior. Some scientists, surprisingly enough, believe that the debate is "unhelpful" and "outdated", yet the debate ravages on. Certain researchers hesitate to take a stance, fearing that leaning to one-side over the other may leave the door open to biased narrators who may use the debate to spread false agendas. For example, if someone were to believe that nature is responsible for crime vs. nurture, this could lead to a resurgence in racist propaganda disguised as "scientific discourse". Alternatively, placing an emphasis on nurture could close the door for improvement for those riddled in poverty and other environmental disadvantages<ref>{{Cite journal|last=Levitt|first=Mairi|date=2013-12-12|title=Perceptions of nature, nurture and behaviour|url=https://lsspjournal.biomedcentral.com/articles/10.1186/2195-7819-9-13|journal=Life Sciences, Society and Policy|volume=9|issue=1|pages=13|doi=10.1186/2195-7819-9-13|issn=2195-7819|pmc=PMC4513026}}</ref>. As detailed, there is significant controversy regarding which side of the nature vs. nurture debate is correct, but what is the scientific consensus concerning nature vs. nurture for pedophilia? Which side is more responsible for the disorder at hand and what are some measures that can be taken depending on whether nature or nurture is the culprit? ----A 2009 study done on the etiology of pedophila by researcher Juan Antonio Becerra García of the International University of La Rioja found several "structural deteriorations" within brain regions that were essential to sexual development, including a smaller right amygdala (less control over ability to inhibit certain behaviors), a significant decline of gray matter in the hypothalamus (which leads to a score of neurological issues, including memory loss and other cognitive impairments), and a decline in the activity of the dorsolateral prefrontal cortex (which leads to poor executive functioning)<ref>{{Cite journal|last=Becerra García|first=Juan Antonio|date=2009-01-01|title=Etiology of pedophilia from a neurodevelopmental perspective: markers and brain alterations|url=https://linkinghub.elsevier.com/retrieve/pii/S2173505009700512|journal=Revista de Psiquiatría y Salud Mental (English Edition)|volume=2|issue=4|pages=190–196|doi=10.1016/S2173-5050(09)70051-2|issn=2173-5050}}</ref>. Another review of the disorder published in 2015 affirmed that other studies conducted on pedophiles found similar findings, including a reduction of inhibition and executive functioning<ref>{{Cite journal|last=Tenbergen|first=Gilian|last2=Wittfoth|first2=Matthias|last3=Frieling|first3=Helge|last4=Ponseti|first4=Jorge|last5=Walter|first5=Martin|last6=Walter|first6=Henrik|last7=Beier|first7=Klaus M.|last8=Schiffer|first8=Boris|last9=Kruger|first9=Tillmann H. C.|date=2015-06-24|title=The Neurobiology and Psychology of Pedophilia: Recent Advances and Challenges|url=http://journal.frontiersin.org/Article/10.3389/fnhum.2015.00344/abstract|journal=Frontiers in Human Neuroscience|volume=9|doi=10.3389/fnhum.2015.00344|issn=1662-5161|pmc=PMC4478390|pmid=26157372}}</ref>. == References == {{Reflist}} [[Category:Atcovi's Work]] gocvvlaz2b125mmlar42kx6v7fx7oex 2684083 2684082 2024-11-12T01:33:22Z Atcovi 276019 correct spelling mistake 2684083 wikitext text/x-wiki '''Topic''': Exploring pedophilia through nature vs nurture, while assessing it through 2 theories from the eyes of Lombroso (Atavist theory) and the social learning theory. Provide peer reviews for both, then provide a final input on which one is more plausible to explain pedophilia and the sexual crimes attached with it. <center>'''''Pedophila Through Nature vs. Nurture'''''</center> Pedophilia is, as defined by notable Canadian sexologist and forensic psychologist Micheal C. Seto in his 2009 review of pedophilia, the "persistent sexual interest in prepubescent children [children generally younger than 13]"<ref>{{Cite journal|last=Seto|first=Michael C.|date=2009-04-01|title=Pedophilia|url=https://www.annualreviews.org/doi/10.1146/annurev.clinpsy.032408.153618|journal=Annual Review of Clinical Psychology|language=en|volume=5|issue=1|pages=391–407|doi=10.1146/annurev.clinpsy.032408.153618|issn=1548-5943}}</ref>. ICD-11 (the 11th revision of the International Classification of Diseases) requires, in order for a pedophilia diagnosis to be made, that the individual has consistent sexual thoughts, urges, and illusions of pre-pubertal children & to have either acted on these urges or be clearly distraught by these feelings. The diagnosee cannot be a child (pre-pubertal) and extreme caution is urged when assessing an adolescene for this disorder<ref name="ICD-11">{{cite web|url=https://icd.who.int/browse11/l-m/en#/http%3a%2f%2fid.who.int%2ficd%2fentity%2f517058174|title=ICD-11 for Mortality and Morbidity Statistics|date=2024|publisher=[[World Health Organization]]/[[ICD-11]]|at=See section 6D32 Pedophilic disorder|access-date=November 6, 2024|quote=Pedophilic disorder is characterized by a sustained, focused, and intense pattern of sexual arousal—as manifested by persistent sexual thoughts, fantasies, urges, or behaviours—involving pre-pubertal children. In addition, in order for Pedophilic Disorder to be diagnosed, the individual must have acted on these thoughts, fantasies or urges or be markedly distressed by them. This diagnosis does not apply to sexual behaviours among pre- or post-pubertal children with peers who are close in age.}}</ref>. Pedophilia is problematic, dangerous, and is a contributing factor behind many sexual crimes done against children. To assess the reason behind the development of pedophilia, it is essential to first cover the nature vs. nurture debate in criminology. The nature vs. nurture debate concerns which origin is more likely to be the source and cause of criminal behavior as one reaches an age where they can be held responsible for their behavior. The "nature" aspect puts fault on one's genetic predispositions, or the chance of developing certain traits due to one's genes<ref>{{Cite web|url=https://library.fiveable.me/key-terms/introduction-brain-behavior/genetic-predisposition|title=Genetic predisposition - (Intro to Brain and Behavior) - Vocab, Definition, Explanations {{!}} Fiveable|website=library.fiveable.me|access-date=2024-11-07}}</ref>. On the other hand, the "nurture" aspect is concerned with one's upbringing and environmental living conditions. Throughout history, several theories have been posed on whether nature or nurture play a bigger role in one's development into embracing a criminal lifestyle. In this review, two theories will be analyzed and applied regarding pedophilia. The first theory is atavism, as applied to the field of criminology, by 1800s Italian criminologist Cesare Lombroso. Cesare Lombroso proposed that a criminal can be identified by physical features that are a result of an evolutive degression. Criminals possess physical features, or atavistic anomalies, that are abnormal and distinct from normal human begins, with these atavistic anomalies closely resembling a "savage" or a "primitive man"<ref name=":0">{{Cite journal|last=Ellwood|first=Charles|date=1912-01-01|title=Lombroso's Theory of Crime|url=https://scholarlycommons.law.northwestern.edu/jclc/vol2/iss5/6/|journal=Journal of Criminal Law and Criminology|volume=2|issue=5|pages=716}}</ref><ref name=":1">{{Cite book|url=https://www.worldcat.org/title/on1285696621|title=Criminology|last=Siegel|first=Larry J.|date=2023|publisher=Cengage|isbn=978-0-357-62474-6|edition=Eighth edition|location=Boston, MA|oclc=on1285696621}}</ref>. According to Lombroso, these traits could be darker skin, a bulky jaw, sharper teeth, ears akin to a monkey, and an insensitivity to pain<ref name=":1" /><ref>{{Cite journal|last=Mazzarello|first=Paolo|date=2011|title=Cesare Lombroso: an anthropologist between evolution and degeneration|url=https://pubmed.ncbi.nlm.nih.gov/21729591/|journal=Functional Neurology|volume=26|issue=2|pages=97–101|issn=0393-5264|pmc=3814446|pmid=21729591}}</ref>. One could derive these traits via either "indirect heredity", where the criminal's lineage were afflicted by monstrous illnesses (such as mental illnesses) and these traits were passed down to the criminal, or "direct heredity", where these criminal traits were given to the criminal directly from their parents<ref name=":1" />. Despite Lombroso's atavist theory being rejected on the grounds of having been inspired by racist underpinnings & and maintaining little to no scientific backing, Lombroso laid out an important road to studying the criminals themselves rather than just the crime<ref name=":0" />. ----On the other hand, the social learning theory states that people are not inherently criminals, but exhibit criminal-like behavior due to their upbringing or environment. Individuals witness criminal behavior and perceive the reward higher than the consequences. Notable psychologists, such as Albert Bandura, advocated for this theory. An example of this theory being demonstrated is like a son who watches his father abuse his mother and goes on to model his father's behavior when dealing with his significant other and his children<ref name=":1" />. The social learning theory expanded upon the "tremendous complexity of human responsiveness" by adding an additional element to the learning process: learning via rewards and consequences<ref>{{Cite book|title=Social learning theory|last=Bandura|first=Albert|date=1977|publisher=Prentice-Hall|isbn=978-0-13-816751-6|series=Prentice-Hall series in social learning theory|location=Englewood Cliffs, New Jersey}}</ref>. The social learning theory is more accepted compared to the atavist theory by Lombroso. The nature vs. nurture debate in criminology has been a heated topic in the world of psychology & criminology for centuries. Another popular take on the debate, as propagated by geneticists, is that neither origin is solely responsible for criminal behavior, and that criminal behavior is a combination of both nature and nurture done in a very "complex and not yet fully understood [way]", which leads to offensive and law-breaking behavior. Some scientists, surprisingly enough, believe that the debate is "unhelpful" and "outdated", yet the debate ravages on. Certain researchers hesitate to take a stance, fearing that leaning to one-side over the other may leave the door open to biased narrators who may use the debate to spread false agendas. For example, if someone were to believe that nature is responsible for crime vs. nurture, this could lead to a resurgence in racist propaganda disguised as "scientific discourse". Alternatively, placing an emphasis on nurture could close the door for improvement for those riddled in poverty and other environmental disadvantages<ref>{{Cite journal|last=Levitt|first=Mairi|date=2013-12-12|title=Perceptions of nature, nurture and behaviour|url=https://lsspjournal.biomedcentral.com/articles/10.1186/2195-7819-9-13|journal=Life Sciences, Society and Policy|volume=9|issue=1|pages=13|doi=10.1186/2195-7819-9-13|issn=2195-7819|pmc=PMC4513026}}</ref>. As detailed, there is significant controversy regarding which side of the nature vs. nurture debate is correct, but what is the scientific consensus concerning nature vs. nurture for pedophilia? Which side is more responsible for the disorder at hand and what are some measures that can be taken depending on whether nature or nurture is the culprit? ----A 2009 study done on the etiology of pedophilia by researcher Juan Antonio Becerra García of the International University of La Rioja found several "structural deteriorations" within brain regions that were essential to sexual development, including a smaller right amygdala (less control over ability to inhibit certain behaviors), a significant decline of gray matter in the hypothalamus (which leads to a score of neurological issues, including memory loss and other cognitive impairments), and a decline in the activity of the dorsolateral prefrontal cortex (which leads to poor executive functioning)<ref>{{Cite journal|last=Becerra García|first=Juan Antonio|date=2009-01-01|title=Etiology of pedophilia from a neurodevelopmental perspective: markers and brain alterations|url=https://linkinghub.elsevier.com/retrieve/pii/S2173505009700512|journal=Revista de Psiquiatría y Salud Mental (English Edition)|volume=2|issue=4|pages=190–196|doi=10.1016/S2173-5050(09)70051-2|issn=2173-5050}}</ref>. Another review of the disorder published in 2015 affirmed that other studies conducted on pedophiles found similar findings, including a reduction of inhibition and executive functioning<ref>{{Cite journal|last=Tenbergen|first=Gilian|last2=Wittfoth|first2=Matthias|last3=Frieling|first3=Helge|last4=Ponseti|first4=Jorge|last5=Walter|first5=Martin|last6=Walter|first6=Henrik|last7=Beier|first7=Klaus M.|last8=Schiffer|first8=Boris|last9=Kruger|first9=Tillmann H. C.|date=2015-06-24|title=The Neurobiology and Psychology of Pedophilia: Recent Advances and Challenges|url=http://journal.frontiersin.org/Article/10.3389/fnhum.2015.00344/abstract|journal=Frontiers in Human Neuroscience|volume=9|doi=10.3389/fnhum.2015.00344|issn=1662-5161|pmc=PMC4478390|pmid=26157372}}</ref>. == References == {{Reflist}} [[Category:Atcovi's Work]] nmw1at6gra01p22zw7g89znniaqzwts 2684088 2684083 2024-11-12T01:51:47Z Atcovi 276019 2684088 wikitext text/x-wiki '''Topic''': Exploring pedophilia through nature vs nurture, while assessing it through 2 theories from the eyes of Lombroso (Atavist theory) and the social learning theory. Provide peer reviews for both, then provide a final input on which one is more plausible to explain pedophilia and the sexual crimes attached with it. <center>'''''Pedophila Through Nature vs. Nurture'''''</center> Pedophilia is, as defined by notable Canadian sexologist and forensic psychologist Micheal C. Seto in his 2009 review of pedophilia, the "persistent sexual interest in prepubescent children [children generally younger than 13]"<ref>{{Cite journal|last=Seto|first=Michael C.|date=2009-04-01|title=Pedophilia|url=https://www.annualreviews.org/doi/10.1146/annurev.clinpsy.032408.153618|journal=Annual Review of Clinical Psychology|language=en|volume=5|issue=1|pages=391–407|doi=10.1146/annurev.clinpsy.032408.153618|issn=1548-5943}}</ref>. ICD-11 (the 11th revision of the International Classification of Diseases) requires, in order for a pedophilia diagnosis to be made, that the individual has consistent sexual thoughts, urges, and illusions of pre-pubertal children & to have either acted on these urges or be clearly distraught by these feelings. The diagnosee cannot be a child (pre-pubertal) and extreme caution is urged when assessing an adolescene for this disorder<ref name="ICD-11">{{cite web|url=https://icd.who.int/browse11/l-m/en#/http%3a%2f%2fid.who.int%2ficd%2fentity%2f517058174|title=ICD-11 for Mortality and Morbidity Statistics|date=2024|publisher=[[World Health Organization]]/[[ICD-11]]|at=See section 6D32 Pedophilic disorder|access-date=November 6, 2024|quote=Pedophilic disorder is characterized by a sustained, focused, and intense pattern of sexual arousal—as manifested by persistent sexual thoughts, fantasies, urges, or behaviours—involving pre-pubertal children. In addition, in order for Pedophilic Disorder to be diagnosed, the individual must have acted on these thoughts, fantasies or urges or be markedly distressed by them. This diagnosis does not apply to sexual behaviours among pre- or post-pubertal children with peers who are close in age.}}</ref>. Pedophilia is problematic, dangerous, and is a contributing factor behind many sexual crimes done against children. To assess the reason behind the development of pedophilia, it is essential to first cover the nature vs. nurture debate in criminology. The nature vs. nurture debate concerns which origin is more likely to be the source and cause of criminal behavior as one reaches an age where they can be held responsible for their behavior. The "nature" aspect puts fault on one's genetic predispositions, or the chance of developing certain traits due to one's genes<ref>{{Cite web|url=https://library.fiveable.me/key-terms/introduction-brain-behavior/genetic-predisposition|title=Genetic predisposition - (Intro to Brain and Behavior) - Vocab, Definition, Explanations {{!}} Fiveable|website=library.fiveable.me|access-date=2024-11-07}}</ref>. On the other hand, the "nurture" aspect is concerned with one's upbringing and environmental living conditions. Throughout history, several theories have been posed on whether nature or nurture play a bigger role in one's development into embracing a criminal lifestyle. In this review, two theories will be analyzed and applied regarding pedophilia. The first theory is atavism, as applied to the field of criminology, by 1800s Italian criminologist Cesare Lombroso. Cesare Lombroso proposed that a criminal can be identified by physical features that are a result of an evolutive degression. Criminals possess physical features, or atavistic anomalies, that are abnormal and distinct from normal human begins, with these atavistic anomalies closely resembling a "savage" or a "primitive man"<ref name=":0">{{Cite journal|last=Ellwood|first=Charles|date=1912-01-01|title=Lombroso's Theory of Crime|url=https://scholarlycommons.law.northwestern.edu/jclc/vol2/iss5/6/|journal=Journal of Criminal Law and Criminology|volume=2|issue=5|pages=716}}</ref><ref name=":1">{{Cite book|url=https://www.worldcat.org/title/on1285696621|title=Criminology|last=Siegel|first=Larry J.|date=2023|publisher=Cengage|isbn=978-0-357-62474-6|edition=Eighth edition|location=Boston, MA|oclc=on1285696621}}</ref>. According to Lombroso, these traits could be darker skin, a bulky jaw, sharper teeth, ears akin to a monkey, and an insensitivity to pain<ref name=":1" /><ref>{{Cite journal|last=Mazzarello|first=Paolo|date=2011|title=Cesare Lombroso: an anthropologist between evolution and degeneration|url=https://pubmed.ncbi.nlm.nih.gov/21729591/|journal=Functional Neurology|volume=26|issue=2|pages=97–101|issn=0393-5264|pmc=3814446|pmid=21729591}}</ref>. One could derive these traits via either "indirect heredity", where the criminal's lineage were afflicted by monstrous illnesses (such as mental illnesses) and these traits were passed down to the criminal, or "direct heredity", where these criminal traits were given to the criminal directly from their parents<ref name=":1" />. Despite Lombroso's atavist theory being rejected on the grounds of having been inspired by racist underpinnings & and maintaining little to no scientific backing, Lombroso laid out an important road to studying the criminals themselves rather than just the crime<ref name=":0" />. ----On the other hand, the social learning theory states that people are not inherently criminals, but exhibit criminal-like behavior due to their upbringing or environment. Individuals witness criminal behavior and perceive the reward higher than the consequences. Notable psychologists, such as Albert Bandura, advocated for this theory. An example of this theory being demonstrated is like a son who watches his father abuse his mother and goes on to model his father's behavior when dealing with his significant other and his children<ref name=":1" />. The social learning theory expanded upon the "tremendous complexity of human responsiveness" by adding an additional element to the learning process: learning via rewards and consequences<ref>{{Cite book|title=Social learning theory|last=Bandura|first=Albert|date=1977|publisher=Prentice-Hall|isbn=978-0-13-816751-6|series=Prentice-Hall series in social learning theory|location=Englewood Cliffs, New Jersey}}</ref>. The social learning theory is more accepted compared to the atavist theory by Lombroso. The nature vs. nurture debate in criminology has been a heated topic in the world of psychology & criminology for centuries. Another popular take on the debate, as propagated by geneticists, is that neither origin is solely responsible for criminal behavior, and that criminal behavior is a combination of both nature and nurture done in a very "complex and not yet fully understood [way]", which leads to offensive and law-breaking behavior. Some scientists, surprisingly enough, believe that the debate is "unhelpful" and "outdated", yet the debate ravages on. Certain researchers hesitate to take a stance, fearing that leaning to one-side over the other may leave the door open to biased narrators who may use the debate to spread false agendas. For example, if someone were to believe that nature is responsible for crime vs. nurture, this could lead to a resurgence in racist propaganda disguised as "scientific discourse". Alternatively, placing an emphasis on nurture could close the door for improvement for those riddled in poverty and other environmental disadvantages<ref>{{Cite journal|last=Levitt|first=Mairi|date=2013-12-12|title=Perceptions of nature, nurture and behaviour|url=https://lsspjournal.biomedcentral.com/articles/10.1186/2195-7819-9-13|journal=Life Sciences, Society and Policy|volume=9|issue=1|pages=13|doi=10.1186/2195-7819-9-13|issn=2195-7819|pmc=PMC4513026}}</ref>. As detailed, there is significant controversy regarding which side of the nature vs. nurture debate is correct, but what is the scientific consensus concerning nature vs. nurture for pedophilia? Which side is more responsible for the disorder at hand and what are some measures that can be taken depending on whether nature or nurture is the culprit? ----A 2009 study done on the etiology of pedophilia by researcher Juan Antonio Becerra García of the International University of La Rioja found several "structural deteriorations" within brain regions that were essential to sexual development, including a smaller right amygdala (less control over ability to inhibit certain behaviors), a significant decline of gray matter in the hypothalamus (which leads to a score of neurological issues, including memory loss and other cognitive impairments), and a decline in the activity of the dorsolateral prefrontal cortex (which leads to poor executive functioning)<ref name=":2">{{Cite journal|last=Becerra García|first=Juan Antonio|date=2009-01-01|title=Etiology of pedophilia from a neurodevelopmental perspective: markers and brain alterations|url=https://linkinghub.elsevier.com/retrieve/pii/S2173505009700512|journal=Revista de Psiquiatría y Salud Mental (English Edition)|volume=2|issue=4|pages=190–196|doi=10.1016/S2173-5050(09)70051-2|issn=2173-5050}}</ref>. Another review of the disorder published in 2015 affirmed that other studies conducted on pedophiles found similar findings, including a reduction of inhibition and executive functioning<ref>{{Cite journal|last=Tenbergen|first=Gilian|last2=Wittfoth|first2=Matthias|last3=Frieling|first3=Helge|last4=Ponseti|first4=Jorge|last5=Walter|first5=Martin|last6=Walter|first6=Henrik|last7=Beier|first7=Klaus M.|last8=Schiffer|first8=Boris|last9=Kruger|first9=Tillmann H. C.|date=2015-06-24|title=The Neurobiology and Psychology of Pedophilia: Recent Advances and Challenges|url=http://journal.frontiersin.org/Article/10.3389/fnhum.2015.00344/abstract|journal=Frontiers in Human Neuroscience|volume=9|doi=10.3389/fnhum.2015.00344|issn=1662-5161|pmc=PMC4478390|pmid=26157372}}</ref>. However, García concluded that there really wasn't a "determinant explanation" for one to become a pedophile. García suggested that the brain abnormalities were brought about during neruodevelopment through "adverse events", but emphasizes that these cognitive shifts in the brain do not render an individual free from such horrific sexual crimes, if one were to act on such impulses<ref name=":2" />. == References == {{Reflist}} [[Category:Atcovi's Work]] rgtwmrcxet56sx7r0xvvgcsjc0adepv 2684089 2684088 2024-11-12T01:52:50Z Atcovi 276019 2684089 wikitext text/x-wiki '''Topic''': Exploring pedophilia through nature vs nurture, while assessing it through 2 theories from the eyes of Lombroso (Atavist theory) and the social learning theory. Provide peer reviews for both, then provide a final input on which one is more plausible to explain pedophilia and the sexual crimes attached with it. <center>'''''Pedophila Through Nature vs. Nurture'''''</center> Pedophilia is, as defined by notable Canadian sexologist and forensic psychologist Micheal C. Seto in his 2009 review of pedophilia, the "persistent sexual interest in prepubescent children [children generally younger than 13]"<ref>{{Cite journal|last=Seto|first=Michael C.|date=2009-04-01|title=Pedophilia|url=https://www.annualreviews.org/doi/10.1146/annurev.clinpsy.032408.153618|journal=Annual Review of Clinical Psychology|language=en|volume=5|issue=1|pages=391–407|doi=10.1146/annurev.clinpsy.032408.153618|issn=1548-5943}}</ref>. ICD-11 (the 11th revision of the International Classification of Diseases) requires, in order for a pedophilia diagnosis to be made, that the individual has consistent sexual thoughts, urges, and illusions of pre-pubertal children & to have either acted on these urges or be clearly distraught by these feelings. The diagnosee cannot be a child (pre-pubertal) and extreme caution is urged when assessing an adolescene for this disorder<ref name="ICD-11">{{cite web|url=https://icd.who.int/browse11/l-m/en#/http%3a%2f%2fid.who.int%2ficd%2fentity%2f517058174|title=ICD-11 for Mortality and Morbidity Statistics|date=2024|publisher=[[World Health Organization]]/[[ICD-11]]|at=See section 6D32 Pedophilic disorder|access-date=November 6, 2024|quote=Pedophilic disorder is characterized by a sustained, focused, and intense pattern of sexual arousal—as manifested by persistent sexual thoughts, fantasies, urges, or behaviours—involving pre-pubertal children. In addition, in order for Pedophilic Disorder to be diagnosed, the individual must have acted on these thoughts, fantasies or urges or be markedly distressed by them. This diagnosis does not apply to sexual behaviours among pre- or post-pubertal children with peers who are close in age.}}</ref>. Pedophilia is problematic, dangerous, and is a contributing factor behind many sexual crimes done against children. To assess the reason behind the development of pedophilia, it is essential to first cover the nature vs. nurture debate in criminology. The nature vs. nurture debate concerns which origin is more likely to be the source and cause of criminal behavior as one reaches an age where they can be held responsible for their behavior. The "nature" aspect puts fault on one's genetic predispositions, or the chance of developing certain traits due to one's genes<ref>{{Cite web|url=https://library.fiveable.me/key-terms/introduction-brain-behavior/genetic-predisposition|title=Genetic predisposition - (Intro to Brain and Behavior) - Vocab, Definition, Explanations {{!}} Fiveable|website=library.fiveable.me|access-date=2024-11-07}}</ref>. On the other hand, the "nurture" aspect is concerned with one's upbringing and environmental living conditions. Throughout history, several theories have been posed on whether nature or nurture play a bigger role in one's development into embracing a criminal lifestyle. In this review, two theories will be analyzed and applied regarding pedophilia. The first theory is atavism, as applied to the field of criminology, by 1800s Italian criminologist Cesare Lombroso. Cesare Lombroso proposed that a criminal can be identified by physical features that are a result of an evolutive degression. Criminals possess physical features, or atavistic anomalies, that are abnormal and distinct from normal human begins, with these atavistic anomalies closely resembling a "savage" or a "primitive man"<ref name=":0">{{Cite journal|last=Ellwood|first=Charles|date=1912-01-01|title=Lombroso's Theory of Crime|url=https://scholarlycommons.law.northwestern.edu/jclc/vol2/iss5/6/|journal=Journal of Criminal Law and Criminology|volume=2|issue=5|pages=716}}</ref><ref name=":1">{{Cite book|url=https://www.worldcat.org/title/on1285696621|title=Criminology|last=Siegel|first=Larry J.|date=2023|publisher=Cengage|isbn=978-0-357-62474-6|edition=Eighth edition|location=Boston, MA|oclc=on1285696621}}</ref>. According to Lombroso, these traits could be darker skin, a bulky jaw, sharper teeth, ears akin to a monkey, and an insensitivity to pain<ref name=":1" /><ref>{{Cite journal|last=Mazzarello|first=Paolo|date=2011|title=Cesare Lombroso: an anthropologist between evolution and degeneration|url=https://pubmed.ncbi.nlm.nih.gov/21729591/|journal=Functional Neurology|volume=26|issue=2|pages=97–101|issn=0393-5264|pmc=3814446|pmid=21729591}}</ref>. One could derive these traits via either "indirect heredity", where the criminal's lineage were afflicted by monstrous illnesses (such as mental illnesses) and these traits were passed down to the criminal, or "direct heredity", where these criminal traits were given to the criminal directly from their parents<ref name=":1" />. Despite Lombroso's atavist theory being rejected on the grounds of having been inspired by racist underpinnings & and maintaining little to no scientific backing, Lombroso laid out an important road to studying the criminals themselves rather than just the crime<ref name=":0" />. ----On the other hand, the social learning theory states that people are not inherently criminals, but exhibit criminal-like behavior due to their upbringing or environment. Individuals witness criminal behavior and perceive the reward higher than the consequences. Notable psychologists, such as Albert Bandura, advocated for this theory. An example of this theory being demonstrated is like a son who watches his father abuse his mother and goes on to model his father's behavior when dealing with his significant other and his children<ref name=":1" />. The social learning theory expanded upon the "tremendous complexity of human responsiveness" by adding an additional element to the learning process: learning via rewards and consequences<ref>{{Cite book|title=Social learning theory|last=Bandura|first=Albert|date=1977|publisher=Prentice-Hall|isbn=978-0-13-816751-6|series=Prentice-Hall series in social learning theory|location=Englewood Cliffs, New Jersey}}</ref>. The social learning theory is more accepted compared to the atavist theory by Lombroso. The nature vs. nurture debate in criminology has been a heated topic in the world of psychology & criminology for centuries. Another popular take on the debate, as propagated by geneticists, is that neither origin is solely responsible for criminal behavior, and that criminal behavior is a combination of both nature and nurture done in a very "complex and not yet fully understood [way]", which leads to offensive and law-breaking behavior. Some scientists, surprisingly enough, believe that the debate is "unhelpful" and "outdated", yet the debate ravages on. Certain researchers hesitate to take a stance, fearing that leaning to one-side over the other may leave the door open to biased narrators who may use the debate to spread false agendas. For example, if someone were to believe that nature is responsible for crime vs. nurture, this could lead to a resurgence in racist propaganda disguised as "scientific discourse". Alternatively, placing an emphasis on nurture could close the door for improvement for those riddled in poverty and other environmental disadvantages<ref>{{Cite journal|last=Levitt|first=Mairi|date=2013-12-12|title=Perceptions of nature, nurture and behaviour|url=https://lsspjournal.biomedcentral.com/articles/10.1186/2195-7819-9-13|journal=Life Sciences, Society and Policy|volume=9|issue=1|pages=13|doi=10.1186/2195-7819-9-13|issn=2195-7819|pmc=PMC4513026}}</ref>. As detailed, there is significant controversy regarding which side of the nature vs. nurture debate is correct, but what is the scientific consensus concerning nature vs. nurture for pedophilia? Which side is more responsible for the disorder at hand and what are some measures that can be taken depending on whether nature or nurture is the culprit? ----A 2009 study done on the etiology of pedophilia by researcher Juan Antonio Becerra García of the International University of La Rioja found several "structural deteriorations" within brain regions that were essential to sexual development, including a smaller right amygdala (less control over ability to inhibit certain behaviors), a significant decline of gray matter in the hypothalamus (which leads to a score of neurological issues, including memory loss and other cognitive impairments), and a decline in the activity of the dorsolateral prefrontal cortex (which leads to poor executive functioning)<ref name=":2">{{Cite journal|last=Becerra García|first=Juan Antonio|date=2009-01-01|title=Etiology of pedophilia from a neurodevelopmental perspective: markers and brain alterations|url=https://linkinghub.elsevier.com/retrieve/pii/S2173505009700512|journal=Revista de Psiquiatría y Salud Mental (English Edition)|volume=2|issue=4|pages=190–196|doi=10.1016/S2173-5050(09)70051-2|issn=2173-5050}}</ref>. Another review of the disorder published in 2015 affirmed that other studies conducted on pedophiles found similar findings, including a reduction of inhibition and executive functioning<ref>{{Cite journal|last=Tenbergen|first=Gilian|last2=Wittfoth|first2=Matthias|last3=Frieling|first3=Helge|last4=Ponseti|first4=Jorge|last5=Walter|first5=Martin|last6=Walter|first6=Henrik|last7=Beier|first7=Klaus M.|last8=Schiffer|first8=Boris|last9=Kruger|first9=Tillmann H. C.|date=2015-06-24|title=The Neurobiology and Psychology of Pedophilia: Recent Advances and Challenges|url=http://journal.frontiersin.org/Article/10.3389/fnhum.2015.00344/abstract|journal=Frontiers in Human Neuroscience|volume=9|doi=10.3389/fnhum.2015.00344|issn=1662-5161|pmc=PMC4478390|pmid=26157372}}</ref>. However, García concluded that there really wasn't a "determinant explanation" for one to become a pedophile. García suggested that the brain abnormalities were brought about during neurodevelopment through "adverse events” but emphasizes that these cognitive shifts in the brain do not render an individual free from such horrific sexual crimes, if one were to act on such impulses<ref name=":2" />. == References == {{Reflist}} [[Category:Atcovi's Work]] q5cjoe49dk6ky9rhhz8lx42gp2uh2fy Illustrated Companion to the Latin Dictionary/Mannulus 0 314521 2683646 2680385 2024-11-11T15:58:11Z CalRis25 911425 Remove transcriber's note. 2683646 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''MAN'NULUS'''. (Plin. ''Ep.'' iv. 2. 3. ) Diminutive of [[Illustrated Companion to the Latin Dictionary/Mannus|MANNUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 2nopzbobnbj7hh66r6izid2zcxsrycx Illustrated Companion to the Latin Dictionary/Mataxa 0 314555 2683702 2680421 2024-11-11T16:07:52Z CalRis25 911425 Convert transcriber's note to footnote. 2683702 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''MATAX'A'''. See METAXA.<ref group="Note" name="Rich1849_Metaxa"/> == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="Rich1849_Metaxa">Article "Metaxa" does not exist in the 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon''.</ref> }} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Dead-end-pages]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 9es5tt166s8pqcj7k3jpqf3jz4jcsjn Illustrated Companion to the Latin Dictionary/Mulleolus 0 314659 2683709 2680533 2024-11-11T16:08:56Z CalRis25 911425 Remove transcriber's note. 2683709 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''MULL'EOLUS'''. (Tertull. ''Pall.'' 4.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Mulleus|MULLEUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0g17laujdk8svj42jdnvh3u96vkrivf Illustrated Companion to the Latin Dictionary/Musivarius 0 314690 2683718 2680691 2024-11-11T16:10:17Z CalRis25 911425 Remove transcriber's link 2683718 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''MUSIVA'RIUS'''. An artist who made mosaic work, the ''opus musivum'', as explained under the following word: [[Illustrated Companion to the Latin Dictionary/Musivum|Musivum]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Mosaic]] fd2asjn1hdcsmkzkbltwcv6mazrvo03 Illustrated Companion to the Latin Dictionary/Navigiolum 0 314722 2683722 2680724 2024-11-11T16:10:53Z CalRis25 911425 Remove transcriber's note. 2683722 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''NAVIG'IOLUM'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Navigium|NAVIGIUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/Ships and Boats]] ekldh1wv6e62189lh4gx5p1y69euuq3 Illustrated Companion to the Latin Dictionary/Operculum 0 314784 2683726 2680788 2024-11-11T16:11:32Z CalRis25 911425 Remove transcriber's note 2683726 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''OPER'CULUM''' ({{lang|grc|πώμα}}). A ''lid'' or cover for a jar, pot, or other vessel of similar description. (Cato, ''R. R.'' 104. Columell. viii. 8. 7.) See the three last illustrations ([[Illustrated Companion to the Latin Dictionary/Olla|OLLA]], [[Illustrated Companion to the Latin Dictionary/Ollarium|OLLARIUM]]). 2. ''Operculum ambulatorium.'' A sliding or moveable lid, which might be depressed or raised, so as to cover exactly the contents in the vessel it belonged to, like that now used for snuff and tobacco jars. The Romans sometimes covered their [[Illustrated Companion to the Latin Dictionary/Alveare|beehives]] with lids of this kind in order that the size of the honeycomb and hive might be exactly proportioned to each other. Plin. ''H. N.'' xxi. 47. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] jyl21uieeucxzzy66nnjcnnrc6hiobt Illustrated Companion to the Latin Dictionary/Pistris 0 314999 2683802 2681011 2024-11-11T16:24:49Z CalRis25 911425 Convert transcriber's note to footnote. 2683802 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''PIS'TRIS''' or '''PRIS'TIS''', and '''PIS'TRIX''' or '''PRIS'TIX''' ({{lang|grc|πίστρις}} and {{lang|grc|πρίστις}}). A sea-monster (Florus, iii. 5. 16. Plin. ''H. N.'' ix. 2.); but always represented by the ancient artists with the same characteristic features as are exhibited in the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Pistris 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 508.jpg|annexed illustration |caption=Pistris/1.1}} from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Pompeii, viz. the head of a dragon, the neck and breast of a beast, with fins in the place of front legs, and the tail and body of a fish (Virg. ''Aen.'' iii. 427.); a form generally adopted by the early Christian artists to represent the whale which swallowed Jonah. 2. The name given to a particular class of ships of war (Liv. xxxv. 26. Polyb. xvii. 1. 1.), doubtless from a certain resemblance in general form to the above figure; perhaps from the [[Illustrated Companion to the Latin Dictionary/Prora|bow]] rising very high out of the water, like the head and neck there portrayed. In Virgil (''Aen.'' v. 116.) ''pistris'' is the adopted name of a vessel, after the image of this monster borne on its bows as a figure-head (''[[Illustrated Companion to the Latin Dictionary/Insigne|insigne]]''). See the woodcut at [[Illustrated Companion to the Latin Dictionary/Insigne|p. 352]].<ref group="Note" name="Rich1849_325/> <gallery> File:Pistris 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 508.jpg|Pistris/1.1 </gallery> == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="Rich1849_325>The 1849-edition of Anythony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek lexicon'' refers to page 325, which is wrong.</ref> }} == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Classed Index-category missing]] 5amrvoyspvzhdafy3mnuhoqio22yojw Illustrated Companion to the Latin Dictionary/Praetorium 0 315085 2683823 2681100 2024-11-11T16:27:45Z CalRis25 911425 Convert transcriber's note to footnote. 2683823 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''PRAETO'RIUM''' ({{lang|grc|στρατηγεῖον}}). The [[Illustrated Companion to the Latin Dictionary/Tentorium|tent]] of the general-in-chief or commander of an army (see the wood-cut [[Illustrated Companion to the Latin Dictionary/Castra|p. 127]],<ref group="Note" name="Rich1849_127/>); so termed because the [[Illustrated Companion to the Latin Dictionary/Consul|consul]] who had the chief command was in early days styled ''[[Illustrated Companion to the Latin Dictionary/Praetor|praetor]]''. Liv. x. 33. Id. vii. 12. 2. The residence of the governor of a province, at which he administered justice (Cic. ''Verr.'' ii. 4. 28. ''Ib.'' ii. 3. 35.); whence transferred to the palace of any king or prince. Juv. x. 161. 3. Latterly the same designation was also given to the splendid country villas of the noble and wealthy Romans, which were built with so much expense and luxury under the imperial period. Suet. ''Aug.'' 72. Id. ''Tib.'' 39. Stat. ''Sylv.'' i. 3. 25. == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="Rich1849_127>The 1849-edition of Anythony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek lexicon'' refers to page 126, which is wrong.</ref> }} == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Camp and Tents]] ta1t5c9gf9gbp0gj9596kaene4ixqxr Illustrated Companion to the Latin Dictionary/Pyxidicula 0 315180 2683829 2681289 2024-11-11T16:28:50Z CalRis25 911425 Remove transcriber's note. 2683829 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''PYXIDIC'ULA'''. Diminutive of [[Illustrated Companion to the Latin Dictionary/Pyxis|PYXIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 8ghh7o4lxb19n90pe8rsujecr07m5at Illustrated Companion to the Latin Dictionary/Sarraculum 0 315343 2683835 2681460 2024-11-11T16:29:37Z CalRis25 911425 Remove transcriber's note. 2683835 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''SARRA'CULUM'''. Ammian. xxxi. 2. 18. Diminutive of [[Illustrated Companion to the Latin Dictionary/Sarracum|SARRACUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] bh5sl0feggm9neizm9a21smr2nx3k6r Illustrated Companion to the Latin Dictionary/Scalper 0 315358 2683841 2681475 2024-11-11T16:30:32Z CalRis25 911425 Remove transcriber's note. 2683841 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''SCAL'PER'''. Same as [[Illustrated Companion to the Latin Dictionary/Scalprum|SCALPRUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] si6b5dxx79d60dh2z474wry7qlx51jp Illustrated Companion to the Latin Dictionary/Socculus 0 315508 2683846 2681633 2024-11-11T16:31:16Z CalRis25 911425 Remove transcriber's note. 2683846 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''SOC'CULUS'''. (Sen. ''Ben.'' ii. 12. Suet. ''Vit.'' 2.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Soccus|SOCCUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 5e7i3yqqejp2url6cpc0vy42ffrdkcf Illustrated Companion to the Latin Dictionary/Strigilecula 0 315581 2683854 2681711 2024-11-11T16:32:24Z CalRis25 911425 Remove transcriber's note. 2683854 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''STRIGILE'CULA''' ({{lang|grc|στλεγγίδιον}}). (Apul. ''Flor.'' ii. 9. 2.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Strigilis|STRIGILIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 2gq18dfhmwofajirkaq0k70chl5m3zu Linear algebra (Osnabrück 2024-2025)/Part II/Lecture 33 0 315633 2683922 2681872 2024-11-11T16:43:04Z Bocardodarapti 289675 2683922 wikitext text/x-wiki {{Subtitle|The cross product}} {{:Cross product/K^3/Introduction/Section|extra1=Footnote|extra2=Footnote|extra3= &nbsp; we will discuss orientations later.}} {{Subtitle|Isometries}} {{:Vector space/K/Inner product/Linear isometry/Introduction/Section}} {{Subtitle|Isometries on a Euclidean vector space}} {{:Euclidean vector space/Isometry/Section|}} {{Subtitle|Eigenvalues of an isometry}} {{ inputfactproof |Unitary vector space/Isometry/Eigenvalues/Fact|Theorem|| }} In general, an isometry does not have necessarily an eigenvalue; however, if the dimension is odd, then there is an eigenvalue, see the following lecture. {{ inputfactproof2 |Linear isometry/Determinant is 1 or -1/Fact|Lemma||pv=2 }} {{Subtitle|Proper isometries}} {{:Euclidean vector space/Proper Isometry/Introduction/Section|}} {{List of footnotes}} 5e32etvhhtx3nkicqvvlqbh52stm2t7 Illustrated Companion to the Latin Dictionary/Sudariolum 0 315656 2683858 2681886 2024-11-11T16:32:55Z CalRis25 911425 Remove transcriber's note. 2683858 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''SUDA'RIOLUM'''. Apul. ''Apol.'' p. 491. Diminutive of [[Illustrated Companion to the Latin Dictionary/Sudarium|SUDARIUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] kzm3u6xsfvkas3fvjtotoykhcc7f0gn Illustrated Companion to the Latin Dictionary/Synthesina 0 315680 2683878 2681910 2024-11-11T16:36:10Z CalRis25 911425 Remove transcriber's note. 2683878 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''SYNTHES'INA'''. (Suet. ''Nero'', 51.) Same as [[Illustrated Companion to the Latin Dictionary/Synthesis|SYNTHESIS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] iqrno6i1tkme4h54mzk7p57pd83i94z Illustrated Companion to the Latin Dictionary/Tomacina 0 315785 2683882 2682015 2024-11-11T16:36:48Z CalRis25 911425 Remove transcriber's note. 2683882 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''TOMA'CINA''' ({{lang|grc|τεμάχιον}}). (Varro, ''R. R.'' ii. 4. 10.) Same as [[Illustrated Companion to the Latin Dictionary/Tomaculum|TOMACULUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 5msxz0gqw709l2v68piiey5edfgd8ar Illustrated Companion to the Latin Dictionary/Torcular 0 315801 2683894 2682031 2024-11-11T16:38:41Z CalRis25 911425 Remove transcriber's note. 2683894 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''TOR'CULAR''' and '''-UM''' ({{lang|grc|ληνός}}). A ''press'' employed in the manufacture of oil and wine (Vitruv. vi. 6. 3. Plin. ''H. N.'' xviii. 74. Varro, ''ap.'' Non. ''s. v.'' p. 47.); the object of which was to extract by violent pressure all the juice remaining in the skins and stalks of the grapes (''pes vinaceorum'') after they had been trodden out by the feet, or the oil from the olive pulps (''samsa'') after they had been bruised in the mill (''[[Illustrated Companion to the Latin Dictionary/Trapetum|trapetum]]'', ''[[Illustrated Companion to the Latin Dictionary/Mola|mola]]''). The earliest contrivance employed for this purpose was of a very simple description; merely consisting of a heavy block of stone, raised up by the aid of a lever beam, under which block the bunches of grapes enclosed in a basket (''[[Illustrated Companion to the Latin Dictionary/Fiscina|fiscina]]'', Columell. xii. 39. 3.), or between laths (''[[Illustrated Companion to the Latin Dictionary/Regula|regulae]]'', Id. xii. 52. 10.), to prevent the mass from bulging out at the sides, were placed, as represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Torcular 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 673.jpg|annexed illustration |caption=Torcular/1.1}}, from a Greek bas-relief of the Neapolitan Museum. The two men on the left steady the stone, whilst the three at the opposite extremity of the lever are occupied in raising it up to give room for placing the basket of grapes underneath it. It is probable, that after the stone had been lowered on to the fruit, the lever was removed to over the top, and made to perform the duties of a press-beam (''[[Illustrated Companion to the Latin Dictionary/Prelum|prelum]]''), by fixing one end in a socket, so that the pressmen at the opposite end could increase the natural weight of the stone by forcing the beam upon it. The next step produced a regular machine, described in detail by Cato (''R. R.'' 18.), which operated by the pressure of a beam (''prelum''), drawn down upon the object to be squeezed by means of ropes attached to one end of the beam, and worked by a capstan (''[[Illustrated Companion to the Latin Dictionary/Sucula|sucula]]'', Plin. ''H. N.'' xviii. 74.) Very considerable vestiges of one of these presses have been discovered in an ancient press-room at Gragnano (formerly ''Stabiae''), after which the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed diagram |imagelink=Media:Torcular 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 673.jpg|annexed diagram |caption=Torcular/1.2}} is designed, with the object of explaining the character of the machine, the parts of which it was composed, and the nomenclature attached to them. 1, 1. Two strong uprights or trunks (''arbores''), firmly planted and wedged into sockets constructed under the [[Illustrated Companion to the Latin Dictionary/Pavimentum|flooring]] of the press-room (see the wood-cut, ''s.'' [[Illustrated Companion to the Latin Dictionary/Torcularium|TORCULARIUM]], No. 4. ''i.''), which served to hold down the tongue (''[[Illustrated Companion to the Latin Dictionary/Ligula|lingula]]'', 2.) of the pressbeam (''[[Illustrated Companion to the Latin Dictionary/Prelum|prelum]]'', 3.), and form a point of resistance when it was in operation. As the entire stress consequent upon the upward action of the press-beam came against this part of the apparatus, when its opposite extremity was forced down, Cato recommends that two trunks should be used, as being more solid, and less likely to be forced out of their sockets than a single one would be; consequently, two are represented in the plan; but in the example at Gragnano, only one was employed, and that had an eye (''foramen'') cut in it, to receive the tongue of the beam. 4, 4. Two posts (''stipites''), also planted in sockets of a similar kind under the flooring (see the wood-cuts, ''s.'' [[Illustrated Companion to the Latin Dictionary/Torcularium|TORCULARIUM]], No. 3., ''g'', ''h''), which held the ends of the capstan (''[[Illustrated Companion to the Latin Dictionary/Sucula|sucula]]'', 5, 5) that worked down the beam. The heads of these posts were tied together by a cross-beam at the top, on which was fixed a pulley, with a cord running through it from the end of the press-beam; by means of which the beam was raised, to make room for the baskets of fruit or pulp, when placed underneath it, upon the bed (''area'', 6.), where they were squeezed. The method of working it is easily understood. When the grapes or olives had been trodden out by the feet or bruised in the mill, the residue was put into a basket, and placed on the ''area''. Over them was then laid a very strong flat board (''[[Illustrated Companion to the Latin Dictionary/Orbis|orbis olearius]]'', Cato, ''R. R.'' 18.), in order to equalise the pressure upon all parts of the surface. The long end of the press-beam was then lowered from above on to the ''orbis'', and there strained down by the capstan until all the juice had been squeezed out. Another kind of wine-press, of undoubted authority, although not actually described by any of the writers now extant, is represented by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Torcular 1.3 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 674.jpg|annexed illustration |caption=Torcular/1.3}}, from a [[Illustrated Companion to the Latin Dictionary/Pictura|painting]] at Herculaneum. It consists of two uprights firmly fixed in the ground, and strengthened by a cross-beam at the top, and another at the bottom, which served as an ''area'' upon which the basket of fruit was placed. Over this there are a number of solid boards (''[[Illustrated Companion to the Latin Dictionary/Tympanum|tympana]]'', Plin. ''H. N.'' xviii. 74.), which perform the office of a press-beam, having their heads fitted into perpendicular channels running down each side of the uprights, and being forced down upon the mass of grapes by means of immense blocks, driven in as wedges between them by blows of a mallet. Presses of this description continued in common use amongst the Romans, until within a century of the age of Pliny, when a simple improvement was first introduced, of working the beam down by means of a screw (''[[Illustrated Companion to the Latin Dictionary/Cochlea|cochlea]]'') instead of the capstan or wedges. (Plin. ''H. N.'' xviii. 74.); but this eventually led to a great change during Pliny's life-time, which very materially altered the form and character of the original machine. The great length of a lever press-beam was very inconvenient, as it required so large a building for the room where it was worked, and the last machine is but a clumsy contrivance; but a remedy was found by the invention of the screw-press, with a mast (''[[Illustrated Companion to the Latin Dictionary/Malus|malus]]'') for the male screw placed in its centre, as shown by the {{Illustrated Companion to the Latin Dictionary/Image Location|text=annexed illustration |imagelink=Media:Torcular 1.4 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 674.jpg|annexed illustration |caption=Torcular/1.4}}, from a painting at Pompeii; in which solid boards (''tympana''), instead of the long beam, are placed over the mass, and screwed down upon it; so that the machine is much smaller, though equally powerful, and requires less room. (Plin. ''l. c.'') The illustration, in reality, is intended for a clothes-press (''[[Illustrated Companion to the Latin Dictionary/Pressorium|pressorium]]''); but as the constructive principle is the same, it will equally serve to illustrate the present subject. 2. ({{lang|grc|ληνός}}). (Plin. ''H. N.'' xviii. 62. Columell. xi. 2. 71.) In these passages, which speak of washing and cleaning the ''torculum'', the word is generally taken to mean a vat in which the grapes were crushed by the feet; but there is no substantial reason for the distinction, since the older lever-press was composed of several pieces, which were put together, or set up, at the time of the vintage and oil-making, and afterwards taken down and stowed out of the way, to leave the room at liberty for other purposes (Varro, ''ap.'' Non. ''s. v.'' ''vineis ubi ampla cella torculum reponant''). Pliny and Columella only enjoin the necessity of cleaning and washing these parts before they were put by. 3. (Vitruv. vi. 6. 2.) The press-room, or building in which the ''torcular'' was worked. Same as [[Illustrated Companion to the Latin Dictionary/Torcularium|TORCULARIUM]]. <gallery> File:Torcular 1.1 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 673.jpg|Torcular/1.1 File:Torcular 1.2 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 673.jpg|Torcular/1.2 File:Torcular 1.3 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 674.jpg|Torcular/1.3 File:Torcular 1.4 - Anthony Rich, Illustrated Companion to the Latin Dictionary, and Greek Lexicon, p. 674.jpg|Torcular/1.4 </gallery> == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:Classed Index/Manufacture of Oil and Wine]] b4ayx78lmozra89c7l1fndj71tuc0j7 Illustrated Companion to the Latin Dictionary/Trabecula 0 315812 2683899 2682043 2024-11-11T16:39:18Z CalRis25 911425 Remove transcriber's note. 2683899 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''TRABEC'ULA'''. (Cato, ''R. R.'' viii. 5.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Trabs|TRABS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 04vh7xiu95dj76xlyg0c48dl71431u6 Illustrated Companion to the Latin Dictionary/Transtillum 0 315823 2683912 2682054 2024-11-11T16:41:29Z CalRis25 911425 Remove transcriber's note. 2683912 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''TRANSTILLUM'''. (Vitruv. v. 12.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Transtrum|TRANSTRUM]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Orphaned articles]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 8tstvhlgpafh0n72f4ohaszyk4b72oz Illustrated Companion to the Latin Dictionary/Urceolus 0 315921 2683916 2682162 2024-11-11T16:42:00Z CalRis25 911425 Remove transcriber's note. 2683916 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''UR'CEOLUS'''. (Juv. iii. 203.) Diminutive of [[Illustrated Companion to the Latin Dictionary/Urceus|URCEUS]]. == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:RICH-2K/Classed Index-category missing]] 0x0dylktay1bt59tw1sjym48bfrl6rb Illustrated Companion to the Latin Dictionary/Xystus 0 316043 2683964 2682286 2024-11-11T18:08:50Z CalRis25 911425 Convert transcriber's note to footnot. 2683964 wikitext text/x-wiki {{Template:Illustrated Companion to the Latin Dictionary/Navbox}} == Illustrated Companion to the Latin Dictionary, and Greek Lexicon (Rich, 1849) == '''XYS'TUS''' or '''-UM''' ({{lang|grc|ξυστός}} or {{lang|grc|-όν}}). Amongst the Greeks, a covered corridor in the gymnasium (see the [[Illustrated Companion to the Latin Dictionary/Gymnasium|plan p. 324. {{Illustrated Companion to the Latin Dictionary/Inscription|text=T T}}]])<ref group="Note" name="Rich1849_324/> where the [[Illustrated Companion to the Latin Dictionary/Athletae|athletes]] exercised in winter. Vitruv. v. 11. 4. Id. vi. 7. 5. 2. Amongst the Romans, an open walk or terrace in a garden, amidst flower-beds edged with box. Plin. ''Ep.'' ii. 17. 17. Id. v. 6. 19. Suet. ''Aug.'' 72. Phaedr. ii. 5. == Notes == {{reflist |group="Note" |refs= <ref group="Note" name="Rich1849_324>The 1849-edition of Anthony Rich's ''Illustrated Companion to the Latin Dictionary, and Greek Lexicon'' refers to page 342, but that is wrong.</ref> }} == References == {{reflist}} [[Category:RICH-2K/Articles]] [[Category:RICH-2K/RICH-1849]] [[Category:RICH-2K/References missing or incomplete]] [[Category:RICH-2K/Comparison with 1890-edition outstanding]] [[Category:RICH-2K/Articles without images]] [[Category:Classed Index/The Garden]] [[Category:Classed Index/The Gymnasium and Palaestra]] mmcrkxh6bom771z819ydv8jr8wlyfjg Empennage 0 316391 2683457 2683413 2024-11-11T15:18:12Z Atcovi 276019 {{subst:Prod}} 2683457 wikitext text/x-wiki <!-- TO CONTEST THIS PROPOSED DELETION, remove the following template, including this comment, up to the CLOSING COMMENT --> {{Ombox | type = delete | image = [[File:Orologio rosso.svg|45x45px|center|No license|link=]] | text = Please [{{fullurl:{{FULLPAGENAME}}|action=edit}} help improve] the [[WV:WIW|educational quality]] of this resource to increase [[Wikiversity:Learning|engagement]] by [[Wikiversity:Who are Wikiversity participants?|participants]]. Any concrete improvements made by '''{{#time:F j, Y|{{REVISIONTIMESTAMP}} +90 days}}''' may allow it to be [[WV:PROD|kept]]. <br> You may remove {{tl|proposed deletion}} from this resource's source text to contest this proposal, with or without [[{{TALKPAGENAME}}|discussion]]. {{#if:|---- <div style="text-align:center; margin-bottom:0em;"> ''The Nominator gave the following reason for their nomination'': {{cquote|{{{1}}}}} </div> }}}}{{center|[[Special:PrefixIndex/{{FULLPAGENAME}}/|''Link to any subpages this page might have'']]}} {{event trigger|date=November 11, 2024|when=90 days|[[Category:Pending deletions|{{PAGENAME}}]]}} {{event trigger|date=November 11, 2024|when=60 days|[[Category:60-day proposed deletions|{{PAGENAME}}]]}} [[Category:Proposed deletions|{{PAGENAME}}]] <!-- CLOSING COMMENT, remove up to and including this comment --> The '''empennage''' also known as the '''tail section''', is the tail section of an aircraft. It typically contains a fixed vertical stabilizer or fin, the rudder, the stabilizer, the elevators, as well as other trimming and control devices. It stabilizes the aircraft similar to how a feather does to an arrow. clvd185bdlnhr0tyigvfcdw8x9fky0u Landing gear 0 316392 2683458 2683414 2024-11-11T15:18:43Z Atcovi 276019 {{subst:Prod}} 2683458 wikitext text/x-wiki <!-- TO CONTEST THIS PROPOSED DELETION, remove the following template, including this comment, up to the CLOSING COMMENT --> {{Ombox | type = delete | image = [[File:Orologio rosso.svg|45x45px|center|No license|link=]] | text = Please [{{fullurl:{{FULLPAGENAME}}|action=edit}} help improve] the [[WV:WIW|educational quality]] of this resource to increase [[Wikiversity:Learning|engagement]] by [[Wikiversity:Who are Wikiversity participants?|participants]]. Any concrete improvements made by '''{{#time:F j, Y|{{REVISIONTIMESTAMP}} +90 days}}''' may allow it to be [[WV:PROD|kept]]. <br> You may remove {{tl|proposed deletion}} from this resource's source text to contest this proposal, with or without [[{{TALKPAGENAME}}|discussion]]. {{#if:|---- <div style="text-align:center; margin-bottom:0em;"> ''The Nominator gave the following reason for their nomination'': {{cquote|{{{1}}}}} </div> }}}}{{center|[[Special:PrefixIndex/{{FULLPAGENAME}}/|''Link to any subpages this page might have'']]}} {{event trigger|date=November 11, 2024|when=90 days|[[Category:Pending deletions|{{PAGENAME}}]]}} {{event trigger|date=November 11, 2024|when=60 days|[[Category:60-day proposed deletions|{{PAGENAME}}]]}} [[Category:Proposed deletions|{{PAGENAME}}]] <!-- CLOSING COMMENT, remove up to and including this comment --> The '''landing gear''' is the undercarriage of an [[aircraft]]. In airplanes, it is used for [[taxiing]], [[takeoff]], and [[landing]]. Attached to it are wheels that allow the airplane to maneuver while making contact with the ground. The landing gear takes [[load]] off the other parts of the airplane when not airborne. 3di83d7413q2wrls4oly3j4fwu12ywq 2684104 2683458 2024-11-12T02:14:38Z CanadianWikiReader 2993500 Added the types of landing gear, their definitions, and their uses 2684104 wikitext text/x-wiki <!-- TO CONTEST THIS PROPOSED DELETION, remove the following template, including this comment, up to the CLOSING COMMENT --> {{Ombox | type = delete | image = [[File:Orologio rosso.svg|45x45px|center|No license|link=]] | text = Please [{{fullurl:{{FULLPAGENAME}}|action=edit}} help improve] the [[WV:WIW|educational quality]] of this resource to increase [[Wikiversity:Learning|engagement]] by [[Wikiversity:Who are Wikiversity participants?|participants]]. Any concrete improvements made by '''{{#time:F j, Y|{{REVISIONTIMESTAMP}} +90 days}}''' may allow it to be [[WV:PROD|kept]]. <br> You may remove {{tl|proposed deletion}} from this resource's source text to contest this proposal, with or without [[{{TALKPAGENAME}}|discussion]]. {{#if:|---- <div style="text-align:center; margin-bottom:0em;"> ''The Nominator gave the following reason for their nomination'': {{cquote|{{{1}}}}} </div> }}}}{{center|[[Special:PrefixIndex/{{FULLPAGENAME}}/|''Link to any subpages this page might have'']]}} {{event trigger|date=November 11, 2024|when=90 days|[[Category:Pending deletions|{{PAGENAME}}]]}} {{event trigger|date=November 11, 2024|when=60 days|[[Category:60-day proposed deletions|{{PAGENAME}}]]}} [[Category:Proposed deletions|{{PAGENAME}}]] <!-- CLOSING COMMENT, remove up to and including this comment --> The '''landing gear''' is the undercarriage of an [[aircraft]]. In airplanes, it is used for [[taxiing]], [[takeoff]], and [[landing]]. Attached to it are wheels that allow the airplane to maneuver while making contact with the ground. The landing gear takes [[load]] off the other parts of the airplane when not airborne. On airplanes, landing gear takes four forms: * tricycle landing gear (nosewheel); * conventional landing gear (tailwheel); * pontoons; * ski-planes. Nosewheel planes have one nose wheel in the front as well as two or more wheels in the back. The wheels in the back are slightly off the [[center of gravity]]. This variant is common in most modern planes. Taildragger planes have one wheel in the back attached to the [[Empennage|tail]] and two wheels slightly off the center of gravity in the front. Planes with this type of landing gear include the Douglas DC-3, some older small aircraft, and most gliders. Pontoons are big and hollow tanks attached to an airplane allowing it to float. Airplanes that can take off and land on water are called amphibious aircraft. Ski-planes have skis below the plane to allow landing on snow or ice. bq13953cx1fx1vt6vn5a1pn1wlo4oxv Fre 0 316395 2683453 2024-11-11T14:40:06Z 65.190.86.250 I used 78 2683453 wikitext text/x-wiki There are diffrent of it From the fre: They also noticed they had speech in other [[File:Necklace made of rough diamonds.jpg|thumb|Necklace in 1903]] languages: <syntaxhighlight lang="ecl" line="1"> Article mode Start Edren In newborn life In starting process they were Medium </syntaxhighlight>Used commanding that they edited and viewed the site after used an lot of speaking that Day they used internal language available. [[File:Movie audience (1924).svg|thumb|210x210px|Also commanded in 67's park]] They where also about to pick who"s making something over these using formats that they had after they had Much Use of out of the Cutting Length In additinal Ways to slove it. They had mentinoned that they used fre most Right over born cities from a year ago. nm068nzxc5fgzo0x1mc1uai0igshho5 Linear algebra (Osnabrück 2024-2025)/Part II/Enumeration of lectures 0 316396 2683454 2024-11-11T15:10:15Z Bocardodarapti 289675 New resource with "{{Lectures enumeration31to58 |Linear algebra (Osnabrück 2024-2025)/Part II| |L31=Vector spaces with inner product |L32=Orthogonality |L33=Isometries I |L34=Isometries II |L35=Set distances |L36=Intercept theorems |L37=Triangle geometry |L38=Bilinear forms |L39=Types of bilinear forms |L40=Minkowski-spaces |L41=Adjoined endomorphism |L42=Normal endomorphism |L43=Quadratic forms |L44=Group homomorphisms |L45=Equivalence relations |L46=Residue class formation |L47=Homomorp..." 2683454 wikitext text/x-wiki {{Lectures enumeration31to58 |Linear algebra (Osnabrück 2024-2025)/Part II| |L31=Vector spaces with inner product |L32=Orthogonality |L33=Isometries I |L34=Isometries II |L35=Set distances |L36=Intercept theorems |L37=Triangle geometry |L38=Bilinear forms |L39=Types of bilinear forms |L40=Minkowski-spaces |L41=Adjoined endomorphism |L42=Normal endomorphism |L43=Quadratic forms |L44=Group homomorphisms |L45=Equivalence relations |L46=Residue class formation |L47=Homomorphy theorems |L48=Residue class spaces |L49=Orientations |L50=Finite symmetry groups I |L51=Finite symmetry groups II |L52=Equivalent norms |L53=Convergence of matrix powers |L54=Stochastic matrices |L55=Tensor product I |L56=Tensor product II |L57=Wedge product I |L58=Wedge product II}} }}<noinclude>[[Category:Linear algebra (Osnabrück 2024-2025)/Part II]]</noinclude> rr8h6ceorqggfrpzd0eusnwx2ex7286 2683455 2683454 2024-11-11T15:10:30Z Bocardodarapti 289675 2683455 wikitext text/x-wiki {{Lectures enumeration31to58 |Linear algebra (Osnabrück 2024-2025)/Part II| |L31=Vector spaces with inner product |L32=Orthogonality |L33=Isometries I |L34=Isometries II |L35=Set distances |L36=Intercept theorems |L37=Triangle geometry |L38=Bilinear forms |L39=Types of bilinear forms |L40=Minkowski-spaces |L41=Adjoined endomorphism |L42=Normal endomorphism |L43=Quadratic forms |L44=Group homomorphisms |L45=Equivalence relations |L46=Residue class formation |L47=Homomorphy theorems |L48=Residue class spaces |L49=Orientations |L50=Finite symmetry groups I |L51=Finite symmetry groups II |L52=Equivalent norms |L53=Convergence of matrix powers |L54=Stochastic matrices |L55=Tensor product I |L56=Tensor product II |L57=Wedge product I |L58=Wedge product II }}<noinclude>[[Category:Linear algebra (Osnabrück 2024-2025)/Part II]]</noinclude> gpxmkgdnzc9um70kv92vrq0stba6i1r Template:Lectures enumeration31to58 10 316397 2683456 2024-11-11T15:14:06Z Bocardodarapti 289675 New resource with "*[[{{{1|}}}/Lecture 31|31 - {{{L31|}}}]] *[[{{{1|}}}/Lecture 32|32 - {{{L32|}}}]] *[[{{{1|}}}/Lecture 33|33 - {{{L33|}}}]] *[[{{{1|}}}/Lecture 34|34 - {{{L34|}}}]] *[[{{{1|}}}/Lecture 35|35 - {{{L35|}}}]] *[[{{{1|}}}/Lecture 36|36 - {{{L36|}}}]] *[[{{{1|}}}/Lecture 37|37 - {{{L37|}}}]] *[[{{{1|}}}/Lecture 38|38 - {{{L38|}}}]] *[[{{{1|}}}/Lecture 39|39 - {{{L39|}}}]] *[[{{{1|}}}/Lecture 40|40 - {{{L40|}}}]] *[[{{{1|}}}/Lecture 41|41 - {{{L41|}}}]] *{{{1|}}}/L..." 2683456 wikitext text/x-wiki *[[{{{1|}}}/Lecture 31|31 - {{{L31|}}}]] *[[{{{1|}}}/Lecture 32|32 - {{{L32|}}}]] *[[{{{1|}}}/Lecture 33|33 - {{{L33|}}}]] *[[{{{1|}}}/Lecture 34|34 - {{{L34|}}}]] *[[{{{1|}}}/Lecture 35|35 - {{{L35|}}}]] *[[{{{1|}}}/Lecture 36|36 - {{{L36|}}}]] *[[{{{1|}}}/Lecture 37|37 - {{{L37|}}}]] *[[{{{1|}}}/Lecture 38|38 - {{{L38|}}}]] *[[{{{1|}}}/Lecture 39|39 - {{{L39|}}}]] *[[{{{1|}}}/Lecture 40|40 - {{{L40|}}}]] *[[{{{1|}}}/Lecture 41|41 - {{{L41|}}}]] *[[{{{1|}}}/Lecture 42|42 - {{{L42|}}}]] *[[{{{1|}}}/Lecture 43|43 - {{{L43|}}}]] *[[{{{1|}}}/Lecture 44|44 - {{{L44|}}}]] *[[{{{1|}}}/Lecture 45|45 - {{{L45|}}}]] *[[{{{1|}}}/Lecture 46|46 - {{{L46|}}}]] *[[{{{1|}}}/Lecture 47|47 - {{{L47|}}}]] *[[{{{1|}}}/Lecture 48|48 - {{{L48|}}}]] *[[{{{1|}}}/Lecture 49|49 - {{{L49|}}}]] *[[{{{1|}}}/Lecture 50|50 - {{{L50|}}}]] *[[{{{1|}}}/Lecture 51|51 - {{{L51|}}}]] *[[{{{1|}}}/Lecture 52|52 - {{{L52|}}}]] *[[{{{1|}}}/Lecture 53|53 - {{{L53|}}}]] *[[{{{1|}}}/Lecture 54|54 - {{{L54|}}}]] *[[{{{1|}}}/Lecture 55|55 - {{{L55|}}}]] *[[{{{1|}}}/Lecture 56|56 - {{{L56|}}}]] *[[{{{1|}}}/Lecture 57|57 - {{{L57|}}}]] *[[{{{1|}}}/Lecture 58|58 - {{{L58|}}}]]<noinclude>{{Semantic template|}}</noinclude> n46erezh1ipnppjpa4c4l6xyf0tpw38 User talk:CanadianWikiReader 3 316398 2683459 2024-11-11T15:22:23Z Atcovi 276019 /* Welcome */ new section 2683459 wikitext text/x-wiki ==Welcome== {{Robelbox|theme=9|title='''[[Wikiversity:Welcome|Welcome]] to [[Wikiversity:What is Wikiversity|Wikiversity]], CanadianWikiReader!'''|width=100%}} <div style="{{Robelbox/pad}}"> You can [[Wikiversity:Contact|contact us]] with [[Wikiversity:Questions|questions]] at the [[Wikiversity:Colloquium|colloquium]] or get in touch with [[User talk:Atcovi|me personally]] if you would like some [[Help:Contents|help]]. 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Thanks and don't hesitate to ask me any questions you may have, —[[User:Atcovi|Atcovi]] [[User talk:Atcovi|(Talk]] - [[Special:Contributions/Atcovi|Contribs)]] 15:22, 11 November 2024 (UTC) bvuimdft0uqfii93mr0k5qgp2xdusjh User:Juanluisgarces 2 316399 2683505 2024-11-11T15:32:51Z Juanluisgarces 2940672 About 2683505 wikitext text/x-wiki == About == Juan Garcés Subject Specialist (Theology, Philosophy, General) and Co-ordinator of Digital Humanities at the SLUB TextLab of the Saxon State and University Library == Courses == qptjxz0egj6s5txdfqjkngevqmmsrw1 2683543 2683505 2024-11-11T15:39:43Z Juanluisgarces 2940672 2683543 wikitext text/x-wiki [[w:de:Benutzer:Juanluisgarces|User page in German]] == About == Juan Garcés Subject Specialist (Theology, Philosophy, General) and Co-ordinator of Digital Humanities at the SLUB TextLab of the Saxon State and University Library == Courses == rvd66r062vrad6j9oc3exjxaszy5tju 2683632 2683543 2024-11-11T15:55:46Z Juanluisgarces 2940672 2683632 wikitext text/x-wiki [[w:de:Benutzer:Juanluisgarces|User page in German]] == About == Juan Garcés === Current employment === Subject Specialist (Theology, Philosophy, General) and Co-ordinator of Digital Humanities at the SLUB TextLab of the Saxon State and University Library === Studies === 2001 D.Th., University of Stellenbosch (South Africa) == Courses == 8afjy7mxa4yg0gtwrv7gruw2dfvsmyw Institute for Mental and Behavioral Health Research (IMBHR) at Nationwide Children's Hospital/Reference Management SOPs 0 316400 2683660 2024-11-11T16:00:26Z Parodda 2936296 created page 2683660 wikitext text/x-wiki === Workflow: === * Pull PDFs for chapters, articles, download a copy of standards or guidelines for web resources (so that we have an offline copy available, as well as the link) * Put in one folder * Add to Zotero IMBHR, with "folders/projects" that reflect source (more on that below) * Share back with EAY to add to JenEric reference library ** Plan for harmonizing with IMBHR is to do ~quarterly harvests *** Where we export the .xml using the methods Marissa described in her excellent email **** Plan for importing based on VIBE protocol: ***** Open the .enl file ***** Ctrl & A to select all references ***** Click arrow icon, change file to XML and save it under .Data folder ***** Import XML to Zotero **** If the file is too big to upload: ***** Zotero will just crash each time you try to import ***** Easiest work-around is to open the .enl file as usual, but then filter at the top by the first letter of the author's last name. ***** Once it filters, you can do Ctrl & A to select only the items with that letter. ***** You can then save the XML by adding (letter) to the last name, so we know what letter the file is for. ***** Update from Marissa: The As have 989 references and it took about 4 minutes for the import into Zotero, the Bs have 2360 and it took over 20 minutes, but it worked and kept the PDFs from EndNote. It seems like this is the way we'll have to go about it, which will take some time. I already did the ones that don't have an author. Each import needs to go to a new collection, otherwise all of the references will go straight to the general IMBHR Library, and you'll have to make a new collection and move them manually (learned this the hard way with the Bs). I made a JenEric main folder so we can drag and drop the new collections there. *** With one tweak: We sort the library by "ascension number" and only add the ones with the newer ascensions (= bigger numbers) than where we left off last time. **** This should accomplish the "smaller" batching that Marissa invented by filtering by the first letter of author name! nsztdi7ru2f9e83fie3o2v0nlh6e43i Isometry/Several characterizations with orthonormal basis/Fact 0 316401 2683772 2024-11-11T16:19:34Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= V |pm=}} and {{mat|term= W |pm=}} be {{ Definitionlink |euclidean vector spaces| |Context=| |pm=, }} and let {{ Mapping/display |name=\varphi |V|W || |pm= }} denote a {{ Definitionlink |linear mapping| |Context=| |pm=. }} |Condition= |Segue=Then the following statements are equivalent. |Conclusion= {{ Enumeration3 |{{mat|term= \varphi|pm=}} is an {{ Definitionlink |isometry| |Context=| |p..." 2683772 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= V |pm=}} and {{mat|term= W |pm=}} be {{ Definitionlink |euclidean vector spaces| |Context=| |pm=, }} and let {{ Mapping/display |name=\varphi |V|W || |pm= }} denote a {{ Definitionlink |linear mapping| |Context=| |pm=. }} |Condition= |Segue=Then the following statements are equivalent. |Conclusion= {{ Enumeration3 |{{mat|term= \varphi|pm=}} is an {{ Definitionlink |isometry| |Context=| |pm=. }} |For every {{ Definitionlink |orthonormal basis| |Context=| |pm= }} {{ mathcond|term= u_i ||condterm1= {{runi|1|n|}} |pm=, }} of {{mat|term= V |pm=,}} {{ mathcond|term= \varphi( u_i ) ||condterm1= {{runi|1|n|}} |pm=, }} is part of an orthonormal basis of {{mat|term= W |pm=.}} |There exists an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} {{ mathcond|term= u_i ||condterm1= {{runi|1|n|}} |pm=, }} of {{mat|term= V |pm=}} such that {{ mathcond|term= \varphi( u_i ) ||condterm1= {{runi|1|n|}} |pm=, }} is part of an orthonormal basis of {{mat|term= W |pm=.}} }} |Extra= }} |Textform=Fact |Category= |Request=Isometry and orthonormal bases }} szmm3wwejoadjvooqftlxagvq7ety6f Euclidean vector space/Isometry with standard space/Fact 0 316402 2683788 2024-11-11T16:22:26Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= For every {{ Definitionlink |euclidean vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} |Condition= |Segue= |Conclusion= there exists a bijective {{ Definitionlink |isometry| |Context=| |pm= }} {{ Mapping/display |name=\varphi |\R^n|V || |pm=, }} where {{mat|term= \R^n|pm=}} carries the {{ Definitionlink |standard inner product| |Context=| |pm=. }} |Extra= }} |Textform=Fact |Category= |Request=Eu..." 2683788 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= For every {{ Definitionlink |euclidean vector space| |Context=| |pm= }} {{mat|term= V |pm=,}} |Condition= |Segue= |Conclusion= there exists a bijective {{ Definitionlink |isometry| |Context=| |pm= }} {{ Mapping/display |name=\varphi |\R^n|V || |pm=, }} where {{mat|term= \R^n|pm=}} carries the {{ Definitionlink |standard inner product| |Context=| |pm=. }} |Extra= }} |Textform=Fact |Category= |Request=Euclidean space and standard space }} lf1d9rsiinh2aiv9unfixzf6ygp4drj Euclidean vector space/Isometry with standard space/Fact/Proof 0 316403 2683804 2024-11-11T16:24:57Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mathl|term= u_1 {{commadots|}} u_n |pm=}} be an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} of {{mat|term= V |pm=,}} and let {{ Mapping/display |name= \varphi | \R^n | V || |pm= }} be the {{ Definitionlink |Premath= |linear mapping| |Context=| |pm= }} given by Relationchain/display | \varphi(e_i) || u_i || || || |pm=. }} Because of {{ Factlink |Factname= Isometrie/Verschi..." 2683804 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mathl|term= u_1 {{commadots|}} u_n |pm=}} be an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} of {{mat|term= V |pm=,}} and let {{ Mapping/display |name= \varphi | \R^n | V || |pm= }} be the {{ Definitionlink |Premath= |linear mapping| |Context=| |pm= }} given by Relationchain/display | \varphi(e_i) || u_i || || || |pm=. }} Because of {{ Factlink |Factname= Isometrie/Verschiedene characterizationen with Orthonormalbasis/Fact |Nr=3 |pm=, }} this is an {{ Definitionlink |isometry| |Context=| |pm=. }} |Closure= }} |Textform=Proof |Category=See }} 18wwfunzkvobgi12mxkcag2ai70zgk3 2683810 2683804 2024-11-11T16:25:49Z Bocardodarapti 289675 2683810 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{mathl|term= u_1 {{commadots|}} u_n |pm=}} be an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} of {{mat|term= V |pm=,}} and let {{ Mapping/display |name= \varphi | \R^n | V || |pm= }} be the {{ Definitionlink |Premath= |linear mapping| |Context=| |pm= }} given by {{ Relationchain/display | \varphi(e_i) || u_i || || || |pm=. }} Because of {{ Factlink |Factname= Isometry/Several characterizations with orthonormal basis/Fact |Nr=3 |pm=, }} this is an {{ Definitionlink |isometry| |Context=| |pm=. }} |Closure= }} |Textform=Proof |Category=See }} 7el48rl9czlwsiaf2def79c8zziecsq Unitary vector space/Isometry/Eigenvalues/Fact 0 316404 2683851 2024-11-11T16:32:03Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure |Situation= |Condition= Let {{mat|term= V |pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath={{KRC|}} |vector space| |pm=, }} and let {{ Mapping/display |name=\varphi |V|V || |pm= }} denote a {{ Definitionlink |linear isometry| |Context=K| |pm=. }} |Segue= |Conclusion= Then the {{ Definitionlink |Premath= |modulus| |Context=K| |pm= }} of every {{ Definitionlink |eigenvalue..." 2683851 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure |Situation= |Condition= Let {{mat|term= V |pm=}} be a {{ Definitionlink |finite-dimensional| |Context=vs| |pm= }} {{ Definitionlink |Premath={{KRC|}} |vector space| |pm=, }} and let {{ Mapping/display |name=\varphi |V|V || |pm= }} denote a {{ Definitionlink |linear isometry| |Context=K| |pm=. }} |Segue= |Conclusion= Then the {{ Definitionlink |Premath= |modulus| |Context=K| |pm= }} of every {{ Definitionlink |eigenvalue| |pm= }} of {{mat|term= \varphi|pm=}} is {{mat|term= 1 |pm=.}} |Extra=In case {{ Relationchain | {{KRC|}} || \R || || || |pm=, }} only the eigenvalues {{ Mathcor|term1= 1 |and|term2= -1 |pm= }} are possible. }} |Textform=Fact |Category= |Request=Eigenvalue of an isometry }} 1emawye58velut8yhdgk08y3ivpnct9 Unitary vector space/Isometry/Eigenvalues/Fact/Proof 0 316405 2683868 2024-11-11T16:34:40Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{ Relationchain | \varphi(v) || \lambda v || || || |pm= }} with {{ Relationchain |v |\neq|0 || || || |pm=, }} that is, {{mat|term= v |pm=}} is an {{ Definitionlink |eigenvector| |pm= }} for the eigenvalue {{ Relationchain | \lambda |\in| {{KRC|}} || || || |pm=. }} Due to the isometry property, we have {{ Relationchain/display | {{op:Norm|v}} || {{op:Norm|\varphi(v)}} || {{op:No..." 2683868 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Let {{ Relationchain | \varphi(v) || \lambda v || || || |pm= }} with {{ Relationchain |v |\neq|0 || || || |pm=, }} that is, {{mat|term= v |pm=}} is an {{ Definitionlink |eigenvector| |pm= }} for the eigenvalue {{ Relationchain | \lambda |\in| {{KRC|}} || || || |pm=. }} Due to the isometry property, we have {{ Relationchain/display | {{op:Norm|v}} || {{op:Norm|\varphi(v)}} || {{op:Norm|\lambda v}} || {{op:Modulus|\lambda }} \cdot {{op:Norm|v}} |pm=. }} Because of {{ Relationchain | {{op:Norm|v}} |\neq| 0 || || || |pm=, }} this implies {{ Relationchain | {{op:Modulus|\lambda }} ||1 || || || |pm=. }} In the real case this means {{ Relationchain | \lambda || \pm 1 || || || |pm=. }} |Closure= }} |Textform=Proof |Category=See }} 1c31qtdr64fm6izu5q6yjcsveo18yf4 Linear isometry/Determinant is 1 or -1/Fact 0 316406 2683885 2024-11-11T16:37:12Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= The {{ Definitionlink |determinant| |Context=| |pm= }} of a {{ Definitionlink |linear isometry| |Context=| |pm= }} {{ Mapping/display |name=\varphi |V|V || |pm= }} on a {{ Definitionlink |euclidean vector space| |Context=| |pm= }} {{mat|term= V |pm=}} |Condition= |Segue= |Conclusion= is {{ Mathcor|term1= 1 |or|term2= -1 |pm=. }} |Extra= }} |Textform=Fact |Category= |Request=Determinant of an isometry }}" 2683885 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= The {{ Definitionlink |determinant| |Context=| |pm= }} of a {{ Definitionlink |linear isometry| |Context=| |pm= }} {{ Mapping/display |name=\varphi |V|V || |pm= }} on a {{ Definitionlink |euclidean vector space| |Context=| |pm= }} {{mat|term= V |pm=}} |Condition= |Segue= |Conclusion= is {{ Mathcor|term1= 1 |or|term2= -1 |pm=. }} |Extra= }} |Textform=Fact |Category= |Request=Determinant of an isometry }} 9hyn1c13yma68yu9cztxvrzfhulwy3i Linear isometry/Determinant is 1 or -1/Fact/Proof2 0 316407 2683947 2024-11-11T16:48:41Z Bocardodarapti 289675 New resource with " {{ Mathematical text/Proof{{{opt|}}} |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Due to {{ Factlink |Factname= Euclidean vector space/Isometry/Orthogonal/Fakt |Nr= |pm=, }} we have {{ Relationchain/display | {{op:Transposed|M|}} M || {{Identity matrix|}} || || || |pm=. }} Therefore, the statement follows from {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication theorem/Fact |Nr= }} and from {{ Factlink |Fa..." 2683947 wikitext text/x-wiki {{ Mathematical text/Proof{{{opt|}}} |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Due to {{ Factlink |Factname= Euclidean vector space/Isometry/Orthogonal/Fakt |Nr= |pm=, }} we have {{ Relationchain/display | {{op:Transposed|M|}} M || {{Identity matrix|}} || || || |pm=. }} Therefore, the statement follows from {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication theorem/Fact |Nr= }} and from {{ Factlink |Factname= Determinant/Transposed matrix/Universal property/Fact |Nr= |pm=. }} |Closure= }} |Textform=Proof |}} 370sbmf3yegvy2tl65i22l4qgrrrrjs 2683963 2683947 2024-11-11T18:06:23Z Bocardodarapti 289675 2683963 wikitext text/x-wiki {{ Mathematical text/Proof{{{opt|}}} |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Due to {{ Factlink |Factname= Euclidean vector space/Isometry/Orthogonal/Fact |Nr= |pm=, }} we have {{ Relationchain/display | {{op:Transposed|M|}} M || {{Identity matrix|}} || || || |pm=. }} Therefore, the statement follows from {{ Factlink |Preword=the|multiplication theorem for the determinant|Factname= Determinant/Multiplication theorem/Fact |Nr= }} and from {{ Factlink |Factname= Determinant/Transposed matrix/Universal property/Fact |Nr= |pm=. }} |Closure= }} |Textform=Proof |}} 9s5olvpkbljekljt3szodrgi0lnm0pf Inquiry Live/Participants 0 316408 2683948 2024-11-11T16:48:52Z 1.46.81.116 Kasikorn Refund 2683948 wikitext text/x-wiki Kasikorn Refund 30s9t4i4vu4kvcqf660b5vf8ehw4dkp Euclidean vector space/Isometry/Section 0 316409 2683949 2024-11-11T16:56:37Z Bocardodarapti 289675 New resource with "{{ Mathematical section{{{opt|}}} |Content= We now discuss isometries of a Euclidean vector space in itself. These are always stets bijective. With respect to any orthonormal basis of {{mat|term= V |pm=,}} they are described in the following way. {{ inputfactproof |Euclidean vector space/Isometry/Orthogonal/Fact|Lemma|| }} The set of isometries on a Euclidean vector space form a group; in fact, it is a {{ Definitionlink |Premath= |subgroup| |Context=| |pm= }} of the gr..." 2683949 wikitext text/x-wiki {{ Mathematical section{{{opt|}}} |Content= We now discuss isometries of a Euclidean vector space in itself. These are always stets bijective. With respect to any orthonormal basis of {{mat|term= V |pm=,}} they are described in the following way. {{ inputfactproof |Euclidean vector space/Isometry/Orthogonal/Fact|Lemma|| }} The set of isometries on a Euclidean vector space form a group; in fact, it is a {{ Definitionlink |Premath= |subgroup| |Context=| |pm= }} of the group of all bijective linear mappings. We recall briefly the corresponding definitions. {{:Matrix/K/General linear group/Definition||}} {{:Matrix/K/Special linear group/Definition||}} {{ inputdefinition |Orthogonal matrix/Orthogonal group/Field/Definition|| }} {{ inputdefinition |Matrix/C/Unitary group/Definition|| }} |Textform=Section |Category= |}} a3a13lvz0n7cwz2lftrfnd59x8fa8kl Dtpwk 0 316410 2683950 2024-11-11T16:56:39Z 65.190.86.250 N27uhreiy76t3grwiuj98e7yu^&^%$^&*(IOUjhbn4k5rior98yguhbnj 2683950 wikitext text/x-wiki They have been there from so long that It was the scale amount to ever to the since in the viewers . [[File:Tab Ornament MET vs1979 206 825.jpg|thumb|Made in Newborns]] They had other types of diffrent speaking or writing.<syntaxhighlight lang="abap" line="1" start="1"> Notanion Commons In live city Other notices </syntaxhighlight> They had been used for an longer times ago it was very soft Who recived it from very intresting times. [[File:Chersonesos Bell.jpg|thumb|[[File:Water fountain near the art museum in Milwaukee, Wisconsin 6178.jpg|thumb|Great Water fountain]]Cherniros bell made longer]] They speak english. That they also noticed terms that covered they can use over hundreds of dollars each day per hour in Newborns. They can have many thongs in the parts of it can be saved longer times ago. 3fu38qm5ukr3hoi0a0k1umb4blbptps 2683951 2683950 2024-11-11T17:00:32Z Borhan 2941897 Requesting deletion 2683951 wikitext text/x-wiki {{delete|Out of project scope}}They have been there from so long that It was the scale amount to ever to the since in the viewers . [[File:Tab Ornament MET vs1979 206 825.jpg|thumb|Made in Newborns]] They had other types of diffrent speaking or writing.<syntaxhighlight lang="abap" line="1" start="1"> Notanion Commons In live city Other notices </syntaxhighlight> They had been used for an longer times ago it was very soft Who recived it from very intresting times. [[File:Chersonesos Bell.jpg|thumb|[[File:Water fountain near the art museum in Milwaukee, Wisconsin 6178.jpg|thumb|Great Water fountain]]Cherniros bell made longer]] They speak english. That they also noticed terms that covered they can use over hundreds of dollars each day per hour in Newborns. They can have many thongs in the parts of it can be saved longer times ago. ivqay86g5r4091dz4js2hpe04ay6mcj Euclidean vector space/Isometry/Orthogonal/Fact 0 316411 2683953 2024-11-11T17:25:46Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= V |pm=}} be a {{ Definitionlink |Euclidean vector space| |Context=| |pm=, }} and let {{mathl|term= u_1 {{commadots|}} u_n |pm=}} denote an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} of {{mat|term= V |pm=.}} Let {{ Mapping/display |name=\varphi |V|V || |pm= }} be a {{ Definitionlink |linear mapping| |Context=| |pm=, }} and let {{mat|term= M |pm=}} be the {{ Definitionlink |d..." 2683953 wikitext text/x-wiki {{ Mathematical text/Fact |Text= {{ Factstructure|typ= |Situation= Let {{mat|term= V |pm=}} be a {{ Definitionlink |Euclidean vector space| |Context=| |pm=, }} and let {{mathl|term= u_1 {{commadots|}} u_n |pm=}} denote an {{ Definitionlink |orthonormal basis| |Context=| |pm= }} of {{mat|term= V |pm=.}} Let {{ Mapping/display |name=\varphi |V|V || |pm= }} be a {{ Definitionlink |linear mapping| |Context=| |pm=, }} and let {{mat|term= M |pm=}} be the {{ Definitionlink |describing matrix| |Context=| |pm= }} of {{mat|term= \varphi |pm=}} with respect to the given basis. |Condition= |Segue= |Conclusion= Then {{mat|term= \varphi |pm=}} is an {{ Definitionlink |isometry| |Context=| |pm= }} if and only if {{ Relationchain/display | {{op:Transposed|M|}} M || E_n || || || |pm= }} holds. |Extra= }} |Textform=Fact |Category= |Factname=Matrix characterization of an isometry }} fojjfo1uvhz7obdpxorks925pr9x8ws Euclidean vector space/Isometry/Orthogonal/Fact/Proof 0 316412 2683955 2024-11-11T17:50:56Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Suppose first that {{mat|term= \varphi |pm=}} is an isometry. Then, {{ Relationchain | v_i || \varphi(u_i) || || || |pm= }} is an orthonormal basis due to {{ Factlink |Factname= Isometry/Several characterizations with orthonormal basis/Fact |Nr= |pm=. }} The coordinates of {{mat|term= v_i |pm=}} with respect to {{mat|term= u_i |pm=}} constitute the columns of the describing matrix {{mat|ter..." 2683955 wikitext text/x-wiki {{ Mathematical text/Proof |Text= {{ Proofstructure |Strategy= |Notation= |Proof= Suppose first that {{mat|term= \varphi |pm=}} is an isometry. Then, {{ Relationchain | v_i || \varphi(u_i) || || || |pm= }} is an orthonormal basis due to {{ Factlink |Factname= Isometry/Several characterizations with orthonormal basis/Fact |Nr= |pm=. }} The coordinates of {{mat|term= v_i |pm=}} with respect to {{mat|term= u_i |pm=}} constitute the columns of the describing matrix {{mat|term= M |pm=.}} Therefore, using {{ Exerciselink |Exercisename= Inner product/Orthonormal basis/Standard evaluation/Exercise |Nr= |pm=, }} we have {{ Relationchain/display | {{op:Transposed|v_i||}} v_j || {{op:Inner product|v_i|v_j}} || \delta_{ij} || || |pm=. }} Read as a matrix equation, this means {{ Relationchain/display | {{op:Transposed|M|}} M || {{Identity matrix|}} || || || |pm=. }} This argument can be read backwards to get the reverse implication. |Closure= }} |Textform=Proof |Category=See }} ll61yfyfvy3ccx2s8l062wmjgonc27e Matrix/K/Special linear group/Definition 0 316413 2683956 2024-11-11T17:54:40Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= For a {{ Definitionlink |field| |Context=| |pm= }} {{mat|term= K |pm=,}} and {{ Relationchain | n |\in| \N_+ || || || |pm=, }} the set of all {{ Definitionlink |invertible| |Context=matrix| |pm= }} {{ Definitionlink |Premath= n \times n |matrices| |Context=| |pm= }} over {{mat|term= K |pm=}} with {{ Relationchain/display | {{op:Determinant|M|}} || 1 || || || |pm= }} is called the {{ Word of definition |special linear group| |pm..." 2683956 wikitext text/x-wiki {{ Mathematical text/Definition |Text= For a {{ Definitionlink |field| |Context=| |pm= }} {{mat|term= K |pm=,}} and {{ Relationchain | n |\in| \N_+ || || || |pm=, }} the set of all {{ Definitionlink |invertible| |Context=matrix| |pm= }} {{ Definitionlink |Premath= n \times n |matrices| |Context=| |pm= }} over {{mat|term= K |pm=}} with {{ Relationchain/display | {{op:Determinant|M|}} || 1 || || || |pm= }} is called the {{ Word of definition |special linear group| |pm= }} over {{mat|term= K |pm=.}} It is denoted by {{mathl|term= {{op:SLG|n|K}} |pm=.}} |Textform=Definition |Category= |Word of definition=Special linear group }} db425yddiowfjdlykxajqewaxq70rlo Template:Op:SLG 10 316414 2683957 2024-11-11T17:55:14Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default= \operatorname{SL}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|K}}} |}}|}} }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2683957 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default= \operatorname{SL}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|K}}} |}}|}} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> hhiea31tbw0yxowacp2zkl6acq0w1sh Orthogonal matrix/Orthogonal group/Field/Definition 0 316415 2683958 2024-11-11T17:59:27Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and {{mat|term= E_n |pm=}} the {{ Definitionlink |identity matrix| |Context=| |pm= }} of length {{mat|term= n |pm=.}} A matrix {{ Relationchain | M |\in| {{op:GLG|n|K}} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Transposed|M||}} M || E_n || || || |pm= }} is called an {{ Word of definition |orthogonal matrix| |pm=. }} The set of all orth..." 2683958 wikitext text/x-wiki {{ Mathematical text/Definition |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and {{mat|term= E_n |pm=}} the {{ Definitionlink |identity matrix| |Context=| |pm= }} of length {{mat|term= n |pm=.}} A matrix {{ Relationchain | M |\in| {{op:GLG|n|K}} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Transposed|M||}} M || E_n || || || |pm= }} is called an {{ Word of definition |orthogonal matrix| |pm=. }} The set of all orthogonal matrices is called {{ Word of definition |orthogonal group| |pm=; }} it is denoted by {{ Relationchain/display | {{op:Orthogonal group|n|K}} || {{Setcond| M \in {{op:GLG|n|K}} | {{op:Transposed|M||}} M {{=}} E_n }} || || || |pm=. }} |Textform=Definition |Category= |Word of definition=Orthogonal group }} gyk7x8flpbo7t40593o92te3u0d8pd8 Template:Op:Orthogonal group 10 316416 2683959 2024-11-11T18:00:00Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default=\operatorname{O}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{makl| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2683959 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default=\operatorname{O}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{makl| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> mwoy3er6m63xo169rdm7kx345imiz6b 2683960 2683959 2024-11-11T18:00:34Z Bocardodarapti 289675 2683960 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default=\operatorname{O}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 01hdbfvn7dxtjauj2finv6edbp1xkcp Matrix/C/Unitary group/Definition 0 316417 2683961 2024-11-11T18:03:09Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= A matrix {{ Relationchain | M |\in| {{op:GLG|n|\Complex }} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Transposed| {{op:Complex conjugation|M||}} ||}} M || E_n || || || |pm= }} is called a {{ Word of definition |unitary matrix| |msw= |pm=. }} The set of all unitary matrices is called {{ Word of definition |unitary group| |pm=; }} it is denoted by {{ Relationchain/display | {{op:Unitary group|n|}} || {{Setcond|..." 2683961 wikitext text/x-wiki {{ Mathematical text/Definition |Text= A matrix {{ Relationchain | M |\in| {{op:GLG|n|\Complex }} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Transposed| {{op:Complex conjugation|M||}} ||}} M || E_n || || || |pm= }} is called a {{ Word of definition |unitary matrix| |msw= |pm=. }} The set of all unitary matrices is called {{ Word of definition |unitary group| |pm=; }} it is denoted by {{ Relationchain/display | {{op:Unitary group|n|}} || {{Setcond| M \in {{op:GLG|n|\Complex }} | {{op:Transposed|{{op:Complex conjugation|M||}}||}} M {{=}} E_n }} || || || |pm=. }} |Textform=Definition |Category= |Word of definition=Unitary group }} iwi2nm0gip3vdg0yha0nses20amkwhu Template:Op:Unitary group 10 316418 2683962 2024-11-11T18:03:50Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default= \operatorname{U}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2683962 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default= \operatorname{U}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 150vdmz3jrek7hh46h9uou0l93vbw9h Euclidean vector space/Proper Isometry/Introduction/Section 0 316419 2683965 2024-11-11T18:12:33Z Bocardodarapti 289675 New resource with "{{ Mathematical section{{{opt|}}} |Content= {{ inputdefinition |Euclidean vector space/Proper isometry/Definition|| }} An isometry that is not proper, that is, its determinant is {{mat|term= -1 |pm=,}} is also called an {{Keyword|improper isometry|pm=.}} {{ inputdefinition |Matrix/Special orthogonal group/Field/Definition|| }} {{ inputdefinition |Matrix/C/Special unitary group/Definition|| }} |Textform=Section |Category= |}}" 2683965 wikitext text/x-wiki {{ Mathematical section{{{opt|}}} |Content= {{ inputdefinition |Euclidean vector space/Proper isometry/Definition|| }} An isometry that is not proper, that is, its determinant is {{mat|term= -1 |pm=,}} is also called an {{Keyword|improper isometry|pm=.}} {{ inputdefinition |Matrix/Special orthogonal group/Field/Definition|| }} {{ inputdefinition |Matrix/C/Special unitary group/Definition|| }} |Textform=Section |Category= |}} 8dqvjf25412gerb3gaf1gzm0ljpbvqi Euclidean vector space/Proper isometry/Definition 0 316420 2683966 2024-11-11T18:16:09Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= An {{ Definitionlink |isometry| |Context=euclidean| |pm= }} on a {{ Definitionlink |euclidean vector space| |pm= }} is called {{Word of definition|proper|pm=}} if its {{ Definitionlink |determinant| |pm= }} is {{mat|term=1 |pm=.}} |Textform=Definition |Category= |Word of definition=Proper isometry }}" 2683966 wikitext text/x-wiki {{ Mathematical text/Definition |Text= An {{ Definitionlink |isometry| |Context=euclidean| |pm= }} on a {{ Definitionlink |euclidean vector space| |pm= }} is called {{Word of definition|proper|pm=}} if its {{ Definitionlink |determinant| |pm= }} is {{mat|term=1 |pm=.}} |Textform=Definition |Category= |Word of definition=Proper isometry }} 2nduzta6yg7dd6imr3n47auzn9n19u1 Matrix/Special orthogonal group/Field/Definition 0 316421 2683968 2024-11-11T18:19:27Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N_+ || || || |pm=. }} An {{ Definitionlink |orthogonal| |Context=matrix| |pm= }} {{ Definitionlink |Premath= n \times n |matrix| |Context=| |pm= }} {{mat|term= M |pm=}} fulfilling {{ Relationchain/display | {{op:Determinant|M||}} || 1 || || || |pm= }} is called a {{ Word of definition |special orthogonal matrix| |pm=. }} T..." 2683968 wikitext text/x-wiki {{ Mathematical text/Definition |Text= Let {{mat|term= K |pm=}} be a {{ Definitionlink |field| |Context=| |pm=, }} and {{ Relationchain | n |\in| \N_+ || || || |pm=. }} An {{ Definitionlink |orthogonal| |Context=matrix| |pm= }} {{ Definitionlink |Premath= n \times n |matrix| |Context=| |pm= }} {{mat|term= M |pm=}} fulfilling {{ Relationchain/display | {{op:Determinant|M||}} || 1 || || || |pm= }} is called a {{ Word of definition |special orthogonal matrix| |pm=. }} The set of all special orthogonal matrices is called {{ Word of definition |special orthogonal group| |pm=; }} it is denoted by {{mathl|term= {{op:Special orthogonal group|n|K}} |pm=.}} |Textform=Definition |Category= |Word of definition=Special orthogonal group }} r5vudf2xy3701tad70hwa6725yxpoc1 Template:Op:Special orthogonal group 10 316422 2683969 2024-11-11T18:20:57Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default=\operatorname{SO}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2683969 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |latex |#default=\operatorname{SO}_{ {{{1|n}}} } {{#if:{{{1|}}}|\!|}} {{#if:{{{2|}}}| {{mabr| {{{2|}}} |}} | }} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 0j8dkei654cli61m67atmiyg0zr2ml6 Matrix/C/Special unitary group/Definition 0 316423 2683970 2024-11-11T18:23:38Z Bocardodarapti 289675 New resource with "{{ Mathematical text/Definition |Text= A {{ Definitionlink |unitary| |Context=matrix| |pm= }} {{ Definitionlink |Premath=n \times n |matrix| |Context=| |pm= }} {{ Relationchain | M |\in| {{op:GLG|n|\Complex }} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Determinant|M||}} || 1 || || || |pm= }} is called a {{ Word of definition |special unitary matrix| |pm=. }} The set of all special unitary matrices is called {{ Word of definition |Special unitary group..." 2683970 wikitext text/x-wiki {{ Mathematical text/Definition |Text= A {{ Definitionlink |unitary| |Context=matrix| |pm= }} {{ Definitionlink |Premath=n \times n |matrix| |Context=| |pm= }} {{ Relationchain | M |\in| {{op:GLG|n|\Complex }} || || || |pm= }} fulfilling {{ Relationchain/display | {{op:Determinant|M||}} || 1 || || || |pm= }} is called a {{ Word of definition |special unitary matrix| |pm=. }} The set of all special unitary matrices is called {{ Word of definition |Special unitary group| |pm=; }} it is denoted by {{mathl|term= {{op:Special unitary group|n|}} |pm=.}} |Textform=Definition |Category= |Word of definition=Special unitary group }} 36495mfj55sibfgbzl6bp1ufuba2so4 Template:Op:Special unitary group 10 316424 2683971 2024-11-11T18:26:20Z Bocardodarapti 289675 New resource with "<includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |#default=\operatorname{SU}_{{{{1|n}}}}{{#if:{{{2|}}}|\,({{{2|}}})}} |latex=\operatorname{SU}_{{{{1|n}}}}{{#if:{{{2|}}}|\,({{{2|}}})}} }}</includeonly><noinclude>{{Semantic template|}}</noinclude>" 2683971 wikitext text/x-wiki <includeonly>{{#switch: {{#titleparts:{{FULLPAGENAME}}|1|-1}} |#default=\operatorname{SU}_{{{{1|n}}}}{{#if:{{{2|}}}|\,({{{2|}}})}} |latex=\operatorname{SU}_{{{{1|n}}}}{{#if:{{{2|}}}|\,({{{2|}}})}} }}</includeonly><noinclude>{{Semantic template|}}</noinclude> 5er45gszxf8tzoil64yeiycsor6ol6u Linear algebra (Osnabrück 2024-2025)/Part II/Lecture 34 0 316425 2683972 2024-11-11T18:34:36Z Bocardodarapti 289675 New resource with " {{Subtitle|Diagonalizability of isometries over the complex numbers}} {{:Isometry/C/Diagonalizability/Section|extra1= &nbsp;In this course, we will get to know further spectral theorems; see {{ Factlink |Preword=||Factname= Vector space/K/Inner product/Endomorphism/Self-adjoint/Spectral theorem/Fact |Nr= |pm= }} and {{ Factlink |Preword=||Factname= Vector space/C/Finite-dimensional/Normal endomorphism/Spectral theorem/Fact |Nr= |pm=. }}}} {{Subtitle|Angles}} {{:Angle..." 2683972 wikitext text/x-wiki {{Subtitle|Diagonalizability of isometries over the complex numbers}} {{:Isometry/C/Diagonalizability/Section|extra1= &nbsp;In this course, we will get to know further spectral theorems; see {{ Factlink |Preword=||Factname= Vector space/K/Inner product/Endomorphism/Self-adjoint/Spectral theorem/Fact |Nr= |pm= }} and {{ Factlink |Preword=||Factname= Vector space/C/Finite-dimensional/Normal endomorphism/Spectral theorem/Fact |Nr= |pm=. }}}} {{Subtitle|Angles}} {{:Angle/Introduction/Section}} {{Subtitle|Plane isometries}} {{:Plane isometries/Section}} {{Subtitle|Isometries of space}} {{:Isometry of space/Rotation axis/Complement/Unitary/Section}} {{ inputimage |Football theorem qtl1|svg|230px {{!}} right {{!}} |Text= |User=Quartl |Domain= |License=CC-by-sa 3.0 }} {{ inputfactproof |Linear isometrie/Space/Fixed point on football/Fact|Corollary|| }} {{Subtitle|The decomposition theorem for isometries}} {{:Isometry/Decomposition/Section}} pddu11tvck967hwver4pl46bmva6b30 Writing/Requesting Feedback 0 316426 2683973 2024-11-11T19:45:45Z Lbeaumont 278565 Created the resource 2683973 wikitext text/x-wiki To gain constructive feedback on creative work, writers, artists and other creative people can make specific requests that focus reviewers’ attention on the most helpful aspects of the work. It is important to be clear about the specific types of feedback you seek and what you don’t want. Be specific about your reasons for requesting feedback, what you’re asking for, and what you hope to learn from it. Express genuine gratitude for the reviewer’s time and consideration. * Directly ask for feedback: "I'd love to hear your thoughts on this piece." * Be open to criticism: "Please be honest with your feedback, even if it's critical." * Show appreciation: "Thank you for taking the time to review this." Here are some effective ways to ask for feedback:<ref>[[w:ChatGPT|ChatGPT]] generated this text responding to the prompt: “As creative individuals like authors progress in their work, they often seek feedback from colleagues. What specific requests are most effective in eliciting constructive criticism on creative works?”</ref> 1. '''Ask for Feedback on Clarity:''' "Do the main ideas and themes come across [[Good Writing is Clear Thinking Made Visible|clearly]]? Are there any points where you felt lost or confused?" This helps identify areas that may need clarification or better explanation. 2. '''Request Emotional Response''': "How did this section make you feel? Did it create the mood or emotion I was aiming for?" Understanding emotional impact can reveal if the tone and mood are aligned with the creator's intentions. 3. '''Inquire About Engagement''': "Did this part hold your attention? Were there any places where your interest waned?" This feedback can show where the work is most engaging or if certain sections need pacing adjustments. 4. '''Focus on Character or Idea Development''': "Do the [[w:Character_development|characters]] (or ideas) feel believable and well-developed? Are their motivations clear and relatable?" This is especially useful for writers who want to ensure their creations are compelling and realistic. 5. '''Ask for Input on Structure and Flow''': "Does the sequence of events or ideas make sense? Do any transitions feel jarring or out of place?" This feedback can be invaluable for creating a smooth narrative or argument. 6. '''Request Suggestions for Improvement''': "Is there anything you’d suggest to improve the piece, either big or small?" This opens the door for specific, actionable ideas that the creator might not have considered. 7. '''Encourage Open-Ended Responses''': "What was your overall impression of the work? Did anything surprise or particularly stand out to you?" These general questions often reveal insights that the creator may not have anticipated. 8. '''Seek Feedback on Originality and Voice''': "Does this feel distinct or original to you? How would you describe the voice or style of the piece?" This can help the creator understand if their unique style or intended voice is coming through and whether it feels fresh or familiar to readers. 9. '''Probe for Theme Resonance''': "Did the central theme or message resonate with you? Did it feel relevant or impactful?" Asking about themes and messages helps ensure that the deeper layers of the work connect with the audience as intended. 10. '''Request Specific Examples''': "Could you point out any specific lines, scenes, or sections that stood out to you—positively or negatively?" This allows the creator to focus on parts of the work that may need refinement or that are particularly effective. 11. '''Ask About Pacing and Rhythm''': "Did the pacing feel right throughout? Were there any moments that felt too slow or rushed?" This is especially useful for creative works that rely on rhythm and timing, as the feedback can guide adjustments to keep readers or viewers fully engaged. 12. '''Inquire About Relatability or Accessibility''': "Did you feel you could relate to the work or understand its concepts? Was anything overly complex or too simple?" This helps gauge if the work is accessible to the intended audience or if adjustments are needed to make it resonate more widely. 13. '''Request Feedback on Visual or Descriptive Elements''': "Did the visuals or descriptions help you picture the setting, character, or action? Were any parts hard to imagine?" For works heavy in imagery, this feedback can reveal whether descriptions need enhancing or simplifying. 14. '''Ask for Honest Reactions to Unusual Choices''': "What did you think of [specific creative choice, e.g., an unconventional plot twist, experimental language, or unique structure]? Did it enhance or detract from your experience?" This helps the creator gauge whether their bold choices serve the story or require refining. 15. '''Check for Consistency in Tone''': "Does the [[Writing/Tone|tone]] stay consistent throughout the work, or are there any shifts that felt unexpected?" Consistency in tone is crucial for immersion, and feedback here can guide creators in balancing mood shifts or keeping a steady narrative voice. 16. '''Encourage Constructive Criticism with Praise and Suggestions''': "What did you like best, and what could use some work?" This approach invites balanced feedback, helping the creator know what’s already working well and where they could focus improvements. 17. '''Seek Insight into Ending or Closure''': "Did the ending feel satisfying? Did it resolve everything you expected, or did it leave you wanting more?" For works with a narrative arc, feedback on the ending is essential to ensure the conclusion feels rewarding or leaves an intended impact. By using these specific, targeted requests, creators can guide their colleagues to offer feedback that is precise, actionable, and relevant to their goals. This structured approach not only helps the creator understand areas for improvement but also fosters a constructive environment where reviewers feel encouraged to engage thoughtfully and supportively. == Non-fiction works == When seeking feedback on non-fiction works, it’s essential to address aspects such as accuracy, argument clarity, structure, and relevance. Here are specific feedback requests that can be particularly helpful for non-fiction:<ref>[[w:ChatGPT|ChatGPT]] generated this additional text rending to the prompt: “include feedback specific to non-fiction works”.</ref> 1'''. Ask for Clarity and Accuracy:''' "Did you find all the information [[Writing/Good Writing is Precise and Concise|clear and accurate]]? Were there any parts that seemed confusing or questionable?" This feedback helps ensure the content is factual, coherent, and credible. 2. '''Probe for Strength of Argument or Thesis''': "Does the central argument come across clearly and compellingly? Are there any weak points that could use stronger support?" This helps authors refine their thesis and ensure their argument is solid and well-supported. 3. '''Request Feedback on Structure and Flow''': "Does the organization of ideas make sense? Are there any sections that felt out of place or could be reordered for better clarity?" Non-fiction works need a logical flow, so feedback on structure is crucial to ensure a smooth reading experience. 4. '''Inquire About Evidence and Support''': "Are the examples and [[Evaluating Evidence|evidence]] provided effective and convincing? Is there any point that could benefit from additional support or sources?" Ensuring that claims are backed by solid evidence is vital for building credibility and persuasiveness. 5. '''Ask About Relevance and Engagement''': "Does the content feel relevant and engaging? Are there any sections that felt less interesting or necessary?" This can reveal areas where the work might need to be more tightly focused or better tailored to the audience’s interests. 6. '''Seek Feedback on [[Writing/Tone|Tone]] and [[Writing/Voice|Voice]]''': "Does the tone feel appropriate for the subject and audience? Are there any places where the tone feels too formal, too casual, or inconsistent?" Tone is critical in non-fiction, as it affects how readers perceive authority and approachability. 7. '''Request Insights on Use of Data and Statistics''': "Are the data and statistics used effectively? Are they easy to understand, and do they strengthen the argument?" Feedback here helps ensure that numerical evidence is both accessible and compelling. 8. '''Ask About the Depth of Research and Analysis''': "Does the work provide sufficient depth on the topic? Are there any areas that feel under-researched or overly detailed?" This can help the author calibrate the level of detail to match reader expectations and maintain engagement. 9. '''Inquire About Practical Application''': "Does the work provide actionable insights or practical takeaways? Are there areas where this could be improved?" For non-fiction that aims to inform or guide, this feedback ensures readers find the work useful and applicable. 10. '''Seek Feedback on Clarity of Language and Jargon:''' "[[Good Writing is Clear Thinking Made Visible|Is the language accessible]]? Were there any terms or jargon that needed further explanation?" This feedback is essential for making sure the work is understandable, especially if it covers technical or specialized topics. 11. '''Ask About Credibility and Author Bias''': "Did the work come across as balanced and objective? Was there any apparent bias that detracted from the work’s credibility?" This feedback helps identify unintentional biases and ensures the author’s perspective aligns with an objective, trustworthy voice. 12. '''Request Feedback on Conclusions and Implications''': "Does the conclusion tie everything together effectively? Does it offer meaningful insights or implications based on the discussion?" Strong endings are essential in non-fiction, leaving readers with a sense of resolution and insight. 13. '''Inquire About the Use of Visuals and Data Presentation''': "Are the visuals, charts, and graphs helpful and easy to understand? Is there any data that could benefit from a visual representation?" Visual aids can enhance understanding in non-fiction, so it’s important to know if they are clear and effective. 14. '''Check for Readability and Accessibility''': "Is the language clear and accessible? Were there any sections that felt too dense or complex?" This helps ensure the work is readable for its target audience and prevents readers from feeling overwhelmed by overly complex language. 15. '''Ask for Big Picture Feedback:''' "Overall, did the work achieve its intended purpose? Were there any main ideas or takeaways that didn’t resonate as strongly as intended? What, if anything did you learn? Big picture feedback ensures that the work’s primary goals—be it to inform, persuade, or enlighten—are achieved effectively. These requests tailor feedback to the unique demands of non-fiction, helping authors create work that is accurate, engaging, credible, and ultimately meaningful to readers. == External Links == * The ''Monday memo #47'' suggests several additional specific feedback requests.<ref>{{Cite web|url=https://schoolofthepossible.substack.com/p/monday-memo-47-182|title=Monday memo #47|last=Gray|first=Dave|date=2024-11-11|website=School of the Possible|access-date=2024-11-11}}</ref> * How to Give and Receive Feedback About Creative Work.<ref>{{Cite news|url=https://hbr.org/2017/11/how-to-give-and-receive-feedback-about-creative-work|title=How to Give and Receive Feedback About Creative Work|last=Harrison|first=Spencer|date=2017-11-13|work=Harvard Business Review|access-date=2024-11-11|issn=0017-8012}}</ref> * How to Get Meaningful Feedback on Your Art.<ref>{{Cite web|url=https://theworkingartist.com/how-to-get-meaningful-feedback-on-your-art/|title=How to Get Meaningful Feedback on Your Art - The Working Artist with Crista Cloutier|last=Cloutier|first=Crista|date=2024-09-11|language=en-CA|access-date=2024-11-11}}</ref> == References == {{CourseCat}} [[Category:Writing]] t3uky9uxblzkjnqhn0u6w5ngmmy6qwg Industrial and organizational psychology/Module 12 0 316427 2683980 2024-11-11T20:52:34Z Atcovi 276019 Create. 2683980 wikitext text/x-wiki '''Leadership in Organizations''' g2h1qzct9auyyua04akfdrg6qkxmgks 2683986 2683980 2024-11-11T21:07:41Z Atcovi 276019 +12.1 2683986 wikitext text/x-wiki '''Leadership in Organizations''' == Module 12.1: The Concept of Leadership == Research shows that emotional stability, extraversion, openness, and conscientiousness are positively related to leader emergence skills. The '''leader''' is the individual within a group that is given tasks to direct their own group's activities, or the individual who takes the leadership role when the ''real'' leader isn't present. === Problems === Leadership has been attached to several different achievements, and it's difficult to trace these outcomes and their respective time frames due to the significant time gap in between them. '''Abusive supervision''', which are acts of aggression done by managers onto their employees, negatively impacts the job commitment and job satisfaction of employees. === Leadership Attempts === Remember that your manager/supervisor deals with ''what'' is being done, while the concept of leadership concerns with ''how'' it is being done. Nowadays, managerial duties are mixed with what is known as "effective leadership". Examples are delegating, maintaining positive work relationship/environments, and handling paperwork akin to an administrator. === Leader Development vs. Leadership Development === '''Leader development''': develops, maintains, and enhances individual leader attributes. '''Leadership development''': concentrates on leader-follower development, sees leadership as a social exchange, and deals with interpersonal competence. So leader development is essentially the focus on the leader, while leadership development deals with the mechanism behind leadership and how to maintain/strengthen this leadership process. === What motivates someone to lead? === People who seek leadership have high power motives, high activity inhibition (so great discipline), and low desire to want approval/connections with others. Break motives into three categories # '''Affective-identity''' --> Want to have control over others/an entity. # '''Instrumental''' --> Benefits the person. # '''Social-normative''' --> Feel as if its a duty to take charge and lead. == Module 12.2 - Traditional Theories of Leadership (slide 14) == bk2zcvyxjkt3ttz5h6wa81vbv2kj9yg File:Link.3A.StaticLinking.20241112.pdf 6 316428 2683982 2024-11-11T20:53:18Z Young1lim 21186 {{Information |Description=Link.3A: Static Linking Overview (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2683982 wikitext text/x-wiki == Summary == {{Information |Description=Link.3A: Static Linking Overview (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} pjqxwtrfo09vukf0eqiv8pwto10u80z File:LCal.8A.Combinator.20241112.pdf 6 316429 2683984 2024-11-11T21:06:15Z Young1lim 21186 {{Information |Description=LCal.8A: Combinator (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2683984 wikitext text/x-wiki == Summary == {{Information |Description=LCal.8A: Combinator (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} otfj3v5o3ju8z2x49vb23yao48ae7r0 File:ARM.2ASM.Thumb.2024112.pdf 6 316430 2683992 2024-11-11T21:14:35Z Young1lim 21186 {{Information |Description=ARM.2ASM: Thumb Programming (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2683992 wikitext text/x-wiki == Summary == {{Information |Description=ARM.2ASM: Thumb Programming (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} c0p2mxedwgzkygvm9bxmq1rj1bs6ayu Foreign policy from Obama to Trump 0 316431 2683994 2024-11-11T21:17:22Z Jaredscribe 2906761 New resource with "{{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel policy|last=Kontorovich|first=Eugene}}" 2683994 wikitext text/x-wiki {{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel policy|last=Kontorovich|first=Eugene}} b8muino9cusvsf4clylib14pvtnc2mc 2683995 2683994 2024-11-11T21:22:00Z Jaredscribe 2906761 2683995 wikitext text/x-wiki Broad scope analysis, post-mortem, and forecast. {{Main|w:Foreign policy of the George W. Bush administration|w:Foreign policy of the Barack Obama administration|w:Foreign policy of the Donald Trump administration|l2 = Barack Obama administration|l3 = Donald Trump administration|w:Foreign policy of the Joe Biden administration|l4 = Joe Biden administration}} {{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel policy|last=Kontorovich|first=Eugene}} mw2dv9htivoqf42yqyc1khrm6cf2rey 2683998 2683995 2024-11-11T21:34:20Z Jaredscribe 2906761 2683998 wikitext text/x-wiki Broad scope analysis, post-mortem, and forecast. {{Main|w:Foreign policy of the George W. Bush administration|w:Foreign policy of the Barack Obama administration|w:Foreign policy of the Donald Trump administration|l2 = Barack Obama administration|l3 = Donald Trump administration|w:Foreign policy of the Joe Biden administration|l4 = Joe Biden administration}} {{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel/Hamas war policy, post-mortem|last=Kontorovich|first=Eugene}} (pro-Israel perspective) Biden's Israel/Palestine policy (pro-Palestinian perspective) td2ftnixb73rs2ftvb7a6mylqlbske2 2683999 2683998 2024-11-11T21:38:31Z Jaredscribe 2906761 2683999 wikitext text/x-wiki Broad scope analysis, post-mortem, and forecast. {{Main|w:Foreign policy of the George W. Bush administration|w:Foreign policy of the Barack Obama administration|w:Foreign policy of the Donald Trump administration|l2 = Barack Obama administration|l3 = Donald Trump administration|w:Foreign policy of the Joe Biden administration|l4 = Joe Biden administration}} == Russia, Ukraine, and the former Soviet states == == Greece, Turkey, Cyprus, and Eastern Mediterranean == == Shiite Iran and proxies versus Sunni Arabia == == Israel/Palestine == {{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel/Hamas war policy, post-mortem|last=Kontorovich|first=Eugene}} (pro-Israel perspective) Biden's Israel/Palestine policy (pro-Palestinian perspective) a6c85d9oqxlayzwsgpgx103wc5hvvs0 2684000 2683999 2024-11-11T21:39:29Z Jaredscribe 2906761 2684000 wikitext text/x-wiki Broad scope analysis, post-mortem, and forecast. {{Main|w:Foreign policy of the George W. Bush administration|w:Foreign policy of the Barack Obama administration|w:Foreign policy of the Donald Trump administration|l2 = Barack Obama administration|l3 = Donald Trump administration|w:Foreign policy of the Joe Biden administration|l4 = Joe Biden administration}} == Russia, Ukraine, and the former Soviet states == == Greece, Turkey, Cyprus, and Eastern Mediterranean == == Shiite Iran and proxies versus Sunni Arabia == == Israel/Palestine == {{Cite web|url=https://www.israelnationalnews.com/news/398872|title=Biden's Israel/Hamas war policy, post-mortem|last=Kontorovich|first=Eugene}} (pro-Israel perspective) Biden's Israel/Palestine policy (pro-Palestinian perspective) == China, Taiwan, and Southeast Asia == 5y8re51fhud41pq71ih952r0eho9sbo File:VLSI.Arith.5A.CSkip.20241112.pdf 6 316432 2684002 2024-11-11T22:04:31Z Young1lim 21186 {{Information |Description=VLSI.Arith: Carry Skip Adders 1A (20241112- 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2684002 wikitext text/x-wiki == Summary == {{Information |Description=VLSI.Arith: Carry Skip Adders 1A (20241112- 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} jnjohc8hrygwnro8mt9xxe3dd8w9ddc File:Python.Work2.Package.1A.20241112.pdf 6 316433 2684113 2024-11-12T02:40:07Z Young1lim 21186 {{Information |Description=Work2.1A: Packages (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} 2684113 wikitext text/x-wiki == Summary == {{Information |Description=Work2.1A: Packages (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} phkaq3sz0kk718w2dgx3vqcfocpzg1u File:Leptospirosis.pdf 6 316434 2684128 2024-11-12T03:35:44Z OhanaUnited 18921 Uploading PDF copy of [[WikiJournal of Medicine/Melioidosis]] 2684128 wikitext text/x-wiki == Summary == Uploading PDF copy of [[WikiJournal of Medicine/Melioidosis]] pk2yw00lz2dp7kixm8vj5oaeuwzktpf 2684132 2684128 2024-11-12T03:37:35Z OhanaUnited 18921 + 2684132 wikitext text/x-wiki == Summary == Uploading PDF copy of [[WikiJournal of Medicine/Leptospirosis]] =={{int:filedesc}}== {{Information |description={{en|1=[[v:WikiJournal of Medicine/Leptospirosis|WikiJournal of Medicine/Leptospirosis]]}} |date=2022-06-21 |source=https://doi.org/10.15347/WJM/2022.002 |author=Raymond Chieng |permission= |other versions= }} =={{int:license-header}}== {{cc-by-sa-3.0}} [[Category:WikiJournal of Medicine]] ehsfjtk2dqyql0te0jch1bluelvnm7o 2684133 2684132 2024-11-12T03:37:59Z OhanaUnited 18921 /* {{int:filedesc}} */ 2684133 wikitext text/x-wiki == Summary == Uploading PDF copy of [[WikiJournal of Medicine/Leptospirosis]] =={{int:filedesc}}== {{Information |description=[[WikiJournal of Medicine/Leptospirosis]] |date=2022-06-21 |source=https://doi.org/10.15347/WJM/2022.002 |author=Raymond Chieng |permission= |other versions= }} =={{int:license-header}}== {{cc-by-sa-3.0}} [[Category:WikiJournal of Medicine]] qzguyjpokv646t3oqn8g5ia9n173xrn File:NM.Diff.1Discrete.20241111.pdf 6 316435 2684165 2024-11-12T07:46:38Z Young1lim 21186 {{Information |Description=Discrete Function Differentiation (20241111 - 20241109) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2684165 wikitext text/x-wiki == Summary == {{Information |Description=Discrete Function Differentiation (20241111 - 20241109) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} abo56s2u335ccbud76bjgdtvaj6j2bo File:NM.Diff.1Discrete.20241112.pdf 6 316436 2684167 2024-11-12T07:50:19Z Young1lim 21186 {{Information |Description=Discrete Function Differentiation (20241111 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2684167 wikitext text/x-wiki == Summary == {{Information |Description=Discrete Function Differentiation (20241111 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 53dgloolu3uc17azsaoogtjmau2t9o4 File:RowEchelon.20241111.pdf 6 316437 2684169 2024-11-12T08:08:09Z Young1lim 21186 {{Information |Description=Reduced Row Echelon Form (20241111 - 20241109) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2684169 wikitext text/x-wiki == Summary == {{Information |Description=Reduced Row Echelon Form (20241111 - 20241109) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} 4ukrs46tmeurz329yc3gn18mbda8c1m File:RowEchelon.20241112.pdf 6 316438 2684171 2024-11-12T08:09:02Z Young1lim 21186 {{Information |Description=Reduced Row Echelon Form (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} 2684171 wikitext text/x-wiki == Summary == {{Information |Description=Reduced Row Echelon Form (20241112 - 20241111) |Source={{own|Young1lim}} |Date=2024-11-12 |Author=Young W. Lim |Permission={{self|GFDL|cc-by-sa-3.0,2.5,2.0,1.0}} }} == Licensing == {{self|GFDL|cc-by-sa-4.0,3.0,2.5,2.0,1.0}} glshbewaa712ecb0jhqedtdo2xuenkp